A changepoint in statistical applications refers to an observational time point at which the structure pattern changes during a somewhat long-term experimentation process. In many cases, the change point time and caus...A changepoint in statistical applications refers to an observational time point at which the structure pattern changes during a somewhat long-term experimentation process. In many cases, the change point time and cause are documented and it is reasonably straightforward to statistically adjust (homogenize) the series for the effects of the changepoint. Sadly many changepoint times are undocumented and the changepoint times themselves are the main purpose of study. In this article, the changepoint analysis in two-phrase linear regression models is developed and discussed. Following Liu and Qian (2010)'s idea in the segmented linear regression models, the modified empirical likelihood ratio statistic is proposed to test if there exists a changepoint during the long-term experiment and observation. The modified empirical likelihood ratio statistic is computation-friendly and its ρ-value can be easily approximated based on the large sample properties. The procedure is applied to the Old Faithful geyser eruption data in October 1980.展开更多
In this paper, we investigate the empirical likelihood diagnosis of modal linear regression models. The empirical likelihood ratio function based on modal regression estimation method for the regression coefficient is...In this paper, we investigate the empirical likelihood diagnosis of modal linear regression models. The empirical likelihood ratio function based on modal regression estimation method for the regression coefficient is introduced. First, the estimation equation based on empirical likelihood method is established. Then, some diagnostic statistics are proposed. At last, we also examine the performance of proposed method for finite sample sizes through simulation study.展开更多
In this paper, three smoothed empirical log-likelihood ratio functions for the parameters of nonlinear models with missing response are suggested. Under some regular conditions, the corresponding Wilks phenomena are o...In this paper, three smoothed empirical log-likelihood ratio functions for the parameters of nonlinear models with missing response are suggested. Under some regular conditions, the corresponding Wilks phenomena are obtained and the confidence regions for the parameter can be constructed easily.展开更多
In this paper, we consider the semiparametric regression model for longitudinal data. Due to the correlation within groups, a generalized empirical log-likelihood ratio statistic for the unknown parameters in the mode...In this paper, we consider the semiparametric regression model for longitudinal data. Due to the correlation within groups, a generalized empirical log-likelihood ratio statistic for the unknown parameters in the model is suggested by introducing the working covariance matrix. It is proved that the proposed statistic is asymptotically standard chi-squared under some suitable conditions, and hence it can be used to construct the confidence regions of the parameters. A simulation study is conducted to compare the proposed method with the generalized least squares method in terms of coverage accuracy and average lengths of the confidence intervals.展开更多
Goodness-of-fit test for regression modes has received much attention in literature. In this paper, empirical likelihood (EL) goodness-of-fit tests for regression models including classical parametric and autoregressi...Goodness-of-fit test for regression modes has received much attention in literature. In this paper, empirical likelihood (EL) goodness-of-fit tests for regression models including classical parametric and autoregressive (AR) time series models are proposed. Unlike the existing locally smoothing and globally smoothing methodologies, the new method has the advantage that the tests are self-scale invariant and that the asymptotic null distribution is chi-squared. Simulations are carried out to illustrate the methodology.展开更多
This paper considers tests for regression coefficients in high dimensional partially linear Models.The authors first use the B-spline method to estimate the unknown smooth function so that it could be linearly express...This paper considers tests for regression coefficients in high dimensional partially linear Models.The authors first use the B-spline method to estimate the unknown smooth function so that it could be linearly expressed.Then,the authors propose an empirical likelihood method to test regression coefficients.The authors derive the asymptotic chi-squared distribution with two degrees of freedom of the proposed test statistics under the null hypothesis.In addition,the method is extended to test with nuisance parameters.Simulations show that the proposed method have a good performance in control of type-I error rate and power.The proposed method is also employed to analyze a data of Skin Cutaneous Melanoma(SKCM).展开更多
This paper proposes a new weighted quantile regression model for longitudinal data with weights chosen by empirical likelihood(EL). This approach efficiently incorporates the information from the conditional quantile ...This paper proposes a new weighted quantile regression model for longitudinal data with weights chosen by empirical likelihood(EL). This approach efficiently incorporates the information from the conditional quantile restrictions to account for within-subject correlations. The resulted estimate is computationally simple and has good performance under modest or high within-subject correlation. The efficiency gain is quantified theoretically and illustrated via simulation and a real data application.展开更多
