Statistical inferences for single-index models with measurement errors

作     者：Huang, Zhensheng Lou, Wen 

作者机构：Nanjing Univ Sci & Technol Sch Sci Nanjing 210094 Jiangsu Peoples R China 

出 版 物：《JOURNAL OF APPLIED STATISTICS》 (应用统计学杂志)

年 卷 期：2021年第48卷第6期

页      面：1033-1052页

核心收录：

学科分类：0202[经济学-应用经济学] 02[经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 

基　　金：National Natural Science Foundation of China [11471160, 11101114] National Statistical Science Research Major Program of China [2018LD01] Fundamental Research Funds for the Central Universities Qing Lan Project 

主　　题：Single-index model measurement errors local linear regression SIMEX generalized likelihood ratio test 

摘      要：An important factor in house prices is its location. However, measurement errors arise frequently in the process of observing variables such as the latitude and longitude of the house. The single-index models with measurement errors are used to study the relationship between house location and house price. We obtain the estimators by a SIMEX method based on the local linear method and the estimating equation. To test the significance of the index coefficient and the linearity of the link function, we establish the generalized likelihood ratio (GLR) tests for the models. We demonstrate that the asymptotic null distributions of the established GLR tests follow -distributions which are independent of nuisance parameters or functions. Finally, two simulated examples and a real estate valuation data set are given to illustrate the effect of GLR tests.