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离散程度矩阵与主成分的稳健估计AI 解读

This paper uses Monte Carlo methods to compare the performances of several robust procedures for estimating a correlation matrix and its principal components. The estimators are formed either from separate bivariate analyses or by simultaneous manipulation of all variables by using techniques such as multivariate trimming and M-estimation. The M-estimators stand up exceptionally well. They and the multivariate trimming procedure are especially effective at estimating the…

低响应概率下逻辑回归的样本量计算AI 解读

The Fisher information matrix for the estimated parameters in a multiple logistic regression can be approximated by the augmented Hessian matrix of the moment-generating function for the covariates. The approximation is valid when the probability of response is small. With its use one can obtain a simple closed-form estimate of the asymptotic covariance matrix of the maximum likelihood parameter estimates, and thus approximate sample sizes needed to test hypotheses about the…

摘要暂缺

因子分析模型中的线性预测AI 解读

For the problem of linear prediction in the factor analysis model, the heuristic predictor suggested by Scott (1966) and the unbiased predictor proposed by King (1969) are shown to be mathematically identical respectively with the optimal biased predictor and the optimal unbiased predictor due to Lawley & Maxwell (1973).

分类数据的因子分析AI 解读

Summary The method of factor analysis is widely used as an exploratory tool to reduce the dimensionality of multivariate data. The fact that the standard model is strictly applicable only when the manifest variables are scaled is a serious limitation in social science where the variables are often categorical. In this paper we aim to provide a theoretical framework within which methods for the factor analysis of categorical data can be devised and compared. Discussion is…

小样本因子模型中似然比统计量的解释AI 解读

The use of the likelihood ratio statistic in testing the goodness of fit of the exploratory factor model has no formal justification when, as is often the case in practice, the usual regularity conditions are not met. In a Monte Carlo experiment it is found that the asymptotic theory seems to be appropriate when the regularity conditions obtain and sample size is at least 30. When the regularity conditions are not satisfied, the asymptotic theory seems to be misleading in…

出生人数时间序列模型及其结构解释AI 解读

Saboia (1977) has developed a theory relating a particular type of births autoregressive moving average (ARMA) model to the classical deterministic cohort model of population growth. Reexamination of the data used by Saboia indicates that his estimated births models contain common factors and insignificant coefficients and cannot be regarded as evidence in favor of his argument. It is shown, however, that well-known theory on the relationship between deterministic and…

因子分析模型中的线性预测AI 解读

For the problem of linear prediction in the factor analysis model, the heuristic predictor suggested by Scott (1966) and the unbiased predictor proposed by King (1969) are shown to be mathematically identical respectively with the optimal biased predictor and the optimal unbiased predictor due to Lawley & Maxwell (1973).

协方差结构分析中的约束估计AI 解读

In covarianoe structure analysis, the method of weighted least squares for estimating parameters that are subject to functional constraints is developed. Statistical properties of the estimator are studied and a goodness-of-fit statistic is presented. Based on the penalty function technique, an algorithm is developed. This algorithm is able to produce not only the constrained weighted least squares estimator but also the constrained maximum likelihood estimator, if we choose…

组间主成分比较AI 解读

A method is given for comparing principal component analyses conducted on the same variables in two different groups of individuals, and an extension to the case of more than two groups is outlined. The technique leads to a latent root and vector problem, which has also arisen in the comparison of factor patterns in separate factor analyses. Emphasis in the present article is on the underlying geometry and interpretation of the results. An illustrative example is provided.

历史时间序列的Karhunen–Loève分析：牙买加种植园出生数据应用AI 解读

A comparison of two spectral analysis procedures is presented: the frequency domain (Fourier transform) model and the Karhunen-Loève time domain model. Both models are used in turn to analyze a plantation births series during the period 1880–1938. The principal components model can be adapted as the discrete analogue of the Karhunen-Loève stochastic integral equation in order to decompose a single time series into trend, cycle, and seasonality. The results indicate that the…

正态离散矩阵的贝叶斯推断及其在随机多元回归中的应用AI 解读

Summary This paper discusses Bayesian inference procedures for a normal dispersion matrix. Structural information for the prior mean of the dispersion matrix is incorporated into the analysis through a Normal-Wishart prior distribution. Many of the resulting Bayes estimates are invariant, consistent and asymptotically efficient. Using this procedure, a coherent Bayesian argument for stochastic multiple regression analysis is developed, where dependent and independent…

