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局部散度与关联性AI 解读

In applications of differential geometry to problems of parametric statistical inference, the notion of divergence is often used to measure the separation between two parametric densities. In this paper we move away from the parametric framework of much of statistical differential geometry and instead employ divergence in a covariate setting. Many data-analyses involve investigation of how the conditional distribution f(y|X = x) of a random variable Y changes with covariate…

相关曲线：回归局部解释方差的度量AI 解读

We call (a model for) an experiment heterocorrelatious if the strength of the relationship between a response variable Y and a covariate X is different in different regions of the covariate space. For such experiments we introduce a correlation curve that measures heter-ocorrelaticity in terms of the variance explained by regression locally at each covariate value. More precisely, the squared correlation curve is obtained by first expressing the usual linear model “variance…

作为回归局部方差解释度量的相关曲线AI 解读

We call (a model for) an experiment heterocorrelatious if the strength of the relationship between a response variable Y and a covariate X is different in different regions of the covariate space. For such experiments we introduce a correlation curve that measures heter-ocorrelaticity in terms of the variance explained by regression locally at each covariate value. More precisely, the squared correlation curve is obtained by first expressing the usual linear model “variance…

局部散度与关联性AI 解读

In applications of differential geometry to problems of parametric statistical inference, the notion of divergence is often used to measure the separation between two parametric densities. In this paper we move away from the parametric framework of much of statistical differential geometry and instead employ divergence in a covariate setting. Many data-analyses involve investigation of how the conditional distribution f(y|X = x) of a random variable Y changes with covariate…

基于功效准则的最优核权重AI 解读

We develop an approach to choosing optimal kernel weights for nonparametric estimation of the slope of the regression function which uses maximization of power, rather than minimization of integrated mean squared error (IMSE), as its optimality criterion. This power criterion leads to optimal kernel weights whose derivation is simpler than under other criteria and which provides an intuitive understanding of the nature of the optimality.