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用于充分降维的协变量信息矩阵AI 解读

Building upon recent research on the applications of the density information matrix, we develop a tool for sufficient dimension reduction (SDR) in regression problems called covariate information matrix (CIM). CIM exhaustively identifies the central subspace (CS) and provides a rank ordering of the reduced covariates in terms of their regression information. Compared to other popular SDR methods, CIM does not require distributional assumptions on the covariates, or…

二次距离拟合优度检验的核、自由度与功效性质AI 解读

In this article, we study the power properties of quadratic-distance-based goodness-of-fit tests.First, we introduce the concept of a root kernel and discuss the considerations that enter the selection of this kernel.We derive an easy to use normal approximation to the power of quadratic distance goodness-of-fit tests and base the construction of a noncentrality index, an analogue of the traditional noncentrality parameter, on it.This leads to a method akin to the…

随机缺失相关数据的高效聚合无偏估计函数方法AI 解读

We develop a consistent and highly efficient marginal model for missing at random data using an estimating function approach. Our approach differs from inverse weighted estimating equations (Robins, Rotnitzky, and Zhao 1995) and the imputation method (Paik 1997) in that our approach does not require estimating the probability of missing or imputing the missing response based on assumed models. The proposed method is based on an aggregate unbiased estimating function…

参数多项分布模型的半参数容忍区域：构建与应用AI 解读

We introduce a semiparametric “tubular neighborhood” of a parametric model in the multinomial setting. It consists of all multinomial distributions lying in a distance-based neighborhood of the parametric model of interest. Fitting such a tubular model allows one to use a parametric model while treating it as an approximation to the true distribution. In this paper, the Kullback–Leibler distance is used to build the tubular region. Based on this idea one can define the…

基于最高后验密度的贝叶斯混合模型标签确定AI 解读

A fundamental problem for Bayesian mixture model analysis is label switching, which occurs as a result of the nonidentifiability of the mixture components under symmetric priors. We propose two labeling methods to solve this problem. The first method, denoted by PM(ALG), is based on the posterior modes and an ascending algorithm generically denoted ALG. We use each Markov chain Monte Carlo sample as the starting point in an ascending algorithm, and label the sample based on…

概率分布二次距离的统一基础AI 解读

This work builds a unified framework for the study of quadratic form distance measures as they are used in assessing the goodness of fit of models. Many important procedures have this structure, but the theory for these methods is dispersed and incomplete. Central to the statistical analysis of these distances is the spectral decomposition of the kernel that generates the distance. We show how this determines the limiting distribution of natural goodness-of-fit tests.…

高维模型选择：基于二次风险的方法AI 解读

Summary We propose a general class of risk measures which can be used for data-based evaluation of parametric models. The loss function is defined as the generalized quadratic distance between the true density and the model proposed. These distances are characterized by a simple quadratic form structure that is adaptable through the choice of a non-negative definite kernel and a bandwidth parameter. Using asymptotic results for the quadratic distances we build a…

总体类别数量的估计AI 解读

Estimating the unknown number of classes in a population has numerous important applications. In a Poisson mixture model, the problem is reduced to estimating the odds that a class is undetected in a sample. The discontinuity of the odds prevents the existence of locally unbiased and informative estimators and restricts confidence intervals to be one-sided. Confidence intervals for the number of classes are also necessarily one-sided. A sequence of lower bounds to the odds…

多元正态混合分布的地形结构AI 解读

Multivariate normal mixtures provide a flexible method of fitting high-dimensional data. It is shown that their topography, in the sense of their key features as a density, can be analyzed rigorously in lower dimensions by use of a ridgeline manifold that contains all critical points, as well as the ridges of the density. A plot of the elevations on the ridgeline shows the key features of the mixed density. In addition, by use of the ridgeline, we uncover a function that…

矩形阵列渐近框架下投影得分方法的效率AI 解读

Summary The paper considers a rectangular array asymptotic embedding for multistratum data sets, in which both the number of strata and the number of within-stratum replications increase, and at the same rate. It is shown that under this embedding the maximum likelihood estimator is consistent but not efficient owing to a non-zero mean in its asymptotic normal distribution. By using a projection operator on the score function, an adjusted maximum likelihood estimator can be…

协方差逆矩阵难以估计时的自适应估计方程AI 解读

Summary To construct an optimal estimating function by weighting a set of score functions, we must either know or estimate consistently the covariance matrix for the individual scores. In problems with high dimensional correlated data the estimated covariance matrix could be unreliable. The smallest eigenvalues of the covariance matrix will be the most important for weighting the estimating equations, but in high dimensions these will be poorly determined. Generalized…

渐近推断的几何基础AI 解读

Overview and Preliminaries. ONE-PARAMETER CURVED EXPONENTIAL FAMILIES. First-Order Asymptotics. Second-Order Asymptotics. MULTIPARAMETER CURVED EXPONENTIAL FAMILIES. Extensions of Results from the One-Parameter Case. Exponential Family Regression and Diagnostics. Curvature in Exponential Family Regression. DIFFERENTIAL-GEOMETRIC METHODS. Information-Metric Riemannian Geometry. Statistical Manifolds. Divergence Functions. Recent Developments. Appendices. References. Indexes.

