A note on the consistency for the estimators of semiparametric regression model

Yi Wu and Xuejun Wang ()
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Yi Wu: Anhui University
Xuejun Wang: Anhui University

Statistical Papers, 2018, vol. 59, issue 3, No 14, 1117-1130

Abstract: Abstract For the semiparametric regression model: $$Y^{(j)}(x_{in},t_{in})=t_{in}\beta +g(x_{in})+e^{(j)}(x_{in}),~~1\le j\le m, 1\le i\le n,$$ Y ( j ) ( x i n , t i n ) = t i n β + g ( x i n ) + e ( j ) ( x i n ) , 1 ≤ j ≤ m , 1 ≤ i ≤ n , where $$t_{in}\in \mathbb {R}$$ t i n ∈ R and $$x_{in}\in \mathbb {R}^{p}$$ x i n ∈ R p are known to be nonrandom, g is an unknown continuous function on a compact set A in $$\mathbb {R}^{p}$$ R p , $$e^{j}(x_{in})$$ e j ( x i n ) are $$\rho ^{*}$$ ρ ∗ -mixing random errors with mean zero, $$Y^{(j)}(x_{in},t_{in})$$ Y ( j ) ( x i n , t i n ) represent the j-th response variables which are observable at points $$x_{in},t_{in}$$ x i n , t i n . In this paper, we study the strong consistency and r-th ( $$1

Keywords: Semiparametric regression model; Strong consistency; Mean consistency; $$\rho ^{*}$$ ρ ∗ -mixing random variables; 62G05 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s00362-016-0807-2

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