# Unbiased estimators of multivariate discrete distributions and chi-square goodness-of-fit test.

Mikhail S. Nikulin; Vassiliy G. Voinov

Qüestiió (1993)

- Volume: 17, Issue: 3, page 301-326
- ISSN: 0210-8054

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topNikulin, Mikhail S., and Voinov, Vassiliy G.. "Unbiased estimators of multivariate discrete distributions and chi-square goodness-of-fit test.." Qüestiió 17.3 (1993): 301-326. <http://eudml.org/doc/40093>.

@article{Nikulin1993,

abstract = {We consider the problem of estimation of the value of a real-valued function u(θ), θ = (θ1, ..., θk)T, on the basis of a sample from non-truncated or truncated multivariate Modified Power Series Distributions. Using the general theory of estimation and the results of Patil (1965) and Patel (1978) we give the tables of MVUE's for functions of parameter θ of trinomial, multinomial, negative-multinomial and left-truncated modified power series distributions. We have applied the properties of MVUE's and the results from the theory of MVU estimation to construct a goodness-of-fit chi-squared test for multivariate modified power series distributions.},

author = {Nikulin, Mikhail S., Voinov, Vassiliy G.},

journal = {Qüestiió},

keywords = {multivariate modified power series distributions; sufficient statistic; MVUE; Rao-Kolmogorov-Blackwell method; -squared goodness-of-fit test; minimum -squared estimator; maximum likelihood estimator; Chernoff-Lehmann theorem; BAN estimator},

language = {eng},

number = {3},

pages = {301-326},

title = {Unbiased estimators of multivariate discrete distributions and chi-square goodness-of-fit test.},

url = {http://eudml.org/doc/40093},

volume = {17},

year = {1993},

}

TY - JOUR

AU - Nikulin, Mikhail S.

AU - Voinov, Vassiliy G.

TI - Unbiased estimators of multivariate discrete distributions and chi-square goodness-of-fit test.

JO - Qüestiió

PY - 1993

VL - 17

IS - 3

SP - 301

EP - 326

AB - We consider the problem of estimation of the value of a real-valued function u(θ), θ = (θ1, ..., θk)T, on the basis of a sample from non-truncated or truncated multivariate Modified Power Series Distributions. Using the general theory of estimation and the results of Patil (1965) and Patel (1978) we give the tables of MVUE's for functions of parameter θ of trinomial, multinomial, negative-multinomial and left-truncated modified power series distributions. We have applied the properties of MVUE's and the results from the theory of MVU estimation to construct a goodness-of-fit chi-squared test for multivariate modified power series distributions.

LA - eng

KW - multivariate modified power series distributions; sufficient statistic; MVUE; Rao-Kolmogorov-Blackwell method; -squared goodness-of-fit test; minimum -squared estimator; maximum likelihood estimator; Chernoff-Lehmann theorem; BAN estimator

UR - http://eudml.org/doc/40093

ER -

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