结合自助法根搜索的加权似然方程AI 解读

We discuss a method of weighting likelihood equations with the aim of obtaining fully efficient and robust estimators. We discuss the case of continuous probability models using unimodal weighting functions. These weighting functions downweight observations that are inconsistent with the assumed model. At the true model, therefore, the proposed estimating equations behave like the ordinary likelihood equations. We investigate the number of solutions of the estimating…

观测 Fisher 信息的二阶最优性AI 解读

The realized error of an estimate is determined not only by the efficiency of the estimator, but also by chance. For example, suppose that we have observed a bivariate normal vector whose expectation is known to be on a circle. Then, intuitively, the longer that vector happens to be, the more accurately its angle is likely to be estimated. Yet this chance, though its information is contained in the data, cannot be accounted for by the variance of the estimate. One way to…

协变量含误差的病例对照研究：半参数混合方法AI 解读

Methods are devised for estimating the parameters of a prospective logistic model in a case-control study with dichotomous response D that depends on a covariate X. For a portion of the sample, both the gold standard X and a surrogate covariate W are available; however, for the greater portion of the data, only the surrogate covariate W is available. By using a mixture model, the relationship between the true covariate and the response can be modeled appropriately for both…

SUMMARY A simple method for approximate conditional inference is described. The methodology is applied to natural exponential family models where it is shown to provide accurate approximations to fully conditional estimates. The approximation technique can be applied much more generally than in this particular class of models. The technique depends only on the construction of certain 'projected scores' derived from higher order likelihood derivatives and their covariances…

多元正态混合：快速且一致的矩估计方法AI 解读

A longstanding difficulty in multivariate statistics is identifying and evaluating nonnormal data structures in high dimensions with high statistical efficiency and low search effort. Here the possibilities of using sample moments to identify mixtures of multivariate normals are investigated. A particular system of moment equations is devised and then shown to be one that identifies the true mixing distribution, with some limitations (indicated in the text), and thus…

混合模型的残差诊断AI 解读

A sample is commonly modeled by a mixture distribution if the observations follow a common distribution, but the parameter of interest differs between observations. For example, we observe the lengths but not the ages of a sample offish. It may be reasonable to assume that length is normally distributed about an unknown mean that depends on the age of the fish. Provided there is more than one age class in the sample, then the data are distributed as a mixture of normals. In…

矩阵矩及其在混合分布估计中的应用AI 解读

The use of moment matrices and their determinants are shown to elucidate the structure of mixture estimation as carried out using the method of moments. The setting is the estimation of a discrete finite support point mixing distribution. In the important class of quadratic variance exponential families it is shown for any sample there is an integer $\hat{\nu}$ depending on the data which represents the maximal number of support points that one can put in the estimated…

整数参数模型的统一处理AI 解读

It is shown that there is an analog to the score function (the derivative of the log-likelihood with respect to the parameter), here called the difference score, which plays an important theoretical role in integer parameter models. A unified treatment of integer parameter models can be obtained by recognizing that many commonly used models have a linear difference score (LDS). It is established that many of the exact results available for exponential family models also hold…

整数参数模型的统一处理AI 解读

It is shown that there is an analog to the score function (the derivative of the log-likelihood with respect to the parameter), here called the difference score, which plays an important theoretical role in integer parameter models. A unified treatment of integer parameter models can be obtained by recognizing that many commonly used models have a linear difference score (LDS). It is established that many of the exact results available for exponential family models also hold…

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.

指数族混合模型与最小二乘估计量AI 解读

For an arbitrary one parameter exponential family density it is shown how to construct a mixing distribution (prior) on the parameter in such a way that the resulting mixture distribution is a two (or more) parameter exponential family. Reweighted infinitely divisible distributions are shown to be the parametric mixing distributions for which this occurs. As an illustration conditions are given under which a parametric mixture of negative exponentials is in the exponential…

检验误差：有限总体中整数参数的极大似然估计AI 解读

In a probability model for possible errors in the inspection of a finite lot containing defective items, it is shown how maximum likelihood estimation is affected by whether the sampling is carried out with or without replacement. These changes are examined by developing a method for simultaneous maximization over an integer and a scalar parameter. A new method for the bounding of the integer solution is introduced. The results show that the parameter estimates in the…