Estimation of partial linear error-in-variables models for ρ−-mixing dependence data

• Published in: Journal of mathematical chemistry Vol. 43; no. 1; pp. 375 - 385
• Main Author: Cai, Guang-hui
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.01.2008; Springer
• Subjects: Applications; Chemistry; Chemistry and Materials Science; Exact sciences and technology; General and physical chemistry; Global analysis, analysis on manifolds; Insurance, economics, finance; Linear inference, regression; Math. Applications in Chemistry; Mathematics; Physical Chemistry; Probability and statistics; Sciences and techniques of general use; Statistics; Theoretical and Computational Chemistry; Theory of reactions, general kinetics. Catalysis. Nomenclature, chemical documentation, computer chemistry; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; validation data; 62J02; 62G05; ρ; mixing; partial linear model; strong consistency; negatively associated; Mixing; Mixing model; Error estimation; Strong consistency; Error in variable; Linear model; ρ-mixing; Least squares method; Independent set; Linear estimation; Mixed distribution; Validation; Estimation error; Data analysis; Mathematical chemistry; Data dependency; Linear regression; Estimator; Random error; Semiparametric method; Response; negatively associated 62J02; Regression model; Observation; Observation data
• ISSN: 0259-9791; 1572-8897
• DOI: 10.1007/s10910-006-9204-8

Consider the partly linear regression model Y  =  x β +  g ( t ) +  e where the explanatory x is erroneously measured, and both t and the response Y are measured exactly, the random error e is ρ − -mixing. Let be a surrogate variable observed instead of the true x in the primary survey data. Assume that in addition to the primary data set containing N observations of , which is ρ − -mixing data sets, an independent validation data containing n observations of is available. The exact observations on x may be obtained by some expensive or diffcult procedures for only a small subset of subjects enrolled in the study. In this paper, inspired by Berberan-Santos et al. [J. Math. Chem. 37 (2005)101], a semiparametric method with the primary data is employed to obtain the estimators of β and g (·) based on the least squares criterion with the help of validata. The proposed estimators are proved to be strongly consistent.