Structural equation model(SEM) is a multivariate analysis tool that has been widely applied to many fields such as biomedical and social sciences. In the traditional SEM, it is often assumed that random errors and exp...Structural equation model(SEM) is a multivariate analysis tool that has been widely applied to many fields such as biomedical and social sciences. In the traditional SEM, it is often assumed that random errors and explanatory latent variables follow the normal distribution, and the effect of explanatory latent variables on outcomes can be formulated by a mean regression-type structural equation. But this SEM may be inappropriate in some cases where random errors or latent variables are highly nonnormal. The authors develop a new SEM, called as quantile SEM(QSEM), by allowing for a quantile regression-type structural equation and without distribution assumption of random errors and latent variables. A Bayesian empirical likelihood(BEL) method is developed to simultaneously estimate parameters and latent variables based on the estimating equation method. A hybrid algorithm combining the Gibbs sampler and Metropolis-Hastings algorithm is presented to sample observations required for statistical inference. Latent variables are imputed by the estimated density function and the linear interpolation method. A simulation study and an example are presented to investigate the performance of the proposed methodologies.展开更多
Empirical likelihood is a nonparametric method for constructing confidence intervals and tests, notably in enabling the shape of a confidence region determined by the sample data. This paper presents a new version of ...Empirical likelihood is a nonparametric method for constructing confidence intervals and tests, notably in enabling the shape of a confidence region determined by the sample data. This paper presents a new version of the empirical likelihood method for quantiles under kernel regression imputation to adapt missing response data. It eliminates the need to solve nonlinear equations, and it is essy to apply. We also consider exponential empirical likelihood as an alternative method. Numerical results are presented to compare our method with others.展开更多
For complete observation and p-dimensional parameter θ defined by an estimation equation, empirical likelihood method of construction of confidence region is based on the asymptotic χp2 distribution of -2 log（EL ra...For complete observation and p-dimensional parameter θ defined by an estimation equation, empirical likelihood method of construction of confidence region is based on the asymptotic χp2 distribution of -2 log（EL ratio）. For right censored lifetime data with covariables, however, it is shown in literature that -2 log（EL ratio） converges weakly to a scaled χp2 distribution, where the scale parameter is a function of unknown asymptotic covariance matrix. The construction of confidence region requires estimation of this scale parameter. In this paper, by using influence functions in the estimating equation, we show that -2 log（EL ratio） converges weakly to a standard χp2 distribution and hence eliminates the procedure of estimating the scale parameter.展开更多
Empirical likelihood （EL） ratio statistic on θ=g（x） is constructed based on the inverse probability weighted imputation approach in a nonparametric regression model Y = g（x） ＋ε （x ∈ [0, 1]p） with fixed des...Empirical likelihood （EL） ratio statistic on θ=g（x） is constructed based on the inverse probability weighted imputation approach in a nonparametric regression model Y = g（x） ＋ε （x ∈ [0, 1]p） with fixed designs and missing responses, which asymptotically has X1^2 distribution. This result is used to obtain a EL based confidence interval on θ.展开更多
Empirical-likelihood-based inference for the parameters in a partially linear single-index model with randomly censored data is investigated. We introduce an estimated empirical likelihood for the parameters using a s...Empirical-likelihood-based inference for the parameters in a partially linear single-index model with randomly censored data is investigated. We introduce an estimated empirical likelihood for the parameters using a synthetic data approach and show that its limiting distribution is a mixture of central chi-squared distribution. To attack this difficulty we propose an adjusted empirical likelihood to achieve the standard X2-1imit. Furthermore, since the index is of norm 1, we use this constraint to reduce the dimension of parameters, which increases the accuracy of the confidence regions. A simulation study is carried out to compare its finite-sample properties with the existing method. An application to a real data set is illustrated.展开更多
In this article, empirical likelihood inference for estimating equation with missing data is considered. Based on the weighted-corrected estimating function, an empirical log-likelihood ratio is proved to be a standar...In this article, empirical likelihood inference for estimating equation with missing data is considered. Based on the weighted-corrected estimating function, an empirical log-likelihood ratio is proved to be a standard chiqsquare distribution asymptotically under some suitable conditions. This result is different from those derived before. So it is convenient to construct confidence regions for the parameters of interest. We also prove that our proposed maximum empirical likelihood estimator θ is asymptotically normal and attains the semiparametric efficiency bound of missing data. Some simulations indicate that the proposed method performs the best.展开更多
