To better capture the characteristics of asymmetry and structural fluctuations observed in count time series,this study delves into the application of the quantile regression(QR)method for analyzing and forecasting no...To better capture the characteristics of asymmetry and structural fluctuations observed in count time series,this study delves into the application of the quantile regression(QR)method for analyzing and forecasting nonlinear integer-valued time series exhibiting a piecewise phenomenon.Specifically,we focus on the parameter estimation in the first-order Self-Exciting Threshold Integer-valued Autoregressive(SETINAR(2,1))process with symmetry,asymmetry,and contaminated innovations.We establish the asymptotic properties of the estimator under certain regularity conditions.Monte Carlo simulations demonstrate the superior performance of the QR method compared to the conditional least squares(CLS)approach.Furthermore,we validate the robustness of the proposed method through empirical quantile regression estimation and forecasting for larceny incidents and CAD drug call counts in Pittsburgh,showcasing its effectiveness across diverse levels of data heterogeneity.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
This paper develops the theory of the kth power expectile estimation and considers its relevant hypothesis tests for coefficients of linear regression models.We prove that the asymptotic covariance matrix of kth power...This paper develops the theory of the kth power expectile estimation and considers its relevant hypothesis tests for coefficients of linear regression models.We prove that the asymptotic covariance matrix of kth power expectile regression converges to that of quantile regression as k converges to one and hence promise a moment estimator of asymptotic matrix of quantile regression.The kth power expectile regression is then utilized to test for homoskedasticity and conditional symmetry of the data.Detailed comparisons of the local power among the kth power expectile regression tests,the quantile regression test,and the expectile regression test have been provided.When the underlying distribution is not standard normal,results show that the optimal k are often larger than 1 and smaller than 2,which suggests the general kth power expectile regression is necessary.Finally,the methods are illustrated by a real example.展开更多
基金supported by Social Science Planning Foundation of Liaoning Province(Grand No.L22ZD065)National Natural Science Foundation of China(Grand Nos.12271231,1247012719,12001229)。
文摘To better capture the characteristics of asymmetry and structural fluctuations observed in count time series,this study delves into the application of the quantile regression(QR)method for analyzing and forecasting nonlinear integer-valued time series exhibiting a piecewise phenomenon.Specifically,we focus on the parameter estimation in the first-order Self-Exciting Threshold Integer-valued Autoregressive(SETINAR(2,1))process with symmetry,asymmetry,and contaminated innovations.We establish the asymptotic properties of the estimator under certain regularity conditions.Monte Carlo simulations demonstrate the superior performance of the QR method compared to the conditional least squares(CLS)approach.Furthermore,we validate the robustness of the proposed method through empirical quantile regression estimation and forecasting for larceny incidents and CAD drug call counts in Pittsburgh,showcasing its effectiveness across diverse levels of data heterogeneity.
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.
文摘This paper develops the theory of the kth power expectile estimation and considers its relevant hypothesis tests for coefficients of linear regression models.We prove that the asymptotic covariance matrix of kth power expectile regression converges to that of quantile regression as k converges to one and hence promise a moment estimator of asymptotic matrix of quantile regression.The kth power expectile regression is then utilized to test for homoskedasticity and conditional symmetry of the data.Detailed comparisons of the local power among the kth power expectile regression tests,the quantile regression test,and the expectile regression test have been provided.When the underlying distribution is not standard normal,results show that the optimal k are often larger than 1 and smaller than 2,which suggests the general kth power expectile regression is necessary.Finally,the methods are illustrated by a real example.
