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通过平滑经验变换降低核密度估计偏差AI 解读

A modification of kernel density estimation is proposed. The first step is ordinary kernel estimation of the density and its cdf. In the second step the data are transformed, using this estimated cdf, to an approximate uniform (or normal or other target) distribution. The density and cdf of the transformed data are then estimated by the kernel method and, by change of variable, converted to new estimates of the density and the cdf of the original data. This process is…

多元密度的可容许核估计量AI 解读

A kernel density estimator is defined to be admissible if no other kernel estimator has (among all densities and sample sizes) uniformly smaller mean integrated squared error. Admissible kernel density estimators are precisely those using kernels with nonnegative Fourier transforms bounded by 1. Several examples are given.

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利用重复观测估计权重的加权最小二乘渐近理论AI 解读

SUMMARY We consider a heteroscedastic linear regression model with replication. To estimate the variances, one can use the sample variances or the sample average squared errors from a regression fit. We study the large-sample properties of these weighted least-squares estimates with estimated weights when the number of replicates is small. The estimates are generally inconsistent for asymmetrically distributed data. If sample variances are used based on m replicates, the…