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随机系数回归中截距与斜率分布的非参数估计AI 解读

An experiment records stimulus and response for a random sample of cases. The relationship between response and stimulus is thought to be linear, the values of the slope and intercept varying by case. From such data, we construct a consistent, asymptotically normal, nonparametric estimator for the joint density of the slope and intercept. Our methodology incorporates the radial projection-slice theorem for the Radon transform, a technique for locally linear nonparametric…

插值构造的非参数预测区间与置信区间AI 解读

SUMMARY In several important statistical problems, prediction intervals and confidence intervals can be constructed with coverage levels which are known precisely but cannot be rendered equal to predetermined levels such as 0.95. One solution to this difficulty is to interpolate between such intervals. We show that simple linear interpolation reduces the order of coverage error, but that higher orders of interpolation produce no further improvement. The error is reduced by a…

独立非同分布数据模型中的稳健估计AI 解读

This paper concerns robust estimation of the parameter $\theta$ which indexes a parametric model for independent non-identically distributed data. For reasonable choices of contamination neighborhood and of what is to be estimated when the parametric model does not hold, we characterize asymptotically minimax robust estimates of $\theta$. When applied to the normal regression model, the theory yields recipes for the influence curves of optimal robust regression and scale…