Complete consistency for the weighted least squares estimators in semiparametric regression models. (English) Zbl 07753676
Summary: In this article, we consider the semiparametric regression model \(y_i=x_i\beta + g(t_i) + \sigma_ie_i\), \(i=1,2,\dots,n\), where \(\sigma_i^2=f(u_i)\), \((x_i,t_i,u_i)\) are known fixed design points, \( \beta\) is an unknown parameter to be estimated, \(g(\cdot)\) and \(f(\cdot)\) are unknown functions defined on a compact set. Assume that the random errors \(\{e_i,\ i\geq 1\}\) are zero mean widely orthant dependent (WOD, for short) random variables. Under some suitable conditions, we investigate the complete consistency for the least squares estimators (LSE, for short) and the weighted least squares estimators (WLSE, for short) of \(\beta\) and \(g(\cdot)\). In addition, a numerical simulation is given to study the numerical performance based on finite samples.
Keywords:
semiparametric regression model; complete consistency; least squares estimator; weighted least squares estimator; WOD random errorsReferences:
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