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有限混合模型中两组分假设的检验AI 解读

Summary We consider a finite mixture model with k components and a kernel distribution from a general one-parameter family. The problem of testing the hypothesis k=2 versusk⩾3 is studied. There has been no general statistical testing procedure for this problem. We propose a modified likelihood ratio statistic where under the null and the alternative hypotheses the estimates of the parameters are obtained from a modified likelihood function. It is shown that estimators of the…

有限混合模型同质性的修正似然比检验AI 解读

Summary Testing for homogeneity in finite mixture models has been investigated by many researchers. The asymptotic null distribution of the likelihood ratio test (LRT) is very complex and difficult to use in practice. We propose a modified LRT for homogeneity in finite mixture models with a general parametric kernel distribution family. The modified LRT has a χ-type of null limiting distribution and is asymptotically most powerful under local alternatives. Simulations show…

Box–Cox 变换后检验的渐近相对效率界AI 解读

Bounds on the asymptotic relative efficiency (ARE) of the Box-Cox transformed two-sample $t$-test to the ordinary $t$-test are obtained under local alternatives. It is shown that the ARE is at least 1 for location-shift models. In the case of scale-shift models, a similar bound applies provided the limiting value of the estimated power transformation is greater than 1. If instead the Box-Cox transformed $t$-test is compared against the ordinary $t$-test applied to the…

二项分布参数近似置信区间的准确性AI 解读

This article considers the uniform convergence of the coverage probabilities of some approximate confidence intervals for the binomial parameter p, induced by central limit arguments. A uniform upper bound on the coverage probabilities of any such interval obtained by transformation of the sample proportion [pcirc] n is derived. The coverage probability of the interval induced by the arcsine transformation turns out to be very close to the upper bound. Replacing [pcirc] n by…