Weak consistency for the estimators in a semiparametric regression model based on negatively associated random errors. (English) Zbl 07497819
Summary: In this article, we consider the semiparametric regression model: \(y_i^{(n)}=x_i^{(n)}\beta+g(t_i^{(n)})+\varepsilon_i^{(n)}\), \(i=1, 2, \dots, n\), \(n\geq1\), which is an important and very useful statistical model. We investigate the parametric component and nonparametric component estimators in a semiparametric regression model based on negatively associated random errors. The weak consistency for the estimators \(\widehat{\beta}_n\) and \(\widehat{g}_n(t)\) of \(\beta\) and \(g(t)\) respectively are established under some suitable conditions. In addition, a simulation to study the numerical performance of the consistency for the nearest neighbor weight function estimators is provided and a real data application is then presented.
MSC:
| 62G20 | Asymptotic properties of nonparametric inference |
| 62F12 | Asymptotic properties of parametric estimators |
| 62-XX | Statistics |
Keywords:
weak consistency; semiparametric regression model; negatively associated random variables; nearest neighbour weight function estimator; simulation studyReferences:
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