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用于检测依赖的广义决定系数AI 解读

SUMMARY Detecting dependence between two random variables is a fundamental problem. Although the Pearson correlation coefficient is effective for capturing linear dependence, it can be entirely powerless for detecting nonlinear and/or heteroscedastic patterns. We introduce a new measure, G-squared, to test whether two univariate random variables are independent and to measure the strength of their relationship. The G-squared statistic is almost identical to the square of the…

具有变化平滑参数的平滑样条AI 解读

This paper considers the development of spatially adaptive smoothing splines for the estimation of a regression function with nonhomogeneous smoothness across the domain. Two challenging issues arising in this context are the evaluation of the equivalent kernel and the determination of a local penalty. The penalty is a function of the design points in order to accommodate local behaviour of the regression function. We show that the spatially adaptive smoothing spline…

单调回归的分组 Brunk 估计与惩罚样条估计AI 解读

We study a class of monotone univariate regression estimators. We use B-splines to approximate an underlying regression function and estimate spline coefficients based on grouped data. We investigate asymptotic properties of two monotone estimators: a grouped Brunk estimator and a penalized monotone estimator. These estimators are consistent at the boundary and their mean square errors achieve optimal convergence rates under suitable assumptions of the true regression…