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通过期望传播快速准确地分析二元响应混合模型AI 解读

Expectation propagation is a general prescription for approximation of integrals in statistical inference problems. Its literature is mainly concerned with Bayesian inference scenarios. However, expectation propagation can also be used to approximate integrals arising in frequentist statistical inference. We focus on likelihood-based inference for binary response mixed models and show that fast and accurate quadrature-free inference can be realized for the probit link case…

用马尔可夫链片段近似不完整函数数据AI 解读

We consider curve extension and linear prediction for functional data observed only on a part of their domain, in the form of fragments. We suggest an approach based on a combination of Markov chains and nonparametric smoothing techniques, which enables us to extend the observed fragments and construct approximated prediction intervals around them, construct mean and covariance function estimators, and derive a linear predictor. The procedure is illustrated on real and…

考虑稀释效应的组检测数据非参数方法AI 解读

Group testing methods are used widely to assess the presence of a contaminant, based on measurements of the concentration of a biomarker, for example to test the presence of a disease in pooled blood samples. The test would be perfect if it produced a positive result whenever the contaminant was present, and a negative result otherwise. However, in practice the test is always at least somewhat imperfect, for example because it is sensitive to the proportion of contaminated…

每个外层样本仅用一次内层模拟的双重 Bootstrap 方法AI 解读

We show that, when the double bootstrap is used to improve performance of bootstrap methods for bias correction, techniques based on using a single double-bootstrap sample for each single-bootstrap sample can produce third-order accuracy for much less computational expense than is required by conventional double-bootstrap methods. However, this improved level of performance is not available for the single double-bootstrap methods that have been suggested to construct…

单变量与多变量群组检测数据的非参数及半参数回归新方法AI 解读

We consider nonparametric and semiparametric estimation of a conditional probability curve in the case of group testing data, where the individuals are pooled randomly into groups and only the pooled data are available. We derive a nonparametric weighted estimator that has optimality properties accounting for group sizes, and show how to extend it to multivariate settings, including the partially linear model. In the group testing context, it is natural to assume that the…

简单的分层分类器AI 解读

In this paper we propose simple, general tiered classifiers for relatively complex data. Empirical studies on real and simulated data show that three two-tier classifiers, which are respective extensions of linear discriminant analysis, linear logistic regression and support vector machines, can reduce noticeably the relatively high misclassification error of their original single-tier counterparts, without significantly increasing computational labour.

函数型预测变量的最具预测力设计点AI 解读

We suggest a way of reducing the very high dimension of a functional predictor, X, to a low number of dimensions chosen so as to give the best predictive performance. Specifically, if X is observed on a fine grid of design points t1,…, tr, we propose a method for choosing a small subset of these, say ti1,…, tik, to optimize the prediction of a response variable, Y. The values tij are referred to as the most predictive design points, or covariates, for a given value of k, and…

参数极值的 Bootstrap 置信区间与假设检验AI 解读

The bootstrap provides effective and accurate methodology for a wide variety of statistical problems which might not otherwise enjoy practicable solutions. However, there still exist important problems where standard bootstrap estimators are not consistent, and where alternative approaches, for example the m-out-of-n bootstrap and asymptotic methods, also face significant challenges. One of these is the problem of constructing confidence intervals or hypothesis tests for…

在高维分类器中纳入类别先验概率AI 解读

In standard parametric classifiers, or classifiers based on nonparametric methods but where there is an opportunity for estimating population densities, the prior probabilities of the respective populations play a key role. However, those probabilities are largely ignored in the construction of high-dimensional classifiers, partly because there are no likelihoods to be constructed or Bayes risks to be estimated. Nevertheless, including information about prior probabilities…

高维小样本分类器的尺度调整AI 解读

Distance-based classifiers are generally considered to be effective at discriminating between populations that differ in location. Indeed, nearest-neighbour methods and the support vector machine are frequently used in very high-dimensional problems involving gene expression data, where it is believed that elevated levels of expression convey much of the information for classification. However, one problem inherent to distance-based classifiers is that scale differences can…

