Basics of Modern Mathematical Statistics by Wolfgang Karl Härdle Vladimir Spokoiny Vladimir Panov & Weining Wang

Author:Wolfgang Karl Härdle, Vladimir Spokoiny, Vladimir Panov & Weining Wang
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

Exercise 4.9.

Consider the model

(4.11)

and let the true stochastic be

(4.12)

with a fixed covariance matrix . Prove that in this case

In the model (4.11), and . Substituting these values in the general formula for solving MLE esitmator gives

According to the true model (4.12), . Hence,

Exercise 4.10.

Let be the stochastic component of built for the misspecified linear model with . Let the true noise variance be 1. Prove that the variance of is equal to

(4.13)

2. Check that the matrix in the right hand side of (4.13) is of dimension .

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