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Title: Moments of Maximum Likelihood Estimators in the Discrete Case


No abstract prepared.

 [1];  [2]
  1. ORNL
  2. University of Georgia, Athens, GA
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
Work for Others (WFO)
OSTI Identifier:
DOE Contract Number:
Resource Type:
Journal Article
Resource Relation:
Journal Name: Far East Journal of Theoretical Statistics; Journal Volume: 18
Country of Publication:
United States

Citation Formats

Bowman, Kimiko o, and Shenton, LR. Moments of Maximum Likelihood Estimators in the Discrete Case. United States: N. p., 2006. Web.
Bowman, Kimiko o, & Shenton, LR. Moments of Maximum Likelihood Estimators in the Discrete Case. United States.
Bowman, Kimiko o, and Shenton, LR. Sun . "Moments of Maximum Likelihood Estimators in the Discrete Case". United States. doi:.
title = {Moments of Maximum Likelihood Estimators in the Discrete Case},
author = {Bowman, Kimiko o and Shenton, LR},
abstractNote = {No abstract prepared.},
doi = {},
journal = {Far East Journal of Theoretical Statistics},
number = ,
volume = 18,
place = {United States},
year = {Sun Jan 01 00:00:00 EST 2006},
month = {Sun Jan 01 00:00:00 EST 2006}
  • In this paper we apply to gravitational waves (GW) from the inspiral phase of binary systems a recently derived frequentist methodology to calculate analytically the error for a maximum likelihood estimate of physical parameters. We use expansions of the covariance and the bias of a maximum likelihood estimate in terms of inverse powers of the signal-to-noise ration (SNR)s where the square root of the first order in the covariance expansion is the Cramer Rao lower bound (CRLB). We evaluate the expansions, for the first time, for GW signals in noises of GW interferometers. The examples are limited to a single,more » optimally oriented, interferometer. We also compare the error estimates using the first two orders of the expansions with existing numerical Monte Carlo simulations. The first two orders of the covariance allow us to get error predictions closer to what is observed in numerical simulations than the CRLB. The methodology also predicts a necessary SNR to approximate the error with the CRLB and provides new insight on the relationship between waveform properties, SNR, dimension of the parameter space and estimation errors. For example the timing match filtering can achieve the CRLB only if the SNR is larger than the Kurtosis of the gravitational wave spectrum and the necessary SNR is much larger if other physical parameters are also unknown.« less
  • The probability generating function of one version of the negative binomial distribution being (p + 1 - pt){sup -k}, we study elements of the Hessian and in particular Fisher's discovery of a series form for the variance of k, the maximum likelihood estimator, and also for the determinant of the Hessian. There is a link with the Psi function and its derivatives. Basic algebra is excessively complicated and a Maple code implementation is an important task in the solution process. Low order maximum likelihood moments are given and also Fisher's examples relating to data associated with ticks on sheep. Efficiencymore » of moment estimators is mentioned, including the concept of joint efficiency. In an Addendum we give an interesting formula for the difference of two Psi functions.« less
  • No abstract prepared.