降低平滑参数选择中交叉验证的变异性AI 解读

One of the attractions of crossvalidation, as a tool for smoothing-parameter choice, is its applicability to a wide variety of estimator types and contexts. However, its detractors comment adversely on the relatively high variance of crossvalidatory smoothing parameters, noting that this compromises the performance of the estimators in which those parameters are used. We show that the variability can be reduced simply, significantly and reliably by employing bootstrap…

《多元混合模型的非参数推断》勘误AI 解读

The left-hand side of equation (2·8), on p. 671, should read {π 1 (1 − π 1 )}-super-−1/2 (2π 1 − 1) rather than {(1 − π 1 )/π 1 }-super-1/2 (2π 1 − 1). Reflecting this change, the left-hand side of equation (3·1) on the same page should be altered to { π ∧ 1 ( 1 − π ∧ 1 ) } − 1/2 ( 2 π ∧ 1 − 1 ) , and the formula at the foot of p. 677 should be modified to {π 1 (1 − π 1 )}-super-−1/2 (2π 1 − 1) + O p (n-super-−1/2). No other formula is affected, and the left-hand side of…

受试者工作特征曲线的非参数置信区间AI 解读

We study methods for constructing confidence intervals and confidence bands for estimators of receiver operating characteristics. Particular emphasis is placed on the way in which smoothing should be implemented, when estimating either the characteristic itself or its variance. We show that substantial undersmoothing is necessary if coverage properties are not to be impaired. A theoretical analysis of the problem suggests an empirical, plug‐in rule for bandwidth choice,…

高维情形下分布相等性的置换检验AI 解读

Motivated by applications in high‐dimensional settings, we suggest a test of the hypothesis H0 that two sampled distributions are identical. It is assumed that two independent datasets are drawn from the respective populations, which may be very general. In particular, the distributions may be multivariate or infinite‐dimensional, in the latter case representing, for example, the distributions of random functions from one Euclidean space to another. Our test uses a measure…

随机函数分布结构的估计与展示AI 解读

We suggest a nonparametric approach to making inference about the structure of distributions in a potentially infinite‐dimensional space, for example a function space, and displaying information about that structure. It is suggested that the simplest way of presenting the structure is through modes and density ascent lines, the latter being the projections into the sample space of the curves of steepest ascent up the surface of a functional‐data density. Modes are always…

更接近最优值的回归平滑参数AI 解读

Abstract It is well known that data-driven regression smoothing parameters ħ based on cross-validation and related methods exhibit a slow rate of convergence to their optimum. In an earlier article we showed that this rate can be as slow as n –1/10; that is, for a bandwidth ħ 0 optimizing the averaged squared error, n 1/10 (ħ — ħ 0)/ħ 0 tends to an asymptotic normal distribution. In this article we consider mean averaged squared error optimal bandwidths h 0. This (nonrandom)…

接近最优值的回归平滑参数AI 解读

It is well known that data-driven regression smoothing parameters h based on cross-validation and related methods exhibit a slow rate of convergence to their optimum. In an earlier article we showed that this rate can be as slow as n-1/10; that is, for a bandwidth h0 optimizing the averaged squared error, n1/10 (h - h0)/h0 tends to an asymptotic normal distribution. In this article we consider mean averaged squared error optimal bandwidths h0. This (nonrandom) smoothing…

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《基于经验特征函数的正态性检验》的模拟结果更正AI 解读

The last four rows of Table 1 in this paper are in error, due to a mis-set parameter in the simulations. New, extensive simulations show that the empiric characteristic function method, column A, tends to be superior against contaminated normal CN(α,σ2) alternatives when σ2 is small, but tends to be inferior when σ2 is large. We give below corrected versions of the 4th last and 3rd last rows of Table 1, and two new rows which indicate behaviour for smaller values of σ2. The…

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