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高维矩阵值序列的建模与学习AI 解读

We propose a new matrix factor model, named RaDFaM, which is strictly derived based on the general rank decomposition and assumes a structure of a high-dimensional vector factor model for each basis vector. RaDFaM contributes a novel class of low-rank latent structure that makes tradeoff between signal intensity and dimension reduction from the perspective of tensor subspace. Based on the intrinsic separable covariance structure of RaDFaM, for a collection of matrix-valued…

多元二元数据潜变量模型的GEE辅助变量选择AI 解读

Multivariate data are commonly analyzed using one of two approaches: a conditional approach based on generalized linear latent variable models (GLLVMs) or some variation thereof, and a marginal approach based on generalized estimating equations (GEEs). With research on mixed models and GEEs having gone down separate paths, there is a common mindset to treat the two approaches as mutually exclusive, with which to use driven by the question of interest. In this article,…

多元纵向混合模型的稀疏成对似然估计AI 解读

It is becoming increasingly common in longitudinal studies to collect and analyze data on multiple responses. For example, in the social sciences we may be interested in uncovering the factors driving mental health of individuals over time, where mental health is measured using a set of questionnaire items. One approach to analyzing such multi-dimensional data is multivariate mixed models, an extension of the standard univariate mixed model to handle multiple responses.…

利用正则化 PQL 联合选择混合模型效应AI 解读

The application of generalized linear mixed models presents some major challenges for both estimation, due to the intractable marginal likelihood, and model selection, as we usually want to jointly select over both fixed and random effects. We propose to overcome these challenges by combining penalized quasi-likelihood (PQL) estimation with sparsity inducing penalties on the fixed and random coefficients. The resulting approach, referred to as regularized PQL, is a…

组成性支出数据的方向混合效应模型AI 解读

Compositional data are vectors of proportions defined on the unit simplex and this type of constrained data occur frequently in Government surveys. It is also possible for the compositional data to be correlated due to the clustering or grouping of the observations within small domains or areas. We propose a new class of the mixed model for compositional data based on the Kent distribution for directional data, where the random effects also have Kent distributions. One…

幂变换成分数据的稳健主成分分析AI 解读

Geochemical surveys collect sediment or rock samples, measure the concentration of chemical elements, and report these typically either in weight percent or in parts per million (ppm). There are usually a large number of elements measured and the distributions are often skewed, containing many potential outliers. We present a new robust principal component analysis (PCA) method for geochemical survey data, that involves first transforming the compositional data onto a…

利用超球面分布进行成分数据回归AI 解读

Summary Compositional data can be transformed to directional data by the square-root transformation and then modelled by using distributions defined on the hypersphere. One advantage of this approach is that zero components are catered for naturally in the models. The Kent distribution for directional data is a good candidate model because it has a sufficiently general covariance structure. We propose a new regression model which models the mean direction of the Kent…

聚类数据稳健估计的自助推断AI 解读

In mixed models, the use of robust estimates raises several interesting inferential challenges. One of these challenges arises from the realization that the effect of contamination is to increase the variability in the data, but robust estimates of variance components are usually smaller than their nonrobust counterparts. The robust estimates reflect the variability of the bulk of the data, which is not the same as the variability in the data-generating process. This means…

聚类数据的自助法AI 解读

Summary Various bootstraps have been proposed for bootstrapping clustered data from one-way arrays. The simulation results in the literature suggest that some of these methods work quite well in practice; the theoretical results are limited and more mixed in their conclusions. For example, McCullagh reached negative conclusions about the use of non-parametric bootstraps for one-way arrays. The purpose of this paper is to extend our understanding of the issues by discussing…

二项模型的稳健拟合AI 解读

We consider the problem of robust inference for the binomial $(m, \pi)$ model. The discreteness of the data and the fact that the parameter and sample spaces are bounded mean that standard robustness theory gives surprising results. For example, the maximum likelihood estimator (MLE) is quite robust, it cannot be improved on for $m=1$ but can be for $m>1$. We discuss four other classes of estimators: $M$-estimators, minimum disparity estimators, optimal MGP estimators, and a…

Summary A common scenario in finite population inference is that it is possible to find a working superpopulation model which explains the main features of the population but which may not capture all the fine details. In addition, there are often outliers in the population which do not follow the assumed superpopulation model. In situations like these, it is still advantageous to make use of the working model to estimate finite population quantities, provided that we do it…