In the receiver operating characteristic (ROC) analysis,the area under the ROC curve (AUC) is a popular summary index of discriminatory accuracy of a diagnostic test.Incorporating covariates into ROC analysis can impr...In the receiver operating characteristic (ROC) analysis,the area under the ROC curve (AUC) is a popular summary index of discriminatory accuracy of a diagnostic test.Incorporating covariates into ROC analysis can improve the diagnostic accuracy of the test.Regression model for the AUC is a tool to evaluate the effects of the covariates on the diagnostic accuracy.In this paper,empirical likelihood (EL) method is proposed for the AUC regression model.For the regression parameter vector,it can be shown that the asymptotic distribution of its EL ratio statistic is a weighted sum of independent chi-square distributions.Confidence regions are constructed for the parameter vector based on the newly developed empirical likelihood theorem,as well as for the covariate-specific AUC.Simulation studies were conducted to compare the relative performance of the proposed EL-based methods with the existing method in AUC regression.Finally,the proposed methods are illustrated with a real data set.展开更多
Empirical likelihood has been found very useful in many different occasions. It usually runs into serious computational difficulties while jackknife empirical likelihood （JEL） is shown to be effective when applied t...Empirical likelihood has been found very useful in many different occasions. It usually runs into serious computational difficulties while jackknife empirical likelihood （JEL） is shown to be effective when applied to some complicated statistics. In this paper, to test the difference between coefficients of two linear regression models, the authors apply JEL to construct the confidence regions. Based on the 3EL ratio test, a version of Wilks＇ theorem is developed. Furthermore, to improve the coverage accuracy of confidence regions, a Bartlett correction is applied. Simulation studies are carried out to show the effectiveness of the proposed method in aspects of coverage accuracy. A real data set is analyzed with the proposed method as an example.展开更多
文摘A changepoint in statistical applications refers to an observational time point at which the structure pattern changes during a somewhat long-term experimentation process. In many cases, the change point time and cause are documented and it is reasonably straightforward to statistically adjust (homogenize) the series for the effects of the changepoint. Sadly many changepoint times are undocumented and the changepoint times themselves are the main purpose of study. In this article, the changepoint analysis in two-phrase linear regression models is developed and discussed. Following Liu and Qian (2010)'s idea in the segmented linear regression models, the modified empirical likelihood ratio statistic is proposed to test if there exists a changepoint during the long-term experiment and observation. The modified empirical likelihood ratio statistic is computation-friendly and its ρ-value can be easily approximated based on the large sample properties. The procedure is applied to the Old Faithful geyser eruption data in October 1980.
文摘In this paper, we investigate the empirical likelihood diagnosis of modal linear regression models. The empirical likelihood ratio function based on modal regression estimation method for the regression coefficient is introduced. First, the estimation equation based on empirical likelihood method is established. Then, some diagnostic statistics are proposed. At last, we also examine the performance of proposed method for finite sample sizes through simulation study.
文摘In this paper, three smoothed empirical log-likelihood ratio functions for the parameters of nonlinear models with missing response are suggested. Under some regular conditions, the corresponding Wilks phenomena are obtained and the confidence regions for the parameter can be constructed easily.
基金China Postdoctoral Science Foundation Funded Project (20080430633)Shanghai Postdoctoral Scientific Program (08R214121)+3 种基金the National Natural Science Foundation of China (10871013)the Research Fund for the Doctoral Program of Higher Education (20070005003)the Natural Science Foundation of Beijing (1072004)the Basic Research and Frontier Technology Foundation of He'nan (072300410090)
文摘In this paper, we consider the semiparametric regression model for longitudinal data. Due to the correlation within groups, a generalized empirical log-likelihood ratio statistic for the unknown parameters in the model is suggested by introducing the working covariance matrix. It is proved that the proposed statistic is asymptotically standard chi-squared under some suitable conditions, and hence it can be used to construct the confidence regions of the parameters. A simulation study is conducted to compare the proposed method with the generalized least squares method in terms of coverage accuracy and average lengths of the confidence intervals.
