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利用倾斜方法评估分类器中各分量的影响AI 解读

Summary Many contemporary classifiers are constructed to provide good performance for very high dimensional data. However, an issue that is at least as important as good classification is determining which of the many potential variables provide key information for good decisions. Responding to this issue can help us to determine which aspects of the datagenerating mechanism (e.g. which genes in a genomic study) are of greatest importance in terms of distinguishing between…

最近邻分类的贝叶斯重新评估AI 解读

The k-nearest-neighbor (knn) procedure is a well-known deterministic method used in supervised classification. This article proposes a reassessment of this approach as a statistical technique derived from a proper probabilistic model; in particular, we modify the assessment found in Holmes and Adams, and evaluated by Manocha and Girolami, where the underlying probabilistic model is not completely well defined. Once provided with a clear probabilistic basis for the knn…

混合分布的完美采样器AI 解读

Summary We consider the construction of perfect samplers for posterior distributions associated with mixtures of exponential families and conjugate priors, starting with a perfect slice sampler in the spirit of Mira and co-workers. The methods rely on a marginalization akin to Rao–Blackwellization and illustrate the duality principle of Diebolt and Robert. A first approximation embeds the finite support distribution on the latent variables within a continuous support…

含缺失值马尔可夫模型中变分似然下界的推断适用性AI 解读

Summary Variational methods have been proposed for obtaining deterministic lower bounds for log-likelihoods within missing data problems, but with little formal justification or investigation of the worth of the lower bound surfaces as tools for inference. We provide, within a general Markovian context, sufficient conditions under which estimators from the variational approximations are asymptotically equivalent to maximum likelihood estimators, and we show empirically, for…

通过可逆跳跃 MCMC 进行隐马尔可夫模型的贝叶斯推断AI 解读

Summary Hidden Markov models form an extension of mixture models which provides a flexible class of models exhibiting dependence and a possibly large degree of variability. We show how reversible jump Markov chain Monte Carlo techniques can be used to estimate the parameters as well as the number of components of a hidden Markov model in a Bayesian framework. We employ a mixture of zero-mean normal distributions as our main example and apply this model to three sets of data…

摘要暂缺

曲线估计中的部分局部平滑规则AI 解读

We compare the performances of local and global rules for smoothing parameter choice, in terms of asymptotic mean squared errors of the resulting estimators. In some instances there is surprisingly little to choose between local and global approaches; our analysis identifies contexts where the differences are small or large. This work motivates development of smoothing rules that form a ‘half-way house’ between local and global smoothing. There, interpolation provides a…

渐近展开启发的插值规则AI 解读

We suggest a simple interpolation rule, based on Edgeworth and Cornish-Fisher expansions, which permits highly accurate numerical approximation in problems involving calculation of distributions or quantiles without requiring explicit calculation of terms in the expansions.

由渐近展开启发的插值规则AI 解读

We suggest a simple interpolation rule, based on Edgeworth and Cornish-Fisher expansions, which permits highly accurate numerical approximation in problems involving calculation of distributions or quantiles without requiring explicit calculation of terms in the expansions.

摘要暂缺

正则化信号恢复中的噪声估计AI 解读

Several estimators of variance are compared in the context of problems where smoothing is incorporated in the estimation of regression functions. Many of the estimators are scaled quadratic forms in the data, and some incorporate steps that try to accommodate substantial nonconstancy in the response function. The estimators are described and an account is provided of an empirical study based on four one-dimensional source functions of varying degrees of irregularity.

摘要暂缺

模拟阶数对 Monte Carlo 检验水平精度与功效的影响AI 解读

SUMMARY We discuss the effect of simulation order on level accuracy and power of Monte Carlo tests, in a very general setting. Both parametric problems, with or without nuisance parameters, and nonparametric problems are treated by a single unifying argument. It is shown that if the level of a Monte Carlo test is known only nominally, not precisely, then the level error of a Monte Carlo test is an order of magnitude less than that of the corresponding asymptotic test. This…

摘要暂缺

《缺失数据问题的递归估计程序》勘误AI 解读

We are grateful to a colleague for pointing out that the asymptotic normality property (4) cannot hold and that its statement is a misquotation from Fabian (1968). Property (4) is not used in the rest of the paper.

有限混合分布的统计分析AI 解读

Statistical Problems. Applications of Finite Mixture Models. Mathematical Aspects of Mixtures. Learning About the Parameters of a Mixture. Learning About the Components of a Mixture. Sequential Problems and Procedures.

回归问题中平滑参数选择技术的共同结构AI 解读

SUMMARY Two general methods have been used for choosing the degree of smoothing in both linear ridge-regression and nonparametric regression. One is based on a criterion of minimum risk and the other is based on a measure of fit to the data as summarised by a statistic based on the residuals. The comparative effects of these two approaches are investigated and one popular version of the second method is shown to oversmooth quite drastically. The work also generates…

图像恢复中的若干平滑技术AI 解读

SUMMARY The problem is considered of restoring a blurred and/or noisy image using various regularization prescriptions. Preliminary work concerns the invertibility of point spread functions and the construction of a stochastic model for images. A simple linear regularization procedure is introduced, as well as the special cases of constrained deconvolution, maximum entropy restoration and least-squares filtering. Optimal choices for the degree of smoothing are obtained for…

统计推断与序贯设计AI 解读

If an experiment is designed sequentially, repeated-sampling inference may not necessarily be made using distributional results that are valid for fixed designs. A few simple illustrative examples and alternative approaches are given. Sometimes the sequential nature of design can be ignored asymptotically. Links are forged with inference for stochastic processes and missing data problems.

利用未分类数据改进混合分布成分密度的非参数估计AI 解读

SUMMARY We present a very simple, utilitarian technique for combining categorized and uncategorized data to construct a nonparametric estimator of a component mixture density. The method can be used for a wide class of estimators, and provides a reduction in the variance compared with the estimator based solely on categorized data.

统计推断与序贯设计AI 解读

If an experiment is designed sequentially, repeated-sampling inference may not necessarily be made using distributional results that are valid for fixed designs. A few simple illustrative examples and alternative approaches are given. Sometimes the sequential nature of design can be ignored asymptotically. Links are forged with inference for stochastic processes and missing data problems.

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…

混合比例的有效非参数估计AI 解读

SUMMARY By constructing a sequence of multinomial approximations and related maximum likelihood estimators, we derive a Cramér-Rao lower bound for nonparametric estimators of the mixture proportions and thereby characterize asymptotically optimal estimators. For the case of the sampling model M2 of Hosmer (1973) it is shown that the sequence of maximum likelihood estimators, which can be obtained explicitly, is asymptotically optimal in this sense. The results hold true even…

利用不完整数据递归估计参数AI 解读

SUMMARY Stochastic approximation procedures are considered for the estimation of parameters using incomplete data. One procedure is stated and illustrated which often leads to asymptotically efficient estimators. Others are developed which, although possibly not optimal in the above sense, will be very much easier to apply. This will be particularly advantageous when quick recursive estimates are required. Examples are given and a link is made between one of the sub-optimal…