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May 2012 Estimation in semi-parametric regression with non-stationary regressors
Jia Chen, Jiti Gao, Degui Li
Bernoulli 18(2): 678-702 (May 2012). DOI: 10.3150/10-BEJ344


In this paper, we consider a partially linear model of the form $Y_t = X_t^τθ_0 + g(V_t) + ϵ_t, t = 1, …, n$, where $\{V_t\}$ is a $β$ null recurrent Markov chain, {$X_t$} is a sequence of either strictly stationary or non-stationary regressors and $\{ϵ_t\}$ is a stationary sequence. We propose to estimate both $θ_0$ and $g(⋅)$ by a semi-parametric least-squares (SLS) estimation method. Under certain conditions, we then show that the proposed SLS estimator of $θ_0$ is still asymptotically normal with the same rate as for the case of stationary time series. In addition, we also establish an asymptotic distribution for the nonparametric estimator of the function $g(⋅)$. Some numerical examples are provided to show that our theory and estimation method work well in practice.


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Jia Chen. Jiti Gao. Degui Li. "Estimation in semi-parametric regression with non-stationary regressors." Bernoulli 18 (2) 678 - 702, May 2012.


Published: May 2012
First available in Project Euclid: 16 April 2012

zbMATH: 1238.62044
MathSciNet: MR2922466
Digital Object Identifier: 10.3150/10-BEJ344

Rights: Copyright © 2012 Bernoulli Society for Mathematical Statistics and Probability


Vol.18 • No. 2 • May 2012
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