基金This work was supported by the Research Grants Council of Hong Kong of China and the National Natural Science Foundation of China (Grant No. 10661003)
文摘Goodness-of-fit test for regression modes has received much attention in literature. In this paper, empirical likelihood (EL) goodness-of-fit tests for regression models including classical parametric and autoregressive (AR) time series models are proposed. Unlike the existing locally smoothing and globally smoothing methodologies, the new method has the advantage that the tests are self-scale invariant and that the asymptotic null distribution is chi-squared. Simulations are carried out to illustrate the methodology.
基金supported by the University of Chinese Academy of Sciences under Grant No.Y95401TXX2Beijing Natural Science Foundation under Grant No.Z190004Key Program of Joint Funds of the National Natural Science Foundation of China under Grant No.U19B2040。
文摘This paper considers tests for regression coefficients in high dimensional partially linear Models.The authors first use the B-spline method to estimate the unknown smooth function so that it could be linearly expressed.Then,the authors propose an empirical likelihood method to test regression coefficients.The authors derive the asymptotic chi-squared distribution with two degrees of freedom of the proposed test statistics under the null hypothesis.In addition,the method is extended to test with nuisance parameters.Simulations show that the proposed method have a good performance in control of type-I error rate and power.The proposed method is also employed to analyze a data of Skin Cutaneous Melanoma(SKCM).
基金supported by National Natural Science Foundation of China (Grant Nos. 11401048, 11301037, 11571051 and 11201174)the Natural Science Foundation for Young Scientists of Jilin Province of China (Grant Nos. 20150520055JH and 20150520054JH)
文摘This paper proposes a new weighted quantile regression model for longitudinal data with weights chosen by empirical likelihood(EL). This approach efficiently incorporates the information from the conditional quantile restrictions to account for within-subject correlations. The resulted estimate is computationally simple and has good performance under modest or high within-subject correlation. The efficiency gain is quantified theoretically and illustrated via simulation and a real data application.
基金supported by the National Natural Science Foundation of China under Grant No.11165016
文摘Structural equation model(SEM) is a multivariate analysis tool that has been widely applied to many fields such as biomedical and social sciences. In the traditional SEM, it is often assumed that random errors and explanatory latent variables follow the normal distribution, and the effect of explanatory latent variables on outcomes can be formulated by a mean regression-type structural equation. But this SEM may be inappropriate in some cases where random errors or latent variables are highly nonnormal. The authors develop a new SEM, called as quantile SEM(QSEM), by allowing for a quantile regression-type structural equation and without distribution assumption of random errors and latent variables. A Bayesian empirical likelihood(BEL) method is developed to simultaneously estimate parameters and latent variables based on the estimating equation method. A hybrid algorithm combining the Gibbs sampler and Metropolis-Hastings algorithm is presented to sample observations required for statistical inference. Latent variables are imputed by the estimated density function and the linear interpolation method. A simulation study and an example are presented to investigate the performance of the proposed methodologies.
基金Supported by the Initial Research Funding for new faculties in Zhejiang University of Technology (No.109003129)
文摘Empirical likelihood is a nonparametric method for constructing confidence intervals and tests, notably in enabling the shape of a confidence region determined by the sample data. This paper presents a new version of the empirical likelihood method for quantiles under kernel regression imputation to adapt missing response data. It eliminates the need to solve nonlinear equations, and it is essy to apply. We also consider exponential empirical likelihood as an alternative method. Numerical results are presented to compare our method with others.
基金supported by National Natural Science Foundation of China (Grant Nos. 11171230 and 11231010)
文摘For complete observation and p-dimensional parameter θ defined by an estimation equation, empirical likelihood method of construction of confidence region is based on the asymptotic χp2 distribution of -2 log（EL ratio）. For right censored lifetime data with covariables, however, it is shown in literature that -2 log（EL ratio） converges weakly to a scaled χp2 distribution, where the scale parameter is a function of unknown asymptotic covariance matrix. The construction of confidence region requires estimation of this scale parameter. In this paper, by using influence functions in the estimating equation, we show that -2 log（EL ratio） converges weakly to a standard χp2 distribution and hence eliminates the procedure of estimating the scale parameter.
