Asymptotic properties for estimates of nonparametric regression models based on negatively associated sequences

• Published in: Journal of multivariate analysis Vol. 95; no. 2; pp. 227 - 245
• Main Authors: Liang, Han-Ying, Jing, Bing-Yi
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 01.08.2005; Elsevier; Taylor & Francis LLC
• Series: Journal of Multivariate Analysis
• Subjects: Asymptotic normality; Complete convergence; Consistency; Exact sciences and technology; Mathematical models; Mathematics; Multivariate analysis; Negatively associated random error; Nonparametric inference; Nonparametric regression; Nonparametric regression Negatively associated random error Consistency Complete convergence Asymptotic normality; Probability and statistics; Regression analysis; Sciences and techniques of general use; Statistics; Studies; 62G05; Complete convergence; Asymptotic normality; Nonparametric regression; Negatively associated random error; Consistency; Uniform convergence; Asymptotic property; Error estimation; Random error; Non parametric estimation; Statistical method; Fix point; Asymptotic normality 1991 subject classification: 62G05; Regression model
• ISSN: 0047-259X; 1095-7243
• DOI: 10.1016/j.jmva.2004.06.004

Consider the nonparametric regression model Y ni = g ( x ni ) + ε ni for i = 1 , … , n , where g is unknown, x ni are fixed design points, and ε ni are negatively associated random errors. Nonparametric estimator g n ( x ) of g ( x ) will be introduced and its asymptotic properties are studied. In particular, the pointwise and uniform convergence of g n ( x ) and its asymptotic normality will be investigated. This extends the earlier work on independent random errors (e.g. see J. Multivariate Anal. 25(1) (1988) 100).