A class of tests based on U-statistic is proposed for two-sample scale problem. The U-statistic is function of extremes of subsamples taken from random samples of two absolutely continuous distributions. The asymptotic distribution, null distribution and efficacy of the class of tests are studied. A comparison of its performance with respect to other tests is studied in terms of Pitman ARE and small sample performance through its empirical power. Application of the class of tests is illustrated through an example.
Nadaraya-Watson (NW) estimator with fixed bandwidth and its adaptive forms with varying bandwidths are widely used kernel regression estimators in nonparametric regression. In this paper, we propose a generalized class of varying kernel regression estimators with its members based on various statistical measures of pilot density estimates. We study the performance of the members of this class in terms of mean integrated squared error (MISE).
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