Consider the model Yt = βYt-1＋g（Yt-2）＋εt for 3 〈 t 〈 T. Hereg is anunknown function, β is an unknown parameter, εt are i.i.d, random errors with mean 0 andvariance σ2 and the fourth moment α4, and α4 are ...Consider the model Yt = βYt-1＋g（Yt-2）＋εt for 3 〈 t 〈 T. Hereg is anunknown function, β is an unknown parameter, εt are i.i.d, random errors with mean 0 andvariance σ2 and the fourth moment α4, and α4 are independent of Y8 for all t ≥ 3 and s = 1, 2.Pseudo-LS estimators σ, σ2T α4τ and D2T of σ^2,α4 and Var（ε2↑3） are respectively constructedbased on piecewise polynomial approximator of g. The weak consistency of α4T and D2T are proved. The asymptotic normality of σ2T is given, i.e., √T（σ2T -σ^2）/DT converges indistribution to N（0, 1）. The result can be used to establish large sample interval estimatesof σ^2 or to make large sample tests for σ^2.展开更多
In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the l...In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.展开更多
As an extension of linear regression in functional data analysis, functional linear regression has been studied by many researchers and applied in various fields. However, in many cases, data is collected sequentially...As an extension of linear regression in functional data analysis, functional linear regression has been studied by many researchers and applied in various fields. However, in many cases, data is collected sequentially over time, for example the financial series, so it is necessary to consider the autocorrelated structure of errors in functional regression background. To this end, this paper considers a multiple functional linear model with autoregressive errors. Based on the functional principal component analysis, we apply the least square procedure to estimate the functional coefficients and autoregression coefficients. Under some regular conditions, we establish the asymptotic properties of the proposed estimators. A simulation study is conducted to investigate the finite sample performance of our estimators. A real example on China's weather data is applied to illustrate the validity of our model.展开更多
The paper studies a generalized linear model（GLM）yt = h（xt^T β） ＋ εt,t = l,2,...,n,where ε1 = η1,ε1 =ρεt ＋ηt,t = 2,3,...;n,h is a continuous differentiable function,ηt＇s are independent and identically...The paper studies a generalized linear model（GLM）yt = h（xt^T β） ＋ εt,t = l,2,...,n,where ε1 = η1,ε1 =ρεt ＋ηt,t = 2,3,...;n,h is a continuous differentiable function,ηt＇s are independent and identically distributed random errors with zero mean and finite variance σ^2.Firstly,the quasi-maximum likelihood（QML） estimators of β,p and σ^2 are given.Secondly,under mild conditions,the asymptotic properties（including the existence,weak consistency and asymptotic distribution） of the QML estimators are investigated.Lastly,the validity of method is illuminated by a simulation example.展开更多
Based on the empirical likelihood method, the subset selection and hypothesis test for parameters in a partially linear autoregressive model are investigated. We show that the empirical log-likelihood ratio at the tru...Based on the empirical likelihood method, the subset selection and hypothesis test for parameters in a partially linear autoregressive model are investigated. We show that the empirical log-likelihood ratio at the true parameters converges to the standard chi-square distribution. We then present the definitions of the empirical likelihood-based Bayes information criteria （EBIC） and Akaike information criteria （EAIC）. The results show that EBIC is consistent at selecting subset variables while EAIC is not. Simulation studies demonstrate that the proposed empirical likelihood confidence regions have better coverage probabilities than the least square method, while EBIC has a higher chance to select the true model than EAIC.展开更多
The quantile estimation methods are proposed for functional-coefficient partially linear regression （FCPLR） model by combining nonparametric and functional-coefficient regression （FCR） model. The local linear sche...The quantile estimation methods are proposed for functional-coefficient partially linear regression （FCPLR） model by combining nonparametric and functional-coefficient regression （FCR） model. The local linear scheme and the integrated method are used to obtain Focal quantile estimators of all unknown functions in the FCPLR model. These resulting estimators are asymptotically normal, but each of them has big variance. To reduce variances of these quantile estimators, the one-step backfitting technique is used to obtain the efficient quantile estimators of all unknown functions, and their asymptotic normalities are derived. Two simulated examples are carried out to illustrate the proposed estimation methodology.展开更多
