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条件曲线的统计推断：泊松过程方法AI 解读

A Poisson approximation of a truncated, empirical point process enables us to reduce conditional statistical problems to unconditional ones. Let $(\mathbf{X,Y})$ be a $(d + m)$-dimensional random vector and denote by $F(\cdot\mid\mathbf{x})$ the conditional d.f. of $\mathbf{Y}$ given $\mathbf{X} = \mathbf{x}$. Applying our approach, one may study the fairly general problem of evaluating a functional parameter $T(F(\cdot\mid\mathbf{x}_1),\ldots,F(\cdot\mid\mathbf{x}_p))$ based…

某些非参数模型中的分位数估计AI 解读

The deficiency of sample quantiles with respect to quasiquantiles is investigated under the assumption that the true density function has bounded derivatives. Then the sample quantile is still an efficient estimator of the true quantile but the relative deficiency of sample quantiles with respect to suitably defined quasiquantiles quickly tends to infinity for increasing sample sizes. If the second derivative of the true density function is bounded, then adaptive estimators…