The main purpose of this paper is to give a review on recent advances of wavelet in probability and statistics. Many interesting new ideas, new results and new methods are introduced in this review. From many aspects ...The main purpose of this paper is to give a review on recent advances of wavelet in probability and statistics. Many interesting new ideas, new results and new methods are introduced in this review. From many aspects of this paper, probability and statistics researchers may find many new interesting research topics for further studying on wavelets in stochastic processes. New results, such as K- sta-tionarity, wavelet representation of Karhunen processes, hidden periodicities analysis by wavelet approach, hetero-scedasticity in wavelet regression, wavelets and neural networks, etc. are introduced in this paper. Comments, discussions and plentiful references are also involved in this review.展开更多
In this paper, we investigate the model checking problem for a general linear model with nonignorable missing covariates. We show that, without any parametric model assumption for the response probability, the least s...In this paper, we investigate the model checking problem for a general linear model with nonignorable missing covariates. We show that, without any parametric model assumption for the response probability, the least squares method yields consistent estimators for the linear model even if only the complete data are applied. This makes it feasible to propose two testing procedures for the corresponding model checking problem： a score type lack-of-fit test and a test based on the empirical process. The asymptotic properties of the test statistics are investigated. Both tests are shown to have asymptotic power 1 for local alternatives converging to the null at the rate n-r, 0 ≤ r 〈 1/2. Simulation results show that both tests perform satisfactorily.展开更多
基金This work was partly supported by the National Natural Science Foundation of China (Grant No. 10171005), HeungWong and Wai-Cheung Ip's research were supported by the Hong Kong Research Grants Council.
文摘The main purpose of this paper is to give a review on recent advances of wavelet in probability and statistics. Many interesting new ideas, new results and new methods are introduced in this review. From many aspects of this paper, probability and statistics researchers may find many new interesting research topics for further studying on wavelets in stochastic processes. New results, such as K- sta-tionarity, wavelet representation of Karhunen processes, hidden periodicities analysis by wavelet approach, hetero-scedasticity in wavelet regression, wavelets and neural networks, etc. are introduced in this paper. Comments, discussions and plentiful references are also involved in this review.
基金supported by the National Natural Science Foundation of China (No. 10901162,10926073)China Postdoctoral Science Foundation and the President Fund of GUCAS+1 种基金the foundation of the Key Laboratory of Random Complex Structures and Data Science, CASsupported by a research grant from the Research Committee, The Hong Kong Polytechnic University
文摘In this paper, we investigate the model checking problem for a general linear model with nonignorable missing covariates. We show that, without any parametric model assumption for the response probability, the least squares method yields consistent estimators for the linear model even if only the complete data are applied. This makes it feasible to propose two testing procedures for the corresponding model checking problem： a score type lack-of-fit test and a test based on the empirical process. The asymptotic properties of the test statistics are investigated. Both tests are shown to have asymptotic power 1 for local alternatives converging to the null at the rate n-r, 0 ≤ r 〈 1/2. Simulation results show that both tests perform satisfactorily.
