具有Harris递归马尔可夫链的非线性回归的估计
Estimation in nonlinear regression with Harris recurrent Markov chains
摘要：
本文在Harris递归马尔可夫链框架下研究了参数非线性回归。我们首先考虑了同方差情形下参数的非线性最小二乘估计，并建立了估计量的渐近理论。结果表明，估计量的收敛速度不仅依赖于非线性回归函数的性质，而且依赖于Harris回归马尔可夫链的再生次数.此外，我们还讨论了条件波动率函数中参数向量的估计，并将我们的结果应用于具有$I(1)$过程的非线性回归，得到了一个与Park和Phillips [Econometrica 69（2001）117-161]相当的渐近分布理论.提供了一些包括模拟和经验应用在内的数值研究来检验所提出的方法和结果的有限样本性能。
英文摘要：
In this paper, we study parametric nonlinear regression under the Harris recurrent Markov chain framework. We first consider the nonlinear least squares estimators of the parameters in the homoskedastic case, and establish asymptotic theory for the proposed estimators. Our results show that the convergence rates for the estimators rely not only on the properties of the nonlinear regression function, but also on the number of regenerations for the Harris recurrent Markov chain. Furthermore, we discuss the estimation of the parameter vector in a conditional volatility function, and apply our results to the nonlinear regression with $I(1)$ processes and derive an asymptotic distribution theory which is comparable to that obtained by Park and Phillips [Econometrica 69 (2001) 117-161]. Some numerical studies including simulation and empirical application are provided to examine the finite sample performance of the proposed approaches and results.
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