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离散化与插值后的核密度估计AI 解读

The kernel estimate of a probability density function inherits its smoothness properties from the kernel density chosen by the investigator. Nevertheless, for computational (and especially graphical) reasons, exact kernel density estimates are often presented in (piecewise constant) discretized or (piecewise linear) interpolated form, using the exact estimate only at some grid of points. The asymptotic integrated mean squared error properties of these modifications are…

回归收缩预测量对历史与未来数据差异的稳健性AI 解读

SUMMARY Copas (1983) investigates the shrinkage associated with prediction in the usual linear multiple regression model and proposes using Stein-type predictors which anticipate this shrinkage. Assuming that the first two (population) moments of the regressor variables associated with individuals for which predictions are to be made coincide with the first two (sample) moments of those in the construction sample, preshrunk predictors give a uniformly lower prediction mean…