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9.3 Some Type M-Measures of Correlation > 9.3.6 The Winsorized Correlation - Pg. 452

452 Introduction to Robust Estimation and Hypothesis Testing The test statistic, H , for testing the hypothesis that all three correlations are equal to zero, has a p-value approximately equal to 0. To use = 0.1 instead, type the command pball(amat,0.1). I 9.3.6 The Winsorized Correlation Another (type M) robust analog of is the Winsorized correlation. The population Winsorized correlation between two random variables, X 1 and X 2 , is given by w = E w [(X 1 - µ w1 )(X 2 - µ w2 )] , w1 w2 where wj is the population Winsorized standard deviation of X j , and E w (X ) is the Winsorized expected value of X , as defined in Section 2.5 of Chapter 2. The numerator of w is the population Winsorized covariance which is written simply as w12 when convenient. When X 1 and X 2 are independent, w = 0, and -1 w 1. To estimate w , based on the random sample (X 11 , X 12 ), . . . , (X n1 , X n2 ), first Winsorize the