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不同损失函数下的风险控制：折中决策问题AI 解读

Controlling Bayes and/or minimax risks under possibly different loss functions is formulated as a problem faced by two or more statisticians who must compromise and agree on the use of a single decision procedure. The theory characterizing solutions to Bayes compromise problems and minimax-Bayes compromise problems is presented. In a Bayes compromise problem, Bayes risks under different prior distributions and/or loss functions are minimized simultaneously. In a…

平方误差加复杂度成本损失下的正态均值估计AI 解读

Estimating the mean of a $p$-variate normal distribution is considered when the loss is squared error plus a complexity cost. The complexity of estimates is defined using a partition of the parameter space into sets corresponding to models of different complexity. The model implied by the use of an estimate determines the estimate's complexity cost. Complete classes of estimators are developed which consist of preliminary-test estimators. As is the case when loss is just…

回归中观测影响的决策理论度量AI 解读

SUMMARY A Bayesian decision-theoretic framework is used to define the influence of observations when fitting a regression model to data. Measures assessing an observation's influence on the posterior risk depend on the specification of the underlying loss function and prior assumptions. Illustrations are given for normal linear regression models.

最小二乘预测回归中变量选择程序的可容许性AI 解读

Given data with a single dependent variable arising from a normal linear regression model, a variable-selection procedure completely specifies a least squares fit by choosing the subset of the independent variables to include in the model. For loss equal to squared error of prediction, we prove that all variable-selection procedures are admissible for choosing among least-squares fits of the regression model.

双向表加性与乘性最小二乘拟合中的杠杆AI 解读

An additive-plus-multiplicative model can describe both main effects and row x column interactions in two-way tables of data. When each cell contains exactly one observation, a least squares fit for this nonlinear model calculates the main effects, using means of rows and columns, and then fits a multiplicative term to the additive residuals, using the singular value decomposition. A natural extension of the hat matrix for a linear model yields a definition of leverage that…

双向表加性加乘性最小二乘拟合中的杠杆值AI 解读

An additive-plus-multiplicative model can describe both main effects and row x column interactions in two-way tables of data. When each cell contains exactly one observation, a least squares fit for this nonlinear model calculates the main effects, using means of rows and columns, and then fits a multiplicative term to the additive residuals, using the singular value decomposition. A natural extension of the hat matrix for a linear model yields a definition of leverage that…

最小二乘预测回归中变量选择程序的可容许性AI 解读

Given data with a single dependent variable arising from a normal linear regression model, a variable-selection procedure completely specifies a least squares fit by choosing the subset of the independent variables to include in the model. For loss equal to squared error of prediction, we prove that all variable-selection procedures are admissible for choosing among least-squares fits of the regression model.