A comparative study for robust canonical correlation methods

The aim of this study is to obtain robust canonical vectors and correlation coefficients based on the percentage bend correlation and winsorized correlation in the correlation matrix and fast consistent high breakdown (FCH), reweighted fast consistent high breakdown (RFCH), and reweighted multivariate normal (RMVN) estimators to estimate the covariance matrix and then compare these estimators with the existing estimators. In the correlation matrix of canonical correlation analysis (CCA), we present an approach that substitutes the percentage bend correlation and the winsorized correlation in place of the widely employed the Pearson correlation. Moreover, we employ the FCH, RFCH, and RMVN estimators to estimate the covariance matrix in the CCA. We conduct a simulation study and employ real data with the objective of comparing the performance of the different estimators for canonical vectors and correlation with that of our proposed approaches. The breakdown plots and independent tests are employed as differentiating criteria of the robustness and performance of the estimators. Based on our computational and real data studies, we propose suggestions and guidelines on the practical implications of our findings.     

Hierarchical clustering of variables: a comparison among strategies of analysis

In this paper some hierarchical methods for identifying groups of variables are illustrated and compared. It is shown that the use of multivariate association measures between two sets of variables can overcome the drawbacks of the usually employed bivariate correlation coefficient, but the resulting methods are generally not monotonic. Thus a new multivariate association measure is proposed, based on the links existing between canonical correlation analysis and principal component analysis, which can be more suitably used for the purpose at hand. The hierarchical method based on the suggested measure is illustrated and compared with other possible solutions by analysing simulated and real data sets. Finally an extension of the suggested method to the more general situation of mixed (qualitative and quantitative) variables is proposed and theoretically discussed.     

Canonical Correlation Analysis Through Linear Modeling

In this paper, we introduce linear modeling of canonical correlation analysis, which estimates canonical direction matrices by minimising a quadratic objective function. The linear modeling results in a class of estimators of canonical direction matrices, and an optimal class is derived in the sense described herein. The optimal class guarantees several of the following desirable advantages: first, its estimates of canonical direction matrices are asymptotically efficient; second, its test statistic for determining the number of canonical covariates always has a chi‐squared distribution asymptotically; third, it is straight forward to construct tests for variable selection. The standard canonical correlation analysis and other existing methods turn out to be suboptimal members of the class. Finally, we study the role of canonical variates as a means of dimension reduction for predictors and responses in multivariate regression. Numerical studies and data analysis are presented.     

A new alternative to the standard F test for clustered data

The data collection process and the inherent population structure are the main causes for clustered data. The observations in a given cluster are correlated, and the magnitude of such correlation is often measured by the intra-cluster correlation coefficient. The intra-cluster correlation can lead to an inflated size of the standard F test in a linear model. In this paper, we propose a solution to this problem. Unlike previous adjustments, our method does not require estimation of the intra-class correlation, which is problematic especially when the number of clusters is small. Our simulation results show that the new method outperforms the existing methods.     

Using restricted CCA for cross-language information retrieval

Canonical correlation analysis is a method of correlating linear relationship between two sets of variables. When not any linear combination of variables is allowed, restricted canonical correlation analysis is appropriate. The method was implemented with alternating least-squares and applied to the cross-language information retrieval on a dataset with officially translated and aligned documents in eight European languages.     

典型相关分析的延拓研究

在典型相关分析中,求得典型相关变量的表达式并没有全部完成任务,例如需要确定典型相关变量的个数和变量选择。针对典型相关变量的个数问题,发现了常用的卡方检验和冗余分析方法的不足,进而提出了一种新的算法。针对原始变量的选择问题,提出了三种可能的路径。最后利用人体尺寸数据对相关结论进行了验证。     

Assessing conditional independence for log-linear poisson models with random effects

In the context of regression rnodels with random effects, repeated response are traditionally assumed to be mutually independent conditional on the random effects. In order to asseess the validity of such an assumption and its impact on parameter inference, we propose an estimating equation methodology where both random eifects and within-subject correlation are modeled. This fllows a subsequent analysis on the statistical sianificance of the conditional correlation. We illustrate this method with the epilepsy data of Thall and Vail (1990), and find our method useh in a proper representation for khe random effect modeling.     

