Information Geometry and Its Applications by Shun-ichi Amari

Author:Shun-ichi Amari
Language: eng
Format: epub, pdf
Publisher: Springer Japan, Tokyo

(9.25)

This is a good consistent estimator. It is of interest to know how good it is.

4. Total least square solution

Instead of minimizing the vertical errors in the least squares solution, we minimize the square of the lengths of orthogonal projection to the regression line (Fig. 9.3c). This is called the total least squares (TLS) solution. It is given by solving

(9.26)

5. MLE

We estimate all the parameters , jointly by maximizing the likelihood, and we disregard all , keeping only. This is the MLE. We can prove that this is identical with the TLS solution.

We use a semiparametric formulation of the Neyman–Scott problem. Since the sequence is arbitrary and unknown, we assume that it is generated from an unknown probability distribution . In order to generate the ith example ( in the above example), Nature chooses from distribution . Then, is chosen from . Thus, each is subject to one and the same probability distribution

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