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共同主成分及相关多元模型
Preliminaries principal component analysis relationships between matrices common practical components proportional covariance matrices partial common components and common space analysis how different are several covariance matrices? numerical methods. Appendices: spectral decomposition of symmetric matrices some results from matrix algebra a fortran program for the fg algorithm.
广义线性回归的主成分估计
The generalized linear model (Nelder & Wedderburn, 1972) has become an elegant and practical option to classical least-squares linear model building. We consider the specific problem of generalized linear regression utilizing a set of continuous explanatory variables to model an exponential family response. It is the objective of this paper to develop and present an asymptotically biased principal component parameter estimation technique, as an option to traditional maximum…
多元时间序列谱密度矩阵相关统计量的分布渐近展开及应用
Let { X ( t )} be a multivariate Gaussian stationary process with the spectral density matrix f 0 (ω), where θ is an unknown parameter vector. Using a quasi-maximum likelihood estimator θ̂ of θ, we estimate the spectral density matrix f 0 (ω) by f θ̂ (ω). Then we derive asymptotic expansions of the distributions of functions of f θ̂ (ω). Also asymptotic expansions for the distributions of functions of the eigenvalues of f θ̂ (ω) are given. These results can be applied to…
连续谱回归：以交叉验证统一最小二乘、偏最小二乘与主成分回归
SUMMARY The paper addresses the evergreen problem of construction of regressors for use in least squares multiple regression. In the context of a general sequential procedure for doing this, it is shown that, with a particular objective criterion for the construction, the procedures of ordinary least squares and principal components regression occupy the opposite ends of a continuous spectrum, with partial least squares lying in between. There are two adjustable ‘parameters’…
非加性多维分类数据的分析
This article considers the problems of testing additivity and estimating σ2 in unreplicated multiway classifications. To model nonadditivity and jointly estimate σ2, the interaction parameter space must be restricted; otherwise the model is saturated. The parameterization we use is a multiway extension of the two-way multiplicative interaction model of Mandel (1971) and Johnson and Graybill (1972a). For example, in a three-way classification, we model interaction as θijk =…
稳定美国癌症死亡率地图的经验贝叶斯方法
"The geographic mapping of age-standardized, cause-specific death rates is a powerful tool for identifying possible etiologic factors, because the spatial distribution of mortality risks can be examined for correlations with the spatial distribution of disease-specific risk factors. This article presents a two-stage empirical Bayes procedure for calculating age-standardized cancer death rates, for use in mapping, which are adjusted for the stochasticity of rates in small…
由共享脆弱性诱导的二元生存模型
When two observed survival times depend via a proportional-hazards model on the same unobserved variable, called a frailty, this common dependence induces an association between the observed times. This article considers the class of bivariate survival distributions that can arise in this way, extends it to allow negative association, and shows that the observable bivariate distribution determines the unobserved frailty distribution up to a scale parameter. A cross-ratio…
线性因子模型检验中的实验设计
For various reasons, cross-sectional tests of linear factor models have employed the returns on portfolios of assets (as opposed to individual securities). There is a good deal of flexibility in how one goes about choosing which portfolios to examine (the experimental design). This article points out that some choices can lead to collinearity among factor loadings with potentially harmful consequences for power. A diagnostic procedure for detecting collinearity is discussed,…
汇率波动的动态：多变量潜在因子 ARCH 模型
Abstract We study temporal volatility patterns in seven nominal dollar spot exchange rates, all of which display strong evidence of autoregressive conditional heteroskedasticity (ARCH). We first formulate and estimate univariate models, the results of which are subsequently used to guide specification of a multivariate model. The key element of our multivariate approach is exploitation of factor structure, which facilitates tractable estimation via a substantial reduction in…
两组中的共同主成分子空间
E. Keramidas has brought to my attention some related work by Keramidas, Devlin & Gnanadesikan (1987), who compared principal components of several covariance matrices by using a graphical procedure.
通过广义判别分析构建树形分类器
The problem of constructing classification rules that can be represented as decision trees is considered. Each object to be classified has an associated x vector containing possibly incomplete covariate information. Tree construction is based on the information provided in a “learning sample” of objects with known class identities. The x vectors in the learning sample may have missing values as well. Procedures are proposed for each of the components of classifier…
通过广义判别分析构造树形分类规则
The problem of constructing classification rules that can be represented as decision trees is considered. Each object to be classified has an associated x vector containing possibly incomplete covariate information. Tree construction is based on the information provided in a “learning sample” of objects with known class identities. The x vectors in the learning sample may have missing values as well. Procedures are proposed for each of the components of classifier…
一般条件下因子分析估计量的渐近正态分布
Asymptotic properties of estimators for the confirmatory factor analysis model are discussed. The model is identified by restrictions on the elements of the factor loading matrix; the number of restrictions may exceed that required for identification. It is shown that a particular centering of the maximum likelihood estimator derived under assumed normality of observations yields an asymptotic normal distribution that is common to a wide class of distributions of the factor…
两组数据的共同主成分子空间
One important practical application of principal component analysis is to reduce a large number of variables, say p, to a smaller number, m, by making use of the first m principal components. This technique can easily be extended to two or more groups if the subspaces spanned by the first m principal components are the same for all groups. In this paper we develop an approximate procedure for testing such a hypothesis of common subspaces when two groups are involved. The…
By replacing the unknown random factors of factor analysis with observed macroeconomic variables, the arbitrage pricing theory (APT) is recast as a multivariate nonlinear regression model with across-equation restrictions. An explicit theoretical justification for the inclusion of an arbitrary, well-diversified market index is given. Using monthly returns on 70 stocks, iterated nonlinear seemingly unrelated regression techniques are employed to obtain joint estimates of…
Recent papers in financial research focus on identifying a stable factor structure for security returns. The likelihood ratio test typically is used to determine the number of factors from exploratory factor analysis models. In this article, we consider the use of cross-validation to identify a stable factor structure in security returns. When applied to actual stock-return data, cross-validation identifies a smaller number of stable factors than the likelihood ratio test.…
多元分类数据的加权最小二乘对应分析
A generalization of correspondence analysis to multivariate categorical data is proposed, where all two-way contingency tables of a set of categorical variables are simultaneously fitted by weighted least-squares. An alternating least-squares algorithm is developed to perform the fitting. This technique has a number of advantages over the usual generalization known as multiple correspondence analysis. It is also an analogue of least-squares factor analysis for categorical…
两个组的共同主成分子空间
One important practical application of principal component analysis is to reduce a large number of variables, say p, to a smaller number, m, by making use of the first m principal components. This technique can easily be extended to two or more groups if the subspaces spanned by the first m principal components are the same for all groups. In this paper we develop an approximate procedure for testing such a hypothesis of common subspaces when two groups are involved. The…