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论非参数核密度估计AI 解读

The paper introduces the idea of inadmissible kernels and shows that an Epanechnikov type kernel is the only admissible kernel. An analysis of kernel density estimates leads to two new methods of bias reduction. We also discuss a general method of improving kernel density estimates in the sense of having smaller mean squared error. Finally we provide a theoretical framework for the operational method of using Abramson's square root law providing tangible and compact forms…

非参数核密度估计的可容许性与偏差改进AI 解读

The paper introduces the idea of inadmissible kernels and shows that an Epanechnikov type kernel is the only admissible kernel. An analysis of kernel density estimates leads to two new methods of bias reduction. We also discuss a general method of improving kernel density estimates in the sense of having smaller mean squared error. Finally we provide a theoretical framework for the operational method of using Abramson's square root law providing tangible and compact forms…

论参数密度估计AI 解读

The paper makes a critical assessment of Aitchison's criterion of density estimation. It seems not to satisfy certain intuitive requirements. A new criterion based on decisions theoretic considerations is introduced. It is shown through examples that the judgement about the choice of density estimates is seriously dependent on the criterion chosen. Some other density estimates are introduced which look similar to Bayesian predictive density estimates without using a prior…

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Bartlett 检验与立方根方差齐性检验的比较AI 解读

A cube root test of homogeneity of variances was considered by Samiuddin (1976) and Samiuddin & Atiqullah (1976). The present paper gives some modifications of the cube root test and provides results of a simulation study with 4, 6 and 8 groups. The results suggest that the modified cube root test may have some advantage over Bartlett's test.

方差齐性的贝叶斯检验AI 解读

An alternative test of homogeneity of variances in samples from normal populations is developed. The performance of Bartlett's test and the new test proposed here is compared to the F-test in the case of two samples. The performance of Bartlett's test is not particularly good when samples are of unequal sizes, whereas the proposed test performs well for both equal and unequal sample sizes.

方差齐性的贝叶斯检验AI 解读

An alternative test of homogeneity of variances in samples from normal populations is developed. The performance of Bartlett's test and the new test proposed here is compared to the F-test in the case of two samples. The performance of Bartlett's test is not particularly good when samples are of unequal sizes, whereas the proposed test performs well for both equal and unequal sample sizes.

二元正态分布中相关系数给定值的检验AI 解读

A statistic is proposed for testing an assigned value of correlation coefficient Θ in a bivariate normal population, and its asymptotic properties are discussed.