Existing methods for analyzing semi-functional linear models usually assumed that random errors are not serially correlated or serially correlated with the known order.However,in some applications,these assumptions on...Existing methods for analyzing semi-functional linear models usually assumed that random errors are not serially correlated or serially correlated with the known order.However,in some applications,these assumptions on random errors may be unreasonable or questionable.To this end,this paper aims at testing error correlation in a semi-functional linear model(SFLM).Based on the empirical likelihood approach,the authors construct an empirical likelihood ratio statistic to test the serial correlation of random errors and identify the order of autocorrelation if the serial correlation holds.The proposed test statistic does not need to estimate the variance as it is data adaptive and possesses the nonparametric version of Wilks'theorem.Simulation studies are conducted to investigate the performance of the proposed test procedure.Two real examples are illustrated by the proposed test method.展开更多
In this paper, we consider the issue of variable selection in partial linear single-index models under the assumption that the vector of regression coefficients is sparse. We apply penalized spline to estimate the non...In this paper, we consider the issue of variable selection in partial linear single-index models under the assumption that the vector of regression coefficients is sparse. We apply penalized spline to estimate the nonparametric function and SCAD penalty to achieve sparse estimates of regression parameters in both the linear and single-index parts of the model. Under some mild conditions, it is shown that the penalized estimators have oracle property, in the sense that it is asymptotically normal with the same mean and covariance that they would have if zero coefficients are known in advance. Our model owns a least square representation, therefore standard least square programming algorithms can be implemented without extra programming efforts. In the meantime, parametric estimation, variable selection and nonparametric estimation can be realized in one step, which incredibly increases computational stability. The finite sample performance of the penalized estimators is evaluated through Monte Carlo studies and illustrated with a real data set.展开更多
基金This research was supported by the National Natural Science Foundation of China under Grant Nos.11861074,11731011,11731015 and 12261051Applied Basic Research Project of Yunnan Province under Grant No.2019FB138.
文摘Existing methods for analyzing semi-functional linear models usually assumed that random errors are not serially correlated or serially correlated with the known order.However,in some applications,these assumptions on random errors may be unreasonable or questionable.To this end,this paper aims at testing error correlation in a semi-functional linear model(SFLM).Based on the empirical likelihood approach,the authors construct an empirical likelihood ratio statistic to test the serial correlation of random errors and identify the order of autocorrelation if the serial correlation holds.The proposed test statistic does not need to estimate the variance as it is data adaptive and possesses the nonparametric version of Wilks'theorem.Simulation studies are conducted to investigate the performance of the proposed test procedure.Two real examples are illustrated by the proposed test method.
基金Supported by the National Natural Science Foundation of China(No.11671096)
文摘In this paper, we consider the issue of variable selection in partial linear single-index models under the assumption that the vector of regression coefficients is sparse. We apply penalized spline to estimate the nonparametric function and SCAD penalty to achieve sparse estimates of regression parameters in both the linear and single-index parts of the model. Under some mild conditions, it is shown that the penalized estimators have oracle property, in the sense that it is asymptotically normal with the same mean and covariance that they would have if zero coefficients are known in advance. Our model owns a least square representation, therefore standard least square programming algorithms can be implemented without extra programming efforts. In the meantime, parametric estimation, variable selection and nonparametric estimation can be realized in one step, which incredibly increases computational stability. The finite sample performance of the penalized estimators is evaluated through Monte Carlo studies and illustrated with a real data set.