In this paper,we consider the statistical inferences in a partially linear model when the model error follows an autoregressive process.A two-step procedure is proposed for estimating the unknown parameters by taking ...In this paper,we consider the statistical inferences in a partially linear model when the model error follows an autoregressive process.A two-step procedure is proposed for estimating the unknown parameters by taking into account of the special structure in error.Since the asymptotic matrix of the estimator for the parametric part has a complex structure,an empirical likelihood function is also developed.We derive the asymptotic properties of the related statistics under mild conditions.Some simulations,as well as a real data example,are conducted to illustrate the finite sample performance.展开更多
In many application fields of regression analysis,prior information about how explanatory variables affect response variable of interest is often available and can be formulated as constraints on regression coefficien...In many application fields of regression analysis,prior information about how explanatory variables affect response variable of interest is often available and can be formulated as constraints on regression coefficients.In this paper,the authors consider statistical inference of partially linear spatial autoregressive model under constraint conditions.By combining series approximation method,twostage least squares method and Lagrange multiplier method,the authors obtain constrained estimators of the parameters and function in the partially linear spatial autoregressive model and investigate their asymptotic properties.Furthermore,the authors propose a testing method to check whether the parameters in the parametric component of the partially linear spatial autoregressive model satisfy linear constraint conditions,and derive asymptotic distributions of the resulting test statistic under both null and alternative hypotheses.Simulation results show that the proposed constrained estimators have better finite sample performance than the unconstrained estimators and the proposed testing method performs well in finite samples.Furthermore,a real example is provided to illustrate the application of the proposed estimation and testing methods.展开更多
Acute Respiratory Distress Syndrome (ARDS) is a major cause of morbidity and has a high rate of mortality. ARDS patients in the intensive care unit (ICU) require mechan-ical ventilation (MV) for breathing support, but...Acute Respiratory Distress Syndrome (ARDS) is a major cause of morbidity and has a high rate of mortality. ARDS patients in the intensive care unit (ICU) require mechan-ical ventilation (MV) for breathing support, but inappropriate settings of MV can lead to ventilator induced lung injury (VILI). Those complications may be avoided by carefully optimizing ventilation parameters through model-based approaches. In this study we introduced a new model of lung mechanics (mNARX) which is a variation of the NARX model by Langdon et al. A multivariate process was undertaken to deter-mine the optimal parameters of the mNARX model and hence, the final structure of the model fit 25 patient data sets and successfully described all parts of the breathing cycle. The model was highly successful in predicting missing data and showed minimal error. Thus, this model can be used by the clinicians to find the optimal patient specific ventilator settings.展开更多
基金Supported by the National Natural Science Foundation of China（60375003） Supported by the Chinese Aviation Foundation（03153059）
文摘Consider the model Yt = βYt-1＋g（Yt-2）＋εt for 3 〈 t 〈 T. Hereg is anunknown function, β is an unknown parameter, εt are i.i.d, random errors with mean 0 andvariance σ2 and the fourth moment α4, and α4 are independent of Y8 for all t ≥ 3 and s = 1, 2.Pseudo-LS estimators σ, σ2T α4τ and D2T of σ^2,α4 and Var（ε2↑3） are respectively constructedbased on piecewise polynomial approximator of g. The weak consistency of α4T and D2T are proved. The asymptotic normality of σ2T is given, i.e., √T（σ2T -σ^2）/DT converges indistribution to N（0, 1）. The result can be used to establish large sample interval estimatesof σ^2 or to make large sample tests for σ^2.
文摘In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.
基金supported by National Nature Science Foundation of China(No.11861074,No.11371354 and N0.11301464)Key Laboratory of Random Complex Structures and Data Science,Chinese Academy of Sciences,Beijing 100190,China(No.2008DP173182)Applied Basic Research Project of Yunnan Province(No.2019FB138).
文摘As an extension of linear regression in functional data analysis, functional linear regression has been studied by many researchers and applied in various fields. However, in many cases, data is collected sequentially over time, for example the financial series, so it is necessary to consider the autocorrelated structure of errors in functional regression background. To this end, this paper considers a multiple functional linear model with autoregressive errors. Based on the functional principal component analysis, we apply the least square procedure to estimate the functional coefficients and autoregression coefficients. Under some regular conditions, we establish the asymptotic properties of the proposed estimators. A simulation study is conducted to investigate the finite sample performance of our estimators. A real example on China's weather data is applied to illustrate the validity of our model.