距离抽样方法论AI 解读

Summary We consider the method of distance sampling described by Buckland, Anderson, Burnham and Laake in 1993. We explore the properties of the methodology in simple cases chosen to allow direct and accessible comparisons of distance sampling in the design- and model-based frameworks. In particular, we obtain expressions for the bias and variance of the distance sampling estimator of object density and for the expected value of the recommended analytic variance estimator…

含离群值抽样调查的偏差校准估计AI 解读

Summary We discuss the problem of estimating finite population parameters on the basis of a sample containing representative outliers. We clarify the motivation for Chambers's bias-calibrated estimator of the population total and show that bias calibration is a key idea in constructing estimators of finite population parameters. We then link the problem of estimating the population total to distribution function or quantile estimation and explore a methodology based on the…

未知连接函数下的自适应估计AI 解读

We consider the fitting of generalized linear models in which the link function is assumed to be unknown, and propose the following computational method: First, estimate regression coefficients using the canonical link. Then, estimate the link via a kernel smoother, treating the direction in the predictor space determined by the regression coefficients as known. Then reestimate the direction using the estimated link and alternate between these two steps. We show that under…

多元 M 估计量的经验鞍点近似AI 解读

SUMMARY In this paper, we investigate the use of the empirical distribution function in place of the underlying distribution function F to construct an empirical saddlepoint approximation to the density fn of a general multivariate M-estimator. We obtain an explicit form for the error term in the approximation, investigate the effect of renormalizing the estimator, carry out some numerical comparisons and discuss the regression problem.

异方差回归模型的拟合AI 解读

In heteroscedastic regression models assumptions about the error distribution determine the method of consistent estimation of parameters. For example, consider the case where the model specifies the regression and dispersion functions for the data but robustness is of concern and one wishes to use least absolute error regressions. Except in certain special circumstances, parameter estimates obtained in this way are inconsistent. In this article we expand the heteroscedastic…

异方差回归模型的拟合AI 解读

In heteroscedastic regression models assumptions about the error distribution determine the method of consistent estimation of parameters. For example, consider the case where the model specifies the regression and dispersion functions for the data but robustness is of concern and one wishes to use least absolute error regressions. Except in certain special circumstances, parameter estimates obtained in this way are inconsistent. In this article we expand the heteroscedastic…

含不可忽略无应答的调查数据对数线性模型AI 解读

SUMMARY We demonstrate the feasibility of constructing, interpreting and fitting computable log-linear models to categorical survey data with arbitrary non-nested patterns of non-ignorable non-response. Under our approach, the non-response probability for each cell of the classification defined by the categories of interest is modelled separately from the classification probability itself, and we adopt a model formulation which allows the non-response model to depend on…

尺度的稳健L估计及其天文学应用AI 解读

In this article, we investigate the robustness properties of a class of L estimators of scale and then develop robust procedures for making inferences about scale. We pay particular attention to trimmed estimators that should perform well when the underlying model is Gaussian. We find that trimmed versions of the efficient linear L estimator for the Gaussian distribution perform better than trimmed standard deviation estimators. We then apply a trimmed version of the…

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M过程与M估计AI 解读

We relate the asymptotic behavior of $M$-estimators of the regression parameter in a linear model in which the dimension of the regression parameter may increase with the sample size to the stochastic equicontinuity of an associated $M$-process. The approach synthesises a number of results for the dimensionally fixed regression model and then extends these results in a direct unified way. The resulting theorems require only mild conditions on the $\psi$-function and the…

多重插补的渐近结果AI 解读

Imputation and multiple-imputation procedures have been used in practice to handle the problem of ignorable nonresponse in sample surveys. We examine the large-sample properties of these procedures where covariates are available for the case when the complete-data analysis is based on least squares. The results provide a formal justification for the inference procedures discussed by Rubin and Schenker for the location problem and suggest new procedures for the regression…

Mallows型有界影响回归修剪均值AI 解读

The influence functions of the regression trimmed-mean estimators proposed by Koenker and Bassett (1978) and Welsh (1987) are bounded in the dependent-variable space but not in the independent-variable space. This article follows the approach of Mallows (1973, 1975) and modifies these estimators so that the resulting estimators have bounded-influence functions. The large-sample behavior of these estimators is studied, and it is shown that they have the same asymptotic…

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