分野別セミナー

The presentation is started with a proposition of new method to reduce the mean integrated squared error for kernel distribution function estimator. It can be shown that the asymptotic bias of the proposed method is considerably smaller, by using a self-elimination technique between two standard kernel distribution function estimators with different bandwidths. In the second main part, we discuss a new kernel type estimator for density function with nonnegative support. Here, we use a type of gamma density as a kernel function and modify it with the expansions of exponential and logarithmic functions. We propose kernel-type smoothed Kolmogorov-Smirnov and Cramér-von Mises tests for data on general interval using bijective transformations in the third discussion. We use bijective transformations to eliminate the boundary problem. In the last part we discuss two new kernel-type estimators of the mean residual life function of bounded or half-bounded interval supported distributions, by utilizing the property of bijective transformation and change-of-variable properties. Our proposed methods preserve the mean value property, which cannot be done by the naive kernel estimator.


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