测量误差模型只有一个变点的检验和估计

Test and Estimation for a Change-point in the Linear Structural Error-in-Variables Models

  • 摘要: 本文讨论了测量误差模型中参数只有一个变点的检验和估计问题.首先,给出其似然比检验统计量.然后,基于最小信息准则的原理,利用Schwarz信息准则(SIC),在多余参数已知和未知的情况下,分别给出了检验统计量,讨论了利用SIC方法给出的检验统计量的渐近分布.证明了基于似然比方法和SIC方法给出的变点估计是相同的,并且在一定条件下,给出了变点估计的极限分布.运用Monte-Carlo随机模拟的方法,分别给出了以上检验的临界值。

     

    Abstract: In this paper, we discuss the hypothesis tests and estimation for most one change-point in the linear structural error-in-variables model. Firstly, we propose likelihood ratio test statistic by using maximum likelihood ratio method. Applying Schwarz information criterion, we respectively derive the corresponding test statistics in terms of the principle of minimum information criterion, as redundant parameters are known and unknown. The asymptotic problem is considered with test statistic in the case of redundant parameters unknown. By a simple calculation, we conclude that the maximum likelihood estimation of change-point and the estimation of change-point under Schwarz information criterion are the same. We also obtain the limiting distribution of the estimation of change-point. Some Monte-Carlo simulation studies are given under each null hypothesis.

     

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