Bias reduction of a conditional maximum likelihood estimator for a Gaussian second-order moving average model

Modern Stochastics: Theory and Applications

Takeshi Kurosawa¹  Fumiaki Honda¹ 

[1] Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo, 162-8601, Japan;

关键词: Gaussian second-order moving average model;    conditional maximum likelihood estimators;    bias reduction;    asymptotic expansion;   

DOI  :  10.15559/21-VMSTA187

来源: DOAJ

【 摘 要 】

In this study, we consider a bias reduction of the conditional maximum likelihood estimators for the unknown parameters of a Gaussian second-order moving average (MA(2)) model. In many cases, we use the maximum likelihood estimator because the estimator is consistent. However, when the sample size n is small, the error is large because it has a bias of $O({n^{-1}})$. Furthermore, the exact form of the maximum likelihood estimator for moving average models is slightly complicated even for Gaussian models. We sometimes rely on simpler maximum likelihood estimation methods. As one of the methods, we focus on the conditional maximum likelihood estimator and examine the bias of the conditional maximum likelihood estimator for a Gaussian MA(2) model. Moreover, we propose new estimators for the unknown parameters of the Gaussian MA(2) model based on the bias of the conditional maximum likelihood estimators. By performing simulations, we investigate properties of this bias, as well as the asymptotic variance of the conditional maximum likelihood estimators for the unknown parameters. Finally, we confirm the validity of the new estimators through this simulation study.

【 授权许可】

Unknown