This paper studies estimation in partial functional linear quantile regression in which the dependent variable is related to both a vector of finite length and a function-valued random variable as predictor variables....This paper studies estimation in partial functional linear quantile regression in which the dependent variable is related to both a vector of finite length and a function-valued random variable as predictor variables. The slope function is estimated by the functional principal component basis. The asymptotic distribution of the estimator of the vector of slope parameters is derived and the global convergence rate of the quantile estimator of unknown slope function is established under suitable norm. It is showed that this rate is optirnal in a minimax sense under some smoothness assumptions on the covariance kernel of the covariate and the slope function. The convergence rate of the mean squared prediction error for the proposed estimators is also established. Finite sample properties of our procedures are studied through Monte Carlo simulations. A real data example about Berkeley growth data is used to illustrate our proposed methodology.展开更多
We consider the periodic generalized autoregressive conditional heteroskedasticity(P-GARCH) process and propose a robust estimator by composite quantile regression. We study some useful properties about the P-GARCH mo...We consider the periodic generalized autoregressive conditional heteroskedasticity(P-GARCH) process and propose a robust estimator by composite quantile regression. We study some useful properties about the P-GARCH model. Under some mild conditions, we establish the asymptotic results of proposed estimator.The Monte Carlo simulation is presented to assess the performance of proposed estimator. Numerical study results show that our proposed estimation outperforms other existing methods for heavy tailed distributions.The proposed methodology is also illustrated by Va R on stock price data.展开更多
Structural equation model(SEM) is a multivariate analysis tool that has been widely applied to many fields such as biomedical and social sciences. In the traditional SEM, it is often assumed that random errors and exp...Structural equation model(SEM) is a multivariate analysis tool that has been widely applied to many fields such as biomedical and social sciences. In the traditional SEM, it is often assumed that random errors and explanatory latent variables follow the normal distribution, and the effect of explanatory latent variables on outcomes can be formulated by a mean regression-type structural equation. But this SEM may be inappropriate in some cases where random errors or latent variables are highly nonnormal. The authors develop a new SEM, called as quantile SEM(QSEM), by allowing for a quantile regression-type structural equation and without distribution assumption of random errors and latent variables. A Bayesian empirical likelihood(BEL) method is developed to simultaneously estimate parameters and latent variables based on the estimating equation method. A hybrid algorithm combining the Gibbs sampler and Metropolis-Hastings algorithm is presented to sample observations required for statistical inference. Latent variables are imputed by the estimated density function and the linear interpolation method. A simulation study and an example are presented to investigate the performance of the proposed methodologies.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11071120)
文摘This paper studies estimation in partial functional linear quantile regression in which the dependent variable is related to both a vector of finite length and a function-valued random variable as predictor variables. The slope function is estimated by the functional principal component basis. The asymptotic distribution of the estimator of the vector of slope parameters is derived and the global convergence rate of the quantile estimator of unknown slope function is established under suitable norm. It is showed that this rate is optirnal in a minimax sense under some smoothness assumptions on the covariance kernel of the covariate and the slope function. The convergence rate of the mean squared prediction error for the proposed estimators is also established. Finite sample properties of our procedures are studied through Monte Carlo simulations. A real data example about Berkeley growth data is used to illustrate our proposed methodology.
基金supported by National Natural Science Foundation of China(Grant No.11371354)Key Laboratory of Random Complex Structures and Data Science+2 种基金Chinese Academy of Sciences(Grant No.2008DP173182)National Center for Mathematics and Interdisciplinary SciencesChinese Academy of Sciences
文摘We consider the periodic generalized autoregressive conditional heteroskedasticity(P-GARCH) process and propose a robust estimator by composite quantile regression. We study some useful properties about the P-GARCH model. Under some mild conditions, we establish the asymptotic results of proposed estimator.The Monte Carlo simulation is presented to assess the performance of proposed estimator. Numerical study results show that our proposed estimation outperforms other existing methods for heavy tailed distributions.The proposed methodology is also illustrated by Va R on stock price data.
基金supported by the National Natural Science Foundation of China under Grant No.11165016
文摘Structural equation model(SEM) is a multivariate analysis tool that has been widely applied to many fields such as biomedical and social sciences. In the traditional SEM, it is often assumed that random errors and explanatory latent variables follow the normal distribution, and the effect of explanatory latent variables on outcomes can be formulated by a mean regression-type structural equation. But this SEM may be inappropriate in some cases where random errors or latent variables are highly nonnormal. The authors develop a new SEM, called as quantile SEM(QSEM), by allowing for a quantile regression-type structural equation and without distribution assumption of random errors and latent variables. A Bayesian empirical likelihood(BEL) method is developed to simultaneously estimate parameters and latent variables based on the estimating equation method. A hybrid algorithm combining the Gibbs sampler and Metropolis-Hastings algorithm is presented to sample observations required for statistical inference. Latent variables are imputed by the estimated density function and the linear interpolation method. A simulation study and an example are presented to investigate the performance of the proposed methodologies.
