Remarks on the maximum correlation coefficient

Bernoulli (Impact Factor: 1.3). 06/2000; 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.

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    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.
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    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. · 0.94 Impact Factor
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    ABSTRACT: We consider the problem of screening features in an ultrahigh-dimensional setting. Using maximum correlation, we develop a novel procedure called MC-SIS for feature screening, and show that MC-SIS possesses the sure screen property without imposing model or distributional assumptions on the response and predictor variables. Therefore, MC-SIS is a model-free sure independence screening method as in contrast with some other existing model-based sure independence screening methods in the literature. Simulation examples and a real data application are used to demonstrate the performance of MC-SIS as well as to compare MC-SIS with other existing sure screening methods. The results show that MC-SIS outperforms those methods when their model assumptions are violated, and it remains competitive when the model assumptions hold.


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