基金Supported by National Natural Science Foundation of China(Grant Nos.11071022,11471105)Science and Technology Research Projects of the Educational Department of Hubei Province(Grant No.Q20132505)
文摘The paper studies a generalized linear model（GLM）yt = h（xt^T β） ＋ εt,t = l,2,...,n,where ε1 = η1,ε1 =ρεt ＋ηt,t = 2,3,...;n,h is a continuous differentiable function,ηt＇s are independent and identically distributed random errors with zero mean and finite variance σ^2.Firstly,the quasi-maximum likelihood（QML） estimators of β,p and σ^2 are given.Secondly,under mild conditions,the asymptotic properties（including the existence,weak consistency and asymptotic distribution） of the QML estimators are investigated.Lastly,the validity of method is illuminated by a simulation example.
基金Supported by the National Natural Science Foundation of China(No.10871188,10801123)
文摘Based on the empirical likelihood method, the subset selection and hypothesis test for parameters in a partially linear autoregressive model are investigated. We show that the empirical log-likelihood ratio at the true parameters converges to the standard chi-square distribution. We then present the definitions of the empirical likelihood-based Bayes information criteria （EBIC） and Akaike information criteria （EAIC）. The results show that EBIC is consistent at selecting subset variables while EAIC is not. Simulation studies demonstrate that the proposed empirical likelihood confidence regions have better coverage probabilities than the least square method, while EBIC has a higher chance to select the true model than EAIC.
基金supported by the Zhejiang Provincial Natural Science Foundation of China (No. Y6110662)
文摘The quantile estimation methods are proposed for functional-coefficient partially linear regression （FCPLR） model by combining nonparametric and functional-coefficient regression （FCR） model. The local linear scheme and the integrated method are used to obtain Focal quantile estimators of all unknown functions in the FCPLR model. These resulting estimators are asymptotically normal, but each of them has big variance. To reduce variances of these quantile estimators, the one-step backfitting technique is used to obtain the efficient quantile estimators of all unknown functions, and their asymptotic normalities are derived. Two simulated examples are carried out to illustrate the proposed estimation methodology.
基金supported by the NSF of China(Nos.11971208,11601197)the NSSF of China(Grant No.21&ZD152)+2 种基金the China Postdoctoral Science Foundation(Nos.2016M600511,2017T100475)the NSF of Jiangxi Province(Nos.2018ACB21002,20171ACB21030)the Post graduate Innovation Project of Jiangxi Province(No.YC2021CB124)。
文摘In this paper,we consider the statistical inferences in a partially linear model when the model error follows an autoregressive process.A two-step procedure is proposed for estimating the unknown parameters by taking into account of the special structure in error.Since the asymptotic matrix of the estimator for the parametric part has a complex structure,an empirical likelihood function is also developed.We derive the asymptotic properties of the related statistics under mild conditions.Some simulations,as well as a real data example,are conducted to illustrate the finite sample performance.
基金supported by the Natural Science Foundation of Shaanxi Province under Grant No.2021JM349the Natural Science Foundation of China under Grant Nos.11972273 and 52170172。
文摘In many application fields of regression analysis,prior information about how explanatory variables affect response variable of interest is often available and can be formulated as constraints on regression coefficients.In this paper,the authors consider statistical inference of partially linear spatial autoregressive model under constraint conditions.By combining series approximation method,twostage least squares method and Lagrange multiplier method,the authors obtain constrained estimators of the parameters and function in the partially linear spatial autoregressive model and investigate their asymptotic properties.Furthermore,the authors propose a testing method to check whether the parameters in the parametric component of the partially linear spatial autoregressive model satisfy linear constraint conditions,and derive asymptotic distributions of the resulting test statistic under both null and alternative hypotheses.Simulation results show that the proposed constrained estimators have better finite sample performance than the unconstrained estimators and the proposed testing method performs well in finite samples.Furthermore,a real example is provided to illustrate the application of the proposed estimation and testing methods.
文摘Acute Respiratory Distress Syndrome (ARDS) is a major cause of morbidity and has a high rate of mortality. ARDS patients in the intensive care unit (ICU) require mechan-ical ventilation (MV) for breathing support, but inappropriate settings of MV can lead to ventilator induced lung injury (VILI). Those complications may be avoided by carefully optimizing ventilation parameters through model-based approaches. In this study we introduced a new model of lung mechanics (mNARX) which is a variation of the NARX model by Langdon et al. A multivariate process was undertaken to deter-mine the optimal parameters of the mNARX model and hence, the final structure of the model fit 25 patient data sets and successfully described all parts of the breathing cycle. The model was highly successful in predicting missing data and showed minimal error. Thus, this model can be used by the clinicians to find the optimal patient specific ventilator settings.