An Approach of Stocks Substitution Strategy Using Fuzzy Interval Correlation Coefficient

The classical Pearson's correlation coefficient has been widely adopted in various fields of application. However, when the data are composed of fuzzy interval values, it is not feasible to use such a traditional approach to evaluate the correlation coefficient. In this study, we propose the specific calculation of fuzzy interval correlation coefficient with fuzzy interval data to measure the relationship between various stocks. As such, the study is able to offer an improving measure of investment strategy for stocks substitution via the analysis of the fuzzy interval correlation. In addition, we use empirical studies to verify the validity of our proposal on fuzzy interval correlation coefficient using data from companies in electric machinery and plastic sectors in Taiwan.     

Optimal model averaging estimation for correlation structure in generalized estimating equations

Longitudinal data analysis requires a proper estimation of the within-cluster correlation structure in order to achieve efficient estimates of the regression parameters. When applying likelihood-based methods one may select an optimal correlation structure by the AIC or BIC. However, such information criteria are not applicable for estimating equation based approaches. In this paper we develop a model averaging approach to estimate the correlation matrix by a weighted sum of a group of patterned correlation matrices under the GEE framework. The optimal weight is determined by minimizing the difference between the weighted sum and a consistent yet inefficient estimator of the correlation structure. The computation of our proposed approach only involves a standard quadratic programming on top of the standard GEE procedure and can be easily implemented in practice. We provide theoretical justifications and extensive numerical simulations to support the application of the proposed estimator. A couple of well-known longitudinal data sets are revisited where we implement and illustrate our methodology.     

Using Lasso RCCA for cross-language information retrieval

ABSTRACT

Restricted canonical correlation analysis and the lasso shrinkage method were paired together for canonical correlation analysis with non-negativity restrictions on datasets, where a sample size is much smaller than the number of variables. The method was implemented in an alternating least-squares algorithm and applied to cross-language information retrieval on a dataset with aligned documents in eight languages. A set of experiments was ran to evaluate the method and compare it to other methods in the field.     

On the correlation between f-ratios

The coefficient of correlation between noncentral F-ratios sharing a common denominator is given. The correlation between doubly dependent F-ratios is shown to be the correlation between singly dependent F-ratios times a function of the correlation between the F-ratios' numerators. The correlation is positive if at least one of the noncentrality parameters is zero, but may be zero or negative if both noncentrality parameters are positive. These relationships are viewed geometrically. Examples are taken from the NOVA in the unequal-cell-sizes case.     

Stress testing correlation matrix: a maximum empirical likelihood approach

ABSTRACT

Stress testing correlation matrix is a challenging exercise for portfolio risk management. Most existing methods directly modify the estimated correlation matrix to satisfy stress conditions while maintaining positive semidefiniteness. The focus lies on technical optimization issues but the resultant stressed correlation matrices usually lack statistical interpretations. In this article, we suggest a novel approach using Empirical Likelihood method to modify the probability weights of sample observations to construct a stressed correlation matrix. The resultant correlations correspond to a stress scenario that is nearest to the observed scenario in a Kullback–Leibler divergence sense. Besides providing a clearer statistical interpretation, the proposed method is non-parametric in distribution, simple in computation and free from subjective tunings. We illustrate the method through an application to a portfolio of international assets.     

A linear model-based test for the heterogeneity of conditional correlations

Current methods of testing the equality of conditional correlations of bivariate data on a third variable of interest (covariate) are limited due to discretizing of the covariate when it is continuous. In this study, we propose a linear model approach for estimation and hypothesis testing of the Pearson correlation coefficient, where the correlation itself can be modeled as a function of continuous covariates. The restricted maximum likelihood method is applied for parameter estimation, and the corrected likelihood ratio test is performed for hypothesis testing. This approach allows for flexible and robust inference and prediction of the conditional correlations based on the linear model. Simulation studies show that the proposed method is statistically more powerful and more flexible in accommodating complex covariate patterns than the existing methods. In addition, we illustrate the approach by analyzing the correlation between the physical component summary and the mental component summary of the MOS SF-36 form across a fair number of covariates in the national survey data.     