基金Supported by the National Natural Science Foundation of China (No.10971038)the Natural Science Foundation of Guangxi (No.2010GXNSFA013117)
文摘Empirical likelihood （EL） ratio statistic on θ=g（x） is constructed based on the inverse probability weighted imputation approach in a nonparametric regression model Y = g（x） ＋ε （x ∈ [0, 1]p） with fixed designs and missing responses, which asymptotically has X1^2 distribution. This result is used to obtain a EL based confidence interval on θ.
基金Supported by National Social Science Foundation of China (Grant No. 11CTJ004)National Natural Science Foundation of China (Grant Nos. 11171012 and 11101452)+3 种基金National Natural Science Foundation of Beijing (Grant No. 1102008)Natural Science Foundation Project of CQ CSTC (Grant No. cstcjjA00014)Research Foundation of Chongqing Municipal Education Commission (Grant No. KJ110720)Natural Science Foundation of Guangxi (Grant No. 2010GXNSFB013051)
文摘Empirical-likelihood-based inference for the parameters in a partially linear single-index model with randomly censored data is investigated. We introduce an estimated empirical likelihood for the parameters using a synthetic data approach and show that its limiting distribution is a mixture of central chi-squared distribution. To attack this difficulty we propose an adjusted empirical likelihood to achieve the standard X2-1imit. Furthermore, since the index is of norm 1, we use this constraint to reduce the dimension of parameters, which increases the accuracy of the confidence regions. A simulation study is carried out to compare its finite-sample properties with the existing method. An application to a real data set is illustrated.
基金supported by National Natural Science Foundation of China (Grant Nos.11171188, 11201499 and 10921101)Natural Science Foundation of Shandong Province (Grant Nos. ZR2010AZ001 and ZR2011AQ007)+1 种基金Shandong Provincial Scientific Research Reward Foundation for Excellent Young and MiddleAged Scientists (Grant No. BS2011SF006)K.C. Wong-HKBU Fellowship Program for Mainland Visiting Scholars 2010-11
文摘In this article, empirical likelihood inference for estimating equation with missing data is considered. Based on the weighted-corrected estimating function, an empirical log-likelihood ratio is proved to be a standard chiqsquare distribution asymptotically under some suitable conditions. This result is different from those derived before. So it is convenient to construct confidence regions for the parameters of interest. We also prove that our proposed maximum empirical likelihood estimator θ is asymptotically normal and attains the semiparametric efficiency bound of missing data. Some simulations indicate that the proposed method performs the best.
基金supported by Southwest Jiao Tong University(Grant Nos.12BR030and12ZT15)US National Science Foundation(Grant No.MPS/DMS0603913)US National Security Agency(Grant No.H98230-12-1-0228)
文摘In the receiver operating characteristic (ROC) analysis,the area under the ROC curve (AUC) is a popular summary index of discriminatory accuracy of a diagnostic test.Incorporating covariates into ROC analysis can improve the diagnostic accuracy of the test.Regression model for the AUC is a tool to evaluate the effects of the covariates on the diagnostic accuracy.In this paper,empirical likelihood (EL) method is proposed for the AUC regression model.For the regression parameter vector,it can be shown that the asymptotic distribution of its EL ratio statistic is a weighted sum of independent chi-square distributions.Confidence regions are constructed for the parameter vector based on the newly developed empirical likelihood theorem,as well as for the covariate-specific AUC.Simulation studies were conducted to compare the relative performance of the proposed EL-based methods with the existing method in AUC regression.Finally,the proposed methods are illustrated with a real data set.
基金supported by the China Postdoctoral Science Foundation under Grant No.2014M550799the National Science Foundation of China under Grant No.11401561
文摘Empirical likelihood has been found very useful in many different occasions. It usually runs into serious computational difficulties while jackknife empirical likelihood （JEL） is shown to be effective when applied to some complicated statistics. In this paper, to test the difference between coefficients of two linear regression models, the authors apply JEL to construct the confidence regions. Based on the 3EL ratio test, a version of Wilks＇ theorem is developed. Furthermore, to improve the coverage accuracy of confidence regions, a Bartlett correction is applied. Simulation studies are carried out to show the effectiveness of the proposed method in aspects of coverage accuracy. A real data set is analyzed with the proposed method as an example.
