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Determination of Discrete Spectrum in a Random Field
Author(s) -
Kundu Debasis,
Nandi Swagata
Publication year - 2003
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/1467-9574.00230
Subject(s) - estimator , mathematics , asymptotic distribution , least squares function approximation , consistency (knowledge bases) , field (mathematics) , strong consistency , m estimator , function (biology) , statistics , discrete mathematics , evolutionary biology , pure mathematics , biology
We consider a two dimensional frequency model in a random field, which can be used to model textures and also has wide applications in Statistical Signal Processing. First we consider the usual least squares estimators and obtain the consistency and the asymptotic distribution of the least squares estimators. Next we consider an estimator, which can be obtained by maximizing the periodogram function. It is observed that the least squares estimators and the estimators obtained by maximizing the periodogram function are asymptotically equivalent. Some numerical experiments are performed to see how the results work for finite samples. We apply our results on simulated textures to observe how the different estimators perform in estimating the true textures from a noisy data.