For the semiparametric regression model: \(Y^{(j)}(x_{in},~t_{in})=t_{in}\beta +g(x_{in})+e^{(j)}(x_{in}),~1\le j\le m,~1\le i \le n\) , where \(x_{in}\in \mathbb {R}^p\) , \(t_{in}\in \mathbb {R}\) are known to be nonrandom, g is an unknown continuous function on a compact set A in \(\mathbb {R}^p\) , \(e^{(j)}(x_{in})\) are \(\tilde{\rho }\) -mixing random variables with mean zero, \(Y^{(j)}(x_{in},t_{in})\) are random variables which are observable at points \(x_{in}\) and \(t_{in}\) . In the paper, we establish the strong consistency, r-th ( \(r>2\) ) mean consistency and complete consistency for estimators \(\beta _{m,n}\) and \(g_{m,n}(x)\) of \(\beta \) and g, respectively. The results obtained in the paper extend the corresponding ones for independent random variables and \(\varphi \) -mixing random variables.
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