This paper introduces a measure which obviates the need to consult any tables.Average value x’ and standard deviation s’in this measure arc computed without ineluding suspend value xm.If│xm一x’│/s’>2.58.then ...This paper introduces a measure which obviates the need to consult any tables.Average value x’ and standard deviation s’in this measure arc computed without ineluding suspend value xm.If│xm一x’│/s’>2.58.then xm, is an outlying obscrvation;when n≥9,fiducial probability p>95一99%.As the standard deviation of population σ is given,if│xm一x’│/σ>2.58.tht xm is outlying;when n≥4,p>97一99%.This article also demonstrates that comparing with measures of Grubbs,Nair and Chauvenet.ours is more efficient in judgement under the same or large p.展开更多
Linear mixed models are popularly used to fit continuous longitudinal data, and the random effects are commonly assumed to have normal distribution. However, this assumption needs to be tested so that further analysis...Linear mixed models are popularly used to fit continuous longitudinal data, and the random effects are commonly assumed to have normal distribution. However, this assumption needs to be tested so that further analysis can be proceeded well. In this paper, we consider the Baringhaus-Henze-Epps-Pulley （BHEP） tests, which are based on an empirical characteristic function. Differing from their case, we consider the normality checking for the random effects which are unobservable and the test should be based on their predictors. The test is consistent against global alternatives, and is sensitive to the local alternatives converging to the null at a certain rate arbitrarily close to 1/V~ where n is sample size. ^-hlrthermore, to overcome the problem that the limiting null distribution of the test is not tractable, we suggest a new method： use a conditional Monte Carlo test （CMCT） to approximate the null distribution, and then to simulate p-values. The test is compared with existing methods, the power is examined, and several examples are applied to illustrate the usefulness of our test in the analysis of longitudinal data.展开更多
We consider an Error-in-Variable partially linear model where the covariates of linear part are measured with error which follows a normal distribution with a known covariance matrix. We propose a corrected-loss estim...We consider an Error-in-Variable partially linear model where the covariates of linear part are measured with error which follows a normal distribution with a known covariance matrix. We propose a corrected-loss estimation of the covariate effect. The proposed estimator is asymptotically normal. Simulation studies are presented to show that the proposed method performs well with finite samples, and the proposed method is applied to a real data set.展开更多
This paper proposes a unified semiparametric method for the additive risk model under general biased sampling. By using the estimating equation approach, we propose both estimators of the regression parameters and non...This paper proposes a unified semiparametric method for the additive risk model under general biased sampling. By using the estimating equation approach, we propose both estimators of the regression parameters and nonparametric function. An advantage is that our approach is still suitable for the lengthbiased data even without the information of the truncation variable. Meanwhile, large sample properties of the proposed estimators are established, including consistency and asymptotic normality. In addition, the finite sample behavior of the proposed methods and the analysis of three groups of real data are given.展开更多
Normal copula with a correlation coefficient between-1 and 1 is tail independent and so it severely underestimates extreme probabilities. By letting the correlation coefficient in a normal copula depend on the sample ...Normal copula with a correlation coefficient between-1 and 1 is tail independent and so it severely underestimates extreme probabilities. By letting the correlation coefficient in a normal copula depend on the sample size, H¨usler and Reiss(1989) showed that the tail can become asymptotically dependent. We extend this result by deriving the limit of the normalized maximum of n independent observations, where the i-th observation follows from a normal copula with its correlation coefficient being either a parametric or a nonparametric function of i/n. Furthermore, both parametric and nonparametric inference for this unknown function are studied, which can be employed to test the condition by H¨usler and Reiss(1989). A simulation study and real data analysis are presented too.展开更多
A new nonparametric procedure is developed to test the exponentiality against the strict NBUC property of a life distribution. The exact null distribution is derived by the theory of sample spacings, and the asymptoti...A new nonparametric procedure is developed to test the exponentiality against the strict NBUC property of a life distribution. The exact null distribution is derived by the theory of sample spacings, and the asymptotic normality is also established by the large sample theory of L-statistics. Finally, the lower and upper tailed probability of the exact null distribution and some numerical simulation results are presented as well.展开更多
This paper deals with the conditional quantile estimation based on left-truncated and right-censored data.Assuming that the observations with multivariate covariates form a stationary α-mixing sequence,the authors de...This paper deals with the conditional quantile estimation based on left-truncated and right-censored data.Assuming that the observations with multivariate covariates form a stationary α-mixing sequence,the authors derive the strong convergence with rate,strong representation as well as asymptotic normality of the conditional quantile estimator.Also,a Berry-Esseen-type bound for the estimator is established.In addition,the finite sample behavior of the estimator is investigated via simulations.展开更多
文摘This paper introduces a measure which obviates the need to consult any tables.Average value x’ and standard deviation s’in this measure arc computed without ineluding suspend value xm.If│xm一x’│/s’>2.58.then xm, is an outlying obscrvation;when n≥9,fiducial probability p>95一99%.As the standard deviation of population σ is given,if│xm一x’│/σ>2.58.tht xm is outlying;when n≥4,p>97一99%.This article also demonstrates that comparing with measures of Grubbs,Nair and Chauvenet.ours is more efficient in judgement under the same or large p.