协方差结构分析中的约束估计AI 解读

In covarianoe structure analysis, the method of weighted least squares for estimating parameters that are subject to functional constraints is developed. Statistical properties of the estimator are studied and a goodness-of-fit statistic is presented. Based on the penalty function technique, an algorithm is developed. This algorithm is able to produce not only the constrained weighted least squares estimator but also the constrained maximum likelihood estimator, if we choose…

典型分析：比较有限离散分布函数的因子分析方法AI 解读

The methods of factor analysis are adapted to the comparison of finite discrete distribution functions. Each element of a finite class of distribution functions is presented in a canonical form in which components differentiating and uniting the functions are easily distinguished and are readily calculated using factor-analysis algorithms. This technique, which we call canonical analysis, has uses in heterogeneity and goodness-of-fit analysis and in the classification of…

典型分析：比较有限离散分布函数的因子分析方法AI 解读

The methods of factor analysis are adapted to the comparison of finite discrete distribution functions. Each element of a finite class of distribution functions is presented in a canonical form in which components differentiating and uniting the functions are easily distinguished and are readily calculated using factor-analysis algorithms. This technique, which we call canonical analysis, has uses in heterogeneity and goodness-of-fit analysis and in the classification of…

一类收缩估计量AI 解读

Summary In this paper we define a class of shrinkage estimators, all of whose members have a mean square error matrix which is less than that of the ordinary least squares estimator by a positive semidefinite matrix if (β-b *)T X T X (β-b *) ≤ σ2. The ridge regression, principal component and minimum conditional mean square error estimators are members of this class.

回归选择策略与显露的先验AI 解读

The computation and selection of constrained regressions may be motivated by prior information and, if so, a regression selection strategy reveals the implicit prior. The selection strategies of principal component regression, stepwise regression, and imposing equality constraints are connected with prior densities which are uniform on spheres, hyperbolas, and cones, respectively. Omitting variables in a predetermined order reveals lexicographic priors.

回归选择策略与揭示的先验AI 解读

The computation and selection of constrained regressions may be motivated by prior information and, if so, a regression selection strategy reveals the implicit prior. The selection strategies of principal component regression, stepwise regression, and imposing equality constraints are connected with prior densities which are uniform on spheres, hyperbolas, and cones, respectively. Omitting variables in a predetermined order reveals lexicographic priors.

约束最小二乘背景下主成分回归的一项最优性质AI 解读

A new optimal property for principal components regression is presented. In particular, it is shown that the trace of the covariance matrix for estimators obtained by deleting principal components associated with the smallest eigenvalues is at least as small as that for any other least-squares estimator with an equal or smaller number of linear restrictions. This property is useful in suggesting data transformations and determining the maximum variance reduction obtainable…

矩阵的加性与乘性模型最小二乘逼近AI 解读

Summary Reduced rank approximation of matrices by Householder–Young methods is shown to be equivalent to fitting of a bilinear (multiplicative) model and to projection onto an optimally chosen subspace. The relation to linear approximation is made evident. Least squares fitting of a mixed linear (additive) and bilinear (multiplicative) model is proved to be a two-stage process: (1) fit the linear part of the model, then take residuals, and (2) fit the bilinear part to the…

计量经济模型的通用计算程序：SHAZAMAI 解读

to prepare and allow a large number of options. The program can be run in batch mode or interactively at a computer terminal. Computer core storage is dynamically allocated so that large problems are only limited by the size of the machine. SHAZAM is designed to grow so that new algorithms and procedures can easily be added by any programmer familiar with the internal structure of the program. Features of SHAZAM include ordinary least squares, two-stage least squares,…

因子分析中一个无偏预测量的讨论AI 解读

For a factor analysis model in which some or all of the independent variables are subject to errors of measurement, Lawley & Maxwell (1973) claim to have obtained an unbiased predictor of the dependent variable based on the independent variables. This predictor is shown to be biased and an alternative unbiased estimator with minimum mean squared error is derived.

通过 EM 算法对不完整数据进行最大似然估计AI 解读

Summary A broadly applicable algorithm for computing maximum likelihood estimates from incomplete data is presented at various levels of generality. Theory showing the monotone behaviour of the likelihood and convergence of the algorithm is derived. Many examples are sketched, including missing value situations, applications to grouped, censored or truncated data, finite mixture models, variance component estimation, hyperparameter estimation, iteratively reweighted least…

回归中的有偏估计：基于均方误差的评价AI 解读

A mean squared error criterion is used to compare five estimators of the coefficients in a linear regression model: least squares, principal components, ridge regression, latent root, and a shrunken estimator. Each of the biased estimators is shown to offer improvement in mean squared error over least squares for a wide range of choices of the parameters of the model. The results of a simulation involving all five estimators indicate that the principal components and latent…