In Example 6.6, find (boldsymbol{Lambda}) and (mathbf{d}^{prime}(theta) boldsymbol{Lambda} mathbf{d}(theta)). Example 6.6. Let {X} be a sequence of

In Example 6.6, find \(\boldsymbol{\Lambda}\) and \(\mathbf{d}^{\prime}(\theta) \boldsymbol{\Lambda} \mathbf{d}(\theta)\).

Transcribed Image Text:

Example 6.6. Let {X} be a sequence of independent and identically distributed bivariate random variables from a distribution with mean vector and positive definite covariance matrix where we will assume that X = (X1n, X2n) for all n = N, ' = (1, 2), and that T = 9 where all of the elements of and will be assumed to be finite. Suppose we are interested in the correlation coefficient given by p = r, which can be estimated with n = SSS, where -1 n S12= n(X1k-X1)(X2k X2), k=1 - Y n S=nXik-X), k=1 and n X = nXik k=1