Mathematics · Multivariate Analysis

Let X 0 , X 1 , ..., X p (p ≥ 2) be independent and identically distributed random variables with mean 0 and variance 1. Suppose Y i = X 0 + X i , i = 1, ..., p. The first principal component based on the covariance matrix of Y = (Y 1 , ..., Y p ) T is:

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Correct answer

1 √p ∑ i=1 p Y i

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Let X 0 , X 1 , ..., X p (p &ge; 2) be independent and identically distributed random variables with mean 0 and variance 1. Suppose Y i = X 0 + X i , i = 1, ..., p. The first principal component based on the covariance matrix of Y = (Y 1 , ..., Y p ) T is: