Estimation in semi-parametric regression with non-stationary regressors
Estimation in semi-parametric regression with non-stationary regressors
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DOI：
10.3150/10-bej344
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发表时间：
2012-05
期刊：
影响因子：
1.5
通讯作者：
Jia Chen;Jiti Gao;Degui Li
中科院分区：
文献类型：
--
作者：
Jia Chen;Jiti Gao;Degui Li
本文考虑一个形式为$Y_t=X_t^{\tau}\theta_0 +g（V_t）+\theta_t$，$t=1，...，n$，其中$\{V_t\}$是一个$\beta$零递归马尔可夫链，$\{X_t\}$是一个严格平稳或非平稳回归序列，$\{\displaystyle $\{\mathbb_t\}$是一个平稳序列。我们建议估计$\theta_0 $和$g（\cdot）$的半参数最小二乘（SLS）估计方法。在一定的条件下，我们然后表明，所提出的SLS估计的$\theta_0 $仍然是渐近正态的平稳时间序列的情况下，具有相同的速度。此外，我们还建立了函数$g（\cdot）$的非参数估计的渐近分布。最后给出了一些算例，表明我们的理论和估计方法在实践中是有效的。
In this paper, we consider a partially linear model of the form $Y_t=X_t^{\tau}\theta_0+g(V_t)+\epsilon_t$, $t=1,...,n$, where $\{V_t\}$ is a $\beta$ null recurrent Markov chain, $\{X_t\}$ is a sequence of either strictly stationary or non-stationary regressors and $\{\epsilon_t\}$ is a stationary sequence. We propose to estimate both $\theta_0$ and $g(\cdot)$ by a semi-parametric least-squares (SLS) estimation method. Under certain conditions, we then show that the proposed SLS estimator of $\theta_0$ 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 $g(\cdot)$. Some numerical examples are provided to show that our theory and estimation method work well in practice.