A non-iterative approach to estimating parameters in a linear structural equation model

The research described herein was motivated by a study of the relationship between the performance of students in senior high schools and at universities in China. A special linear structural equation model is established, in which some parameters are known and both the responses and the covariables are measured with errors. To explore the relationship between the true responses and latent covariables and to estimate the parameters, we suggest a non-iterative estimation approach that can account for the external dependence between the true responses and latent covariables. This approach can also deal with the collinearity problem because the use of dimension-reduction techniques can remove redundant variables. Combining further with the information that some of parameters are given, we can perform estimation for the other unknown parameters. An easily implemented algorithm is provided. A simulation is carried out to provide evidence of the performance of the approach and to compare it with existing methods. The approach is applied to the education example for illustration, and it can be readily extended to more general models.     

Testing for serial correlation in linear model with validation data

In this paper, we investigate the testing for serial correlation in a linear model with validation data, then we apply the empirical likelihood method to construct the test statistic and derive the asymptotic distribution of the test statistic under null hypothesis. Simulation results show that our method performs well both in size and power with finite same size.     

Globally intensity-reweighted estimators for K- and pair correlation functions

We introduce new estimators of the inhomogeneous K-function and the pair correlation function of a spatial point process as well as the cross K-function and the cross pair correlation function of a bivariate spatial point process under the assumption of second-order intensity-reweighted stationarity. These estimators rely on a ‘global’ normalisation factor which depends on an aggregation of the intensity function, while the existing estimators depend ‘locally’ on the intensity function at the individual observed points. The advantages of our new global estimators over the existing local estimators are demonstrated by theoretical considerations and a simulation study.     

治理机制与企业绩效关系研究——基于治理机制的相关性与替代性视角

治理机制与绩效的关系是国内外研究的一个热点,但现有的研究并没有得到一致的结论。从治理机制之间关系的角度对治理机制与绩效的关系给于说明。治理机制之间既存在相关性,也存在替代性。在分析治理机制作用的基础上选取了四种不同的治理机制,股权集中度、董事独立性、管理层激励和两职设置,实证研究了它们之间的相关性,对治理机制之间的替代性给予了界定,并用理论分析的方法说明了某些治理机制之间存在替代性。治理机制之间相关性的存在会弱化单一治理机制对绩效的影响。     

Empirical-likelihood-based Test for Partially Linear Single-index Models with Error-prone Linear Covariates

In this article, we consider whether the empirical likelihood ratio (ELR) test is applicable to testing for serial correlation in the partially linear single-index models (PLSIM) with error-prone linear covariates. It is shown that under the null hypothesis the proposed ELR statistic follows asymptotically a χ²-distribution with the scale constant and the degrees of freedom. A comparison between the ELR and the normal approximation method is also considered. Both simulated and real data examples are used to illustrate our proposed methodology.     

Covariance structure of wavelet coefficients: theory and models in a Bayesian perspective

We present theoretical results on the random wavelet coefficients covariance structure. We use simple properties of the coefficients to derive a recursive way to compute the within- and across-scale covariances. We point out a useful link between the algorithm proposed and the two-dimensional discrete wavelet transform. We then focus on Bayesian wavelet shrinkage for estimating a function from noisy data. A prior distribution is imposed on the coefficients of the unknown function. We show how our findings on the covariance structure make it possible to specify priors that take into account the full correlation between coefficients through a parsimonious number of hyperparameters. We use Markov chain Monte Carlo methods to estimate the parameters and illustrate our method on bench-mark simulated signals.     

Estimating Intraclass Correlation Coefficient and Identifying Influential Observations Under One-Way Random Effects Model

In this paper we consider the estimation of intraclass correlation coefficient and identification of influential observations under one-way random effects model. We introduce an approach to correct negative estimation values induced by the method of moments estimator, and provide an interval estimation for intraclass correlation coefficient. We present the diagnostic tools to identify influential observations through the uncorrected estimate of intraclass correlation coefficient. A simulation study is conducted to investigate the performance of our procedure for identifying influential observations. We also apply the method on a real data of repeated blood pressure measurements.