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概率与概率密度非参数估计中的交叉验证AI 解读

We examine large-sample properties of cross-validation for estimating cell probabilities, starting from a completely general measure of loss. Necessary and sufficient conditions on the loss function are derived for the resulting estimator to be consistent, or to minimize expected loss. These results reveal that cross-validation is extremely sensitive to the shape of the loss function. Nevertheless, when the loss function is chosen correctly, cross-validation can be relied on…

最优实验设计的一般微分与拉格朗日理论AI 解读

The problem of optimal experimental design for estimating parameters in linear regression models is placed in a general convex analysis setting. Duality results are obtained using two approaches, one based on subgradients and the other on Lagrangian theory. The subgradient concept is also used to derive a potentially useful equivalence theorm for establishing the optimality of a singular design and, finally, general versions of the original equivalence theorems of Kiefer and…

缺失数据问题的递归估计程序AI 解读

Titterington (1984) proposes recursive methods for dealing with incomplete data. The present paper concentrates on versions of these for multiparameter problems involving missing data. Theorems are outlined from which asymptotic properties of the recursive procedures can be established and versions of the recursions, some of which are particularly easy to use, are written down for problems in which the missing data are missing at random. After illustration with exponential…

混合比例的最小距离非参数估计AI 解读

SUMMARY Hall (1981a) develops a method of estimating mixture proportions using empirical distribution functions and a distance measure. A similar approach is suggested here based on density estimates. The method is applicable to general discrete data and multivariate data as well as to univariate continuous data and to ordered categorical data. For convenient quadratic distance measures the asymptotic theory is developed and remarks are made about practical implementation.…

不完整数据的核密度估计AI 解读

SUMMARY The problem of using non-parametric methods to estimate multivariate density functions from incomplete continuous data does not appear to have been considered before. Methods of producing kernel functions on incomplete observations are suggested involving averaging over the missing variables or substitution of them by simulated values. Consistency of the procedures in terms of integrated mean squared error is investigated and optimal choice of smoothing parameter is…

缺失数据问题的递归估计程序AI 解读

Titterington (1984) proposes recursive methods for dealing with incomplete data. The present paper concentrates on versions of these for multiparameter problems involving missing data. Theorems are outlined from which asymptotic properties of the recursive procedures can be established and versions of the recursions, some of which are particularly easy to use, are written down for problems in which the missing data are missing at random. After illustration with exponential…

不完整多元二元数据的核方法分析AI 解读

The procedure, due to Aitchison & Aitken (1976), of analyzing multivariate binary data by kernel methods is extended to deal with missing data problems. The performance of the techniques is discussed for univariate, bivariate and for specific multivariate data. Comparisons are drawn with other approaches.

对角线缺失列联表中最大似然估计的迭代方法比较AI 解读

This paper considers maximum likelihood estimation for the parameters of quasiindepen-dence in a contingency table with a miiming or excluded diagonal. Two of the methods discussed derive from the em algorithm of Dempster, Laird & Rubin (1977), the other two methods being Newton-Raphson and iterative scaling. Iterative scaling is found, empirically, to be the least efficient method.

This paper considers maximum likelihood estimation for the parameters of quasiindepen-dence in a contingency table with a miiming or excluded diagonal. Two of the methods discussed derive from the em algorithm of Dempster, Laird & Rubin (1977), the other two methods being Newton-Raphson and iterative scaling. Iterative scaling is found, empirically, to be the least efficient method.

利用核方法分析不完整多元二元数据AI 解读

The procedure, due to Aitchison & Aitken (1976), of analyzing multivariate binary data by kernel methods is extended to deal with missing data problems. The performance of the techniques is discussed for univariate, bivariate and for specific multivariate data. Comparisons are drawn with other approaches.