Remarks on the maximum correlation coefficient

Department of Mathematics, Stanford University, Palo Alto, California, United States
Bernoulli (Impact Factor: 1.3). 06/2000; 7(2). DOI: 10.2307/3318742
Source: OAI

ABSTRACT The maximum correlation coefficient between partial sums of independent and identically distributed random variables with finite second moment equals the classical (Pearson) correlation coefficient between the sums, and thus does not depend on the distribution of the random variables. This result is proved, and relations between the linearity of regression of each of two random variables on the other and the maximum correlation coefficient are discussed.

  • [Show abstract] [Hide abstract]
    ABSTRACT: We present a method for the obtention of the maximal correlation coefficient that extends the simple method given by Papadatos and Xifara (2013). We illustrate our method with the calculation of the maximal correlation between the kkth largest order statistics of overlapping samples.
    Journal of Multivariate Analysis 10/2014; 131:265–278. DOI:10.1016/j.jmva.2014.07.008 · 0.94 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: A measure of dependence is said to be equitable if it gives similar scores to equally noisy relationship of different types. In practice, we do not know what kind of functional relationship is underlying two given observations, Hence the equitability of dependence measure is critical in analysis and by scoring relationships according to an equitable measure one hopes to find important patterns of any type of further examination. In this paper, we introduce our definition of equitability of a dependence measure, which is naturally from this initial description, and Further more power-equitable(weak-equitable) is introduced which is of the most practical meaning in evaluating the equitablity of a dependence measure.
  • [Show abstract] [Hide abstract]
    ABSTRACT: In most of the regression problems the first task is to select the most influential predictors explaining the response, and removing the others from the model. These problems are usually referred to as the variable selection problems in the statistical literature. Numerous methods have been proposed in this field, most of which address linear models. In this study we propose two variable selection criteria for regression based on two powerful dependence measures, maximal correlation and distance correlation. We focus on these two measures since they fully or partially satisfy the Rényi postulates for dependence measures, and thus they are able to detect nonlinear dependence structures. Therefore, our methods are considered to be appropriate in linear as well as nonlinear regression models. Both methods are easy to implement and they perform well. We illustrate the performances of the proposed methods via simulations, and compare them with two benchmark methods, stepwise Akaike information criterion and lasso. In several cases with linear dependence all four methods turned out to be comparable. In the presence of nonlinear or uncorrelated dependencies, we observed that our proposed methods may be favourable. An application of the proposed methods to a real financial data set is also provided.
    Journal of Statistical Computation and Simulation 03/2014; DOI:10.1080/00949655.2014.895354 · 0.71 Impact Factor


1 Download
Available from

Similar Publications