The loglinear model under product-multinomial sampling with constraints is considered. The asymptotic expansion and normality of the restricted minimum φ-divergence estimator (RMφDE) which is a generalization of the maximum likelihood estimator is presented. Then various statistics based on φ-divergence and RMφDE are used to test various hypothesis test problems under the model considered. These statistics contain the classical loglikelihood ratio test statistics and Pearson chi-squared test statistics. In the last section, a simulation study is implemented.
考虑了乘积多项抽样下的对数线性模型.在这个模型下,文献[Jin Y H,Wu Y H.Mini mumφ-divergence esti mator and hierarchical testing in log-linear models under product-multinomial sampling.Journal of Statistical Planning and Inference,2009,139:3 488-3 500]用基于-散度和最小-散度估计构造的统计量研究了几类假设检验问题,这其中就有嵌套假设.最小-散度估计是极大似然估计的推广.在上述文献的基础上,给出了其中一类检验的功效函数的渐近逼近公式;另外,还研究了在一列近邻假设下检验统计量的渐近分布.通过模拟研究发现,与Pearson型统计量和对数极大似然比统计量相比,Cressie-Read型检验统计量有差不多的甚至更好的模拟功效和水平.
In this article,the Bayes linear unbiased estimator (BALUE) of parameters is derived for the multivariate linear models.The superiorities of the BALUE over the least square estimator (LSE) is studied in terms of the mean square error matrix (MSEM) criterion and Bayesian Pitman closeness (PC) criterion.
Based on the empirical likelihood method, the subset selection and hypothesis test for parameters in a partially linear autoregressive model are investigated. We show that the empirical log-likelihood ratio at the true parameters converges to the standard chi-square distribution. We then present the definitions of the empirical likelihood-based Bayes information criteria(EBIC) and Akaike information criteria(EAIC).The results show that EBIC is consistent at selecting subset variables while EAIC is not. Simulation studies demonstrate that the proposed empirical likelihood confidence regions have better coverage probabilities than the least square method, while EBIC has a higher chance to select the true model than EAIC.
