In this paper, the performance of existing biased estimators (Ridge Estimator (RE), Almost Unbiased Ridge Estimator (AURE), Liu Estimator (LE), Almost Unbiased Liu Estimator (AULE), Principal Component Regression Esti...In this paper, the performance of existing biased estimators (Ridge Estimator (RE), Almost Unbiased Ridge Estimator (AURE), Liu Estimator (LE), Almost Unbiased Liu Estimator (AULE), Principal Component Regression Estimator (PCRE), r-k class estimator and r-d class estimator) and the respective predictors were considered in a misspecified linear regression model when there exists multicollinearity among explanatory variables. A generalized form was used to compare these estimators and predictors in the mean square error sense. Further, theoretical findings were established using mean square error matrix and scalar mean square error. Finally, a numerical example and a Monte Carlo simulation study were done to illustrate the theoretical findings. The simulation study revealed that LE and RE outperform the other estimators when weak multicollinearity exists, and RE, r-k class and r-d class estimators outperform the other estimators when moderated and high multicollinearity exist for certain values of shrinkage parameters, respectively. The predictors based on the LE and RE are always superior to the other predictors for certain values of shrinkage parameters.展开更多
This paper studies relationships between the best linear unbiased estimators （BLUEs） of an estimable parametric functions Kβunder the Gauss-Markov model {y, Xβ, σ^2]E} and its misspecified model {y, X0β,σ^2∑0}...This paper studies relationships between the best linear unbiased estimators （BLUEs） of an estimable parametric functions Kβunder the Gauss-Markov model {y, Xβ, σ^2]E} and its misspecified model {y, X0β,σ^2∑0}. In addition, relationships between BLUEs under a restricted Gauss Markov model and its misspecified model are also investigated.展开更多
Misspecified models have attracted much attention in some fields such as statistics and econometrics. When a global misspecification exists, even the model contains a large number of parameters and predictors,the miss...Misspecified models have attracted much attention in some fields such as statistics and econometrics. When a global misspecification exists, even the model contains a large number of parameters and predictors,the misspecification cannot disappear and sometimes it instead goes further away from the true one. Then the inference and correction for such a model are of very importance. In this paper we use the generalized method of moments(GMM) to infer the misspecified model with diverging numbers of parameters and predictors, and to investigate its asymptotic behaviors, such as local and global consistency, and asymptotic normality. Furthermore, we suggest a semiparametric correction to reduce the global misspefication and, consequently, to improve the estimation and enhance the modeling. The theoretical results and the numerical comparisons show that the corrected estimation and fitting are better than the existing ones.展开更多
Depending on the asymptotical independence of periodograms,exponential tilted(ET)likelihood,as an effective nonparametric statistical method,is developed to deal with time series in this paper.Similar to empirical lik...Depending on the asymptotical independence of periodograms,exponential tilted(ET)likelihood,as an effective nonparametric statistical method,is developed to deal with time series in this paper.Similar to empirical likelihood(EL),it still suffers from two drawbacks:the nondefinition problem of the likelihood function and the under-coverage probability of confidence region.To overcome these two problems,we further proposed the adjusted ET(AET)likelihood.With a specific adjustment level,our simulation studies indicate that the AET method achieves a higher-order coverage precision than the unadjusted ET method.In addition,due to the good performance of ET under moment model misspecification[Schennach,S.M.(2007).Point estimation with exponentially tilted empirical likelihood.The Annals of Statistics,35(2),634–672.https://doi.org/10.1214/009053606000001208],we show that the one-order property of point estimate is preserved for the misspecified spectral estimating equations of the autoregressive coefficient of AR(1).The simulation results illustrate that the point estimates of the ET outperform those of the EL and their hybrid in terms of standard deviation.A real data set is analyzed for illustration purpose.展开更多
In this paper we show the occurrence of cubic-root asymptotics in misspecified conditional quantile models where the approximating functions are restricted to be binary decision trees. Inference procedure for the opti...In this paper we show the occurrence of cubic-root asymptotics in misspecified conditional quantile models where the approximating functions are restricted to be binary decision trees. Inference procedure for the optimal split point in the decision tree is conducted by inverting a t-test or a deviation measure test, both involving Chemoff type limiting distributions. In order to avoid estimating the nuisance parameters in the complicated limiting distribution, subsampling is proved to deliver the correct confidence interval/set.展开更多
文摘In this paper, the performance of existing biased estimators (Ridge Estimator (RE), Almost Unbiased Ridge Estimator (AURE), Liu Estimator (LE), Almost Unbiased Liu Estimator (AULE), Principal Component Regression Estimator (PCRE), r-k class estimator and r-d class estimator) and the respective predictors were considered in a misspecified linear regression model when there exists multicollinearity among explanatory variables. A generalized form was used to compare these estimators and predictors in the mean square error sense. Further, theoretical findings were established using mean square error matrix and scalar mean square error. Finally, a numerical example and a Monte Carlo simulation study were done to illustrate the theoretical findings. The simulation study revealed that LE and RE outperform the other estimators when weak multicollinearity exists, and RE, r-k class and r-d class estimators outperform the other estimators when moderated and high multicollinearity exist for certain values of shrinkage parameters, respectively. The predictors based on the LE and RE are always superior to the other predictors for certain values of shrinkage parameters.
