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相依删失下边际比例风险回归的似然方法AI 解读

In many public health problems, an important goal is to identify the effect of some treatment/intervention on the risk of failure for the whole population. A marginal proportional hazards regression model is often used to analyze such an effect. When dependent censoring is explained by many auxiliary covariates, we utilize two working models to condense high-dimensional covariates to achieve dimension reduction. Then the estimator of the treatment effect is obtained by…

通过交叉验证选择似然权重AI 解读

The (relevance) weighted likelihood was introduced to formally embrace a variety of statistical procedures that trade bias for precision. Unlike its classical counterpart, the weighted likelihood combines all relevant information while inheriting many of its desirable features including good asymptotic properties. However, in order to be effective, the weights involved in its construction need to be judiciously chosen. Choosing those weights is the subject of this article in…

广义函数型线性模型AI 解读

We propose a generalized functional linear regression model for a regression situation where the response variable is a scalar and the predictor is a random function. A linear predictor is obtained by forming the scalar product of the predictor function with a smooth parameter function, and the expected value of the response is related to this linear predictor via a link function. If, in addition, a variance function is specified, this leads to a functional estimating…

基于尖峰—平板先验的变量选择：频率学派与贝叶斯策略AI 解读

Variable selection in the linear regression model takes many apparent faces from both frequentist and Bayesian standpoints. In this paper we introduce a variable selection method referred to as a rescaled spike and slab model. We study the importance of prior hierarchical specifications and draw connections to frequentist generalized ridge regression estimation. Specifically, we study the usefulness of continuous bimodal priors to model hypervariance parameters, and the…

流形上的不变贝叶斯估计AI 解读

A frequent and well-founded criticism of the maximum a posteriori (MAP) and minimum mean squared error (MMSE) estimates of a continuous parameter γ taking values in a differentiable manifold Γ is that they are not invariant to arbitrary “reparameterizations” of Γ. This paper clarifies the issues surrounding this problem, by pointing out the difference between coordinate invariance, which is a sine qua non for a mathematically well-defined problem, and diffeomorphism…

高斯过程的默认先验AI 解读

Motivated by the statistical evaluation of complex computer models, we deal with the issue of objective prior specification for the parameters of Gaussian processes. In particular, we derive the Jeffreys-rule, independence Jeffreys and reference priors for this situation, and prove that the resulting posterior distributions are proper under a quite general set of conditions. A proper flat prior strategy, based on maximum likelihood estimates, is also considered, and all…

总体分位数的迭代平滑自助法置信区间AI 解读

This paper investigates the effects of smoothed bootstrap iterations on coverage probabilities of smoothed bootstrap and bootstrap-t confidence intervals for population quantiles, and establishes the optimal kernel bandwidths at various stages of the smoothing procedures. The conventional smoothed bootstrap and bootstrap-t methods have been known to yield one-sided coverage errors of orders O(n−1/2) and o(n−2/3), respectively, for intervals based on the sample quantile of a…

估计方程的广义自助法AI 解读

We introduce a generalized bootstrap technique for estimators obtained by solving estimating equations. Some special cases of this generalized bootstrap are the classical bootstrap of Efron, the delete-d jackknife and variations of the Bayesian bootstrap. The use of the proposed technique is discussed in some examples. Distributional consistency of the method is established and an asymptotic representation of the resampling variance estimator is obtained.

深度加权散布矩阵估计量AI 解读

General depth weighted scatter estimators are introduced and investigated. For general depth functions, we find out that these affine equivariant scatter estimators are Fisher consistent and unbiased for a wide range of multivariate distributions, and show that the sample scatter estimators are strong and $\sqrt{n}$-consistent and asymptotically normal, and the influence functions of the estimators exist and are bounded in general. We then concentrate on a specific case of…

半参数模型中 Banach 参数的有效估计AI 解读

Consider a semiparametric model with a Euclidean parameter and an infinite-dimensional parameter, to be called a Banach parameter. Assume: (a) There exists an efficient estimator of the Euclidean parameter. (b) When the value of the Euclidean parameter is known, there exists an estimator of the Banach parameter, which depends on this value and is efficient within this restricted model. Substituting the efficient estimator of the Euclidean parameter for the value of this…

非参数分类中的带宽选择AI 解读

It is shown that, for kernel-based classification with univariate distributions and two populations, optimal bandwidth choice has a dichotomous character. If the two densities cross at just one point, where their curvatures have the same signs, then minimum Bayes risk is achieved using bandwidths which are an order of magnitude larger than those which minimize pointwise estimation error. On the other hand, if the curvature signs are different, or if there are multiple…

半参数部分线性变系数模型的有效估计AI 解读

In this paper we propose a general series method to estimate a semiparametric partially linear varying coefficient model. We establish the consistency and $\sqrt{n}$-normality property of the estimator of the finite-dimensional parameters of the model. We further show that, when the error is conditionally homoskedastic, this estimator is semiparametrically efficient in the sense that the inverse of the asymptotic variance of the estimator of the finite-dimensional parameter…

