Maximum Likelihood Estimation of a Class of Non-Gaussian Densities with Application to Deconvolution,
RICE UNIV HOUSTON TX DEPT OF ELECTRICAL AND COMPUTER ENGINEERING
Pagination or Media Count:
This paper investigates in detail the properties of the maximum likelihood estimator of the generalized p-Gaussian gpG probability density function pdf from N independent identically distributed iid samples, especially in the context of the deconvolution problem under gpG white noise. The first part describes the properties of the estimator independently on the application. The second part obtains the solution of the above mentioned deconvolution problem as the solution of a minimum norm problem in an l sub p normed space. In the present paper, we show that such a minimum norm solution is the maximum likelihood estimate is unbiased, with the lower bound of the variance of the error equal to the Cramer Rao lower bound, and the upper bound derived from the concept of a generalized inverse.
- Theoretical Mathematics