基金Supported in part by National Natural Science Foundation of China (Grant No.70871073)
文摘This paper studies relationships between the best linear unbiased estimators （BLUEs） of an estimable parametric functions Kβunder the Gauss-Markov model {y, Xβ, σ^2]E} and its misspecified model {y, X0β,σ^2∑0}. In addition, relationships between BLUEs under a restricted Gauss Markov model and its misspecified model are also investigated.
基金Supported by National Natural Science Foundation of China(Nos.11971265,11701318,11871294 and 71572097)Shandong Provincial Natural Science Foundation of China(Nos.ZR2019PF012 and ZR2019BA028)+1 种基金National Key R&D Program of China(2018YFA0703900)a Project of Shandong Province Higher Educational Science and Technology Program(No.J18KA356)
文摘Misspecified models have attracted much attention in some fields such as statistics and econometrics. When a global misspecification exists, even the model contains a large number of parameters and predictors,the misspecification cannot disappear and sometimes it instead goes further away from the true one. Then the inference and correction for such a model are of very importance. In this paper we use the generalized method of moments(GMM) to infer the misspecified model with diverging numbers of parameters and predictors, and to investigate its asymptotic behaviors, such as local and global consistency, and asymptotic normality. Furthermore, we suggest a semiparametric correction to reduce the global misspefication and, consequently, to improve the estimation and enhance the modeling. The theoretical results and the numerical comparisons show that the corrected estimation and fitting are better than the existing ones.
基金supported by Natural Science Foundation of Shanghai(17ZR1409000)National Natural Science Foundation of China(11831008,11971171)the Open Research Fundof KeyLaboratory of Advanced Theory andApplication in Statistics and Data Science-MOE,ECNU.
文摘Depending on the asymptotical independence of periodograms,exponential tilted(ET)likelihood,as an effective nonparametric statistical method,is developed to deal with time series in this paper.Similar to empirical likelihood(EL),it still suffers from two drawbacks:the nondefinition problem of the likelihood function and the under-coverage probability of confidence region.To overcome these two problems,we further proposed the adjusted ET(AET)likelihood.With a specific adjustment level,our simulation studies indicate that the AET method achieves a higher-order coverage precision than the unadjusted ET method.In addition,due to the good performance of ET under moment model misspecification[Schennach,S.M.(2007).Point estimation with exponentially tilted empirical likelihood.The Annals of Statistics,35(2),634–672.https://doi.org/10.1214/009053606000001208],we show that the one-order property of point estimate is preserved for the misspecified spectral estimating equations of the autoregressive coefficient of AR(1).The simulation results illustrate that the point estimates of the ET outperform those of the EL and their hybrid in terms of standard deviation.A real data set is analyzed for illustration purpose.
文摘In this paper we show the occurrence of cubic-root asymptotics in misspecified conditional quantile models where the approximating functions are restricted to be binary decision trees. Inference procedure for the optimal split point in the decision tree is conducted by inverting a t-test or a deviation measure test, both involving Chemoff type limiting distributions. In order to avoid estimating the nuisance parameters in the complicated limiting distribution, subsampling is proved to deliver the correct confidence interval/set.