高斯向量均值的凸假设检验及回归函数定性假设的应用AI 解读

In this paper we propose a general methodology, based on multiple testing, for testing that the mean of a Gaussian vector in ℝn belongs to a convex set. We show that the test achieves its nominal level, and characterize a class of vectors over which the tests achieve a prescribed power. In the functional regression model this general methodology is applied to test some qualitative hypotheses on the regression function. For example, we test that the regression function is…

收缩邻域上的非参数估计：超效率与自适应AI 解读

A theory of superefficiency and adaptation is developed under flexible performance measures which give a multiresolution view of risk and bridge the gap between pointwise and global estimation. This theory provides a useful benchmark for the evaluation of spatially adaptive estimators and shows that the possible degree of superefficiency for minimax rate optimal estimators critically depends on the size of the neighborhood over which the risk is measured. Wavelet procedures…

通过置信分布合并独立来源的信息AI 解读

This paper develops new methodology, together with related theories, for combining information from independent studies through confidence distributions. A formal definition of a confidence distribution and its asymptotic counterpart (i.e., asymptotic confidence distribution) are given and illustrated in the context of combining information. Two general combination methods are developed: the first along the lines of combining p-values, with some notable differences in regard…

具有阈值化性质的极小极大估计及其小波分析应用AI 解读

Many statistical practices involve choosing between a full model and reduced models where some coefficients are reduced to zero. Data were used to select a model with estimated coefficients. Is it possible to do so and still come up with an estimator always better than the traditional estimator based on the full model? The James–Stein estimator is such an estimator, having a property called minimaxity. However, the estimator considers only one reduced model, namely the…

一般经验贝叶斯小波方法与精确自适应极小极大估计AI 解读

In many statistical problems, stochastic signals can be represented as a sequence of noisy wavelet coefficients. In this paper, we develop general empirical Bayes methods for the estimation of true signal. Our estimators approximate certain oracle separable rules and achieve adaptation to ideal risks and exact minimax risks in broad collections of classes of signals. In particular, our estimators are uniformly adaptive to the minimum risk of separable estimators and the…

一种稳健的聚类分析方法AI 解读

Let there be given a contaminated list of n ℝd-valued observations coming from g different, normally distributed populations with a common covariance matrix. We compute the ML-estimator with respect to a certain statistical model with n−r outliers for the parameters of the g populations; it detects outliers and simultaneously partitions their complement into g clusters. It turns out that the estimator unites both the minimum-covariance-determinant rejection method and the…

无矩条件下 Student t 统计量的鞍点近似AI 解读

A saddlepoint approximation of the Student’s t-statistic was derived by Daniels and Young [Biometrika 78 (1991) 169–179] under the very stringent exponential moment condition that requires that the underlying density function go down at least as fast as a Normal density in the tails. This is a severe restriction on the approximation’s applicability. In this paper we show that this strong exponential moment restriction can be completely dispensed with, that is, saddlepoint…

椭圆分布 VARMA 模型适合性的秩最优检验AI 解读

We are deriving optimal rank-based tests for the adequacy of a vector autoregressive-moving average (VARMA) model with elliptically contoured innovation density. These tests are based on the ranks of pseudo-Mahalanobis distances and on normed residuals computed from Tyler’s [Ann. Statist. 15 (1987) 234–251] scatter matrix; they generalize the univariate signed rank procedures proposed by Hallin and Puri [J. Multivariate Anal. 39 (1991) 1–29]. Two types of optimality…

利用多步多尺度自助重抽样构造区域的近似无偏检验AI 解读

Approximately unbiased tests based on bootstrap probabilities are considered for the exponential family of distributions with unknown expectation parameter vector, where the null hypothesis is represented as an arbitrary-shaped region with smooth boundaries. This problem has been discussed previously in Efron and Tibshirani [Ann. Statist. 26 (1998) 1687–1718], and a corrected p-value with second-order asymptotic accuracy is calculated by the two-level bootstrap of Efron,…

贝叶斯动机的函数拟合检验及其渐近频率学性质AI 解读

We propose and analyze nonparametric tests of the null hypothesis that a function belongs to a specified parametric family. The tests are based on BIC approximations, πBIC, to the posterior probability of the null model, and may be carried out in either Bayesian or frequentist fashion. We obtain results on the asymptotic distribution of πBIC under both the null hypothesis and local alternatives. One version of πBIC, call it π*BIC, uses a class of models that are orthogonal…

含 Berkson 型测量误差的非线性模型估计AI 解读

This paper is concerned with general nonlinear regression models where the predictor variables are subject to Berkson-type measurement errors. The measurement errors are assumed to have a general parametric distribution, which is not necessarily normal. In addition, the distribution of the random error in the regression equation is nonparametric. A minimum distance estimator is proposed, which is based on the first two conditional moments of the response variable given the…

有序单因素设计中基于惩罚基的混合收缩估计AI 解读

This paper constructs improved estimators of the means in the Gaussian saturated one-way layout with an ordinal factor. The least squares estimator for the mean vector in this saturated model is usually inadmissible. The hybrid shrinkage estimators of this paper exploit the possibility of slow variation in the dependence of the means on the ordered factor levels but do not assume it and respond well to faster variation if present. To motivate the development, candidate…