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Asymptotics of estimators in semi-parametric model under NA samples. (English) Zbl 1112.62032

Summary: This paper is concerned with the heteroscedastic semi-parametric regression model

y i =x i β+g(t i )+σ i e i ,1in,

where σ i 2 =f(u i ), (x i ,t i ,u i ) are fixed design points, g and f are unknown functions and the random errors e i are negatively associated (NA) random variables. The strong consistency and asymptotic normality for least-squares estimators and weighted least-squares estimators of β are studied. In addition, the strong consistency for the estimators of f(·) and g(·) is investigated. Some results on independent random error settings are extended.

MSC:
62G08Nonparametric regression
62G20Nonparametric asymptotic efficiency