Strong consistency rates for the estimators in a heteroscedastic EV model with missing responses

• Published in: Journal of inequalities and applications 2020-05, Vol.2020 (1), p.1-21, Article 144
• Main Authors: Zhang, Jing-Jing, Xiao, Yun-Peng
• Format: Article
• Language: English
• Subjects: Analysis; Applications of Mathematics; Computer simulation; Estimators; Heteroscedastic; Mathematics; Mathematics and Statistics; Missing responses; Random errors; Random variables; Semi-parametric error-in-variables model; Strong consistent rate
• ISSN: 1029-242X; 1025-5834; 1029-242X
• DOI: 10.1186/s13660-020-02411-y

This article is concerned with the semi-parametric error-in-variables (EV) model with missing responses: y i = ξ i β + g ( t i ) + ϵ i , x i = ξ i + μ i , where ϵ i = σ i e i is heteroscedastic, f ( u i ) = σ i 2 , y i are the response variables missing at random, the design points ( ξ i , t i , u i ) are known and non-random, β is an unknown parameter, g ( ⋅ ) and f ( ⋅ ) are functions defined on closed interval [ 0 , 1 ] , and the ξ i are the potential variables observed with measurement errors μ i , e i are random errors. Under appropriate conditions, we study the strong consistent rates for the estimators of β , g ( ⋅ ) and f ( ⋅ ) . Finite sample behavior of the estimators is investigated via simulations.