The mean square error of the optimum linear estimate

Reference no: EM131083809

Continuing Example 9.10, the 21-dimensional vector X has correlation matrix RX with i, jth element

We use the observation vector Y = Y⁽ⁿ⁾ = [Y₁ ··· Y_n]' to estimate X = X₂₁. Find the LMSE estimate _L (Y⁽ⁿ⁾) = ⁽ⁿ⁾Y⁽ⁿ⁾. Graph the mean square error e∗_L(n) as a function of the number of observations n for φ0 ∈ {0.1, 0.5, 0.9}. Interpret your results. Does smaller φ0 or larger φ0 yield better estimates?

Example 9.10

The correlation matrix R_X of a 21-dimensional random vector X has i, jth element

W is a random vector, independent of X, with expected value E[W] = 0 and diagonal correlation matrix R_W = (0.1) I. Use the first n elements of Y = X+W to form a linear estimate of X₂₁ and plot the mean square error of the optimum linear estimate as a function of n for

Reference no: EM131083809

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