基金supported in part by a grant of Research Grants Council of Hong Kong,and National Natural Science Foundation of China (Grant No. 11101157)
文摘Linear mixed models are popularly used to fit continuous longitudinal data, and the random effects are commonly assumed to have normal distribution. However, this assumption needs to be tested so that further analysis can be proceeded well. In this paper, we consider the Baringhaus-Henze-Epps-Pulley （BHEP） tests, which are based on an empirical characteristic function. Differing from their case, we consider the normality checking for the random effects which are unobservable and the test should be based on their predictors. The test is consistent against global alternatives, and is sensitive to the local alternatives converging to the null at a certain rate arbitrarily close to 1/V~ where n is sample size. ^-hlrthermore, to overcome the problem that the limiting null distribution of the test is not tractable, we suggest a new method： use a conditional Monte Carlo test （CMCT） to approximate the null distribution, and then to simulate p-values. The test is compared with existing methods, the power is examined, and several examples are applied to illustrate the usefulness of our test in the analysis of longitudinal data.
基金supported by National Natural Science Foundation of China(Grant Nos.10901020 and 11371062)the Fundamental Research Funds for the Central Universities,Beijing Center for Mathematics and Information Interdisciplinary Sciences,China Zhongdian Project(Grant No.11131002)
文摘We consider an Error-in-Variable partially linear model where the covariates of linear part are measured with error which follows a normal distribution with a known covariance matrix. We propose a corrected-loss estimation of the covariate effect. The proposed estimator is asymptotically normal. Simulation studies are presented to show that the proposed method performs well with finite samples, and the proposed method is applied to a real data set.
基金supported by National Institutes of Health of USA (Grant No. R01 HL113548)National Natural Science Foundation of China (Grant Nos. 11271155, 11371168, J1310022, 11571138, 11501241 and 71271128)+3 种基金Science and Technology Research Program of Education Department in Jilin Province for the 12th Five-Year Plan (Grant No. 440020031139)Jilin Province Natural Science Foundation (Grant Nos. 20130101066JC, 20130522102JH and 20150520053JH)the State Key Program of National Natural Science Foundation of China (Grant No. 71331006)National Center for Mathematics and Interdisciplinary Sciences and Shanghai University of Finance and Economics through Project 211 Phase IV and Shanghai Leading Academic Discipline Project A
文摘This paper proposes a unified semiparametric method for the additive risk model under general biased sampling. By using the estimating equation approach, we propose both estimators of the regression parameters and nonparametric function. An advantage is that our approach is still suitable for the lengthbiased data even without the information of the truncation variable. Meanwhile, large sample properties of the proposed estimators are established, including consistency and asymptotic normality. In addition, the finite sample behavior of the proposed methods and the analysis of three groups of real data are given.
基金supported by the Simons FoundationNational Natural Science Foundation of China(Grant No.11171275)the Natural Science Foundation Project of CQ(Grant No.cstc2012jj A00029)
文摘Normal copula with a correlation coefficient between-1 and 1 is tail independent and so it severely underestimates extreme probabilities. By letting the correlation coefficient in a normal copula depend on the sample size, H¨usler and Reiss(1989) showed that the tail can become asymptotically dependent. We extend this result by deriving the limit of the normalized maximum of n independent observations, where the i-th observation follows from a normal copula with its correlation coefficient being either a parametric or a nonparametric function of i/n. Furthermore, both parametric and nonparametric inference for this unknown function are studied, which can be employed to test the condition by H¨usler and Reiss(1989). A simulation study and real data analysis are presented too.
基金This research is supported by the National Natural Science Foundation of Chinaunder Grant No. 10201010 and TY 10126014.
文摘A new nonparametric procedure is developed to test the exponentiality against the strict NBUC property of a life distribution. The exact null distribution is derived by the theory of sample spacings, and the asymptotic normality is also established by the large sample theory of L-statistics. Finally, the lower and upper tailed probability of the exact null distribution and some numerical simulation results are presented as well.
基金supported by the National Natural Science Foundation of China(No.11271286)the Specialized Research Fund for the Doctor Program of Higher Education of China(No.20120072110007)a grant from the Natural Sciences and Engineering Research Council of Canada
文摘This paper deals with the conditional quantile estimation based on left-truncated and right-censored data.Assuming that the observations with multivariate covariates form a stationary α-mixing sequence,the authors derive the strong convergence with rate,strong representation as well as asymptotic normality of the conditional quantile estimator.Also,a Berry-Esseen-type bound for the estimator is established.In addition,the finite sample behavior of the estimator is investigated via simulations.
