Factorization theorem, Advanced Statistics

Assignment Help:

The theorem relating structure of the likelihood to the concept of the sufficient statistic. Officially the necessary and sufficient condition which a statistic S be sufficient for the parameter θ is that the likelihood, l(θ; y) can be expressed in the form given below;

2357_factorization theorem.png 

For instance, if Y1; Y2; ... ; Yn are the independent random variables from the Poisson distribution with the mean of μ, the likelihood is given by the following formula;

550_factorization theorem1.png 
which can be factorized into the following equation


1741_factorization theorem2.png

 


Related Discussions:- Factorization theorem

Empirical bayes method, The procedure in which the prior distribution is re...

The procedure in which the prior distribution is required in the application of Bayesian inference, it is determined from empirical evidence, namely same data for which the posteri

EDUC 606, The GRE has a combined verbal and quantitative mean of 1000 and a...

The GRE has a combined verbal and quantitative mean of 1000 and a standard deviation of 200.

Prevented fraction, Prevented fraction is a measure which can be used to a...

Prevented fraction is a measure which can be used to attribute the protection against the disease directly to an intervention. The measure can given by the proportion of disease w

Em algorithm, The method or technique for producing the sequence of paramet...

The method or technique for producing the sequence of parameter estimates that, under the mild regularity conditions, converges to maximum likelihood estimator. Of particular signi

Case Study, ACC – A pioneer in the Indian cement industry Associated Cemen...

ACC – A pioneer in the Indian cement industry Associated Cement Companies Ltd. (ACC) came into existence in 1936, after the merger of 10 companies belonging to four important bus

Helmert contrast, Helmert contrast is the contrast often used in analysis ...

Helmert contrast is the contrast often used in analysis of the variance, in which each level of a factor is tested against average of the remaining levels. So, for instance, if th

Randomization tests, Randomization tests are the procedures for determinin...

Randomization tests are the procedures for determining the statistical significance directly from the data with- out recourse to some particular sampling distribution. For instanc

Convex hull trimming, Convex hull trimming : A procedure which can be appli...

Convex hull trimming : A procedure which can be applied to the set of bivariate data to permit robust estimation of the Pearson's product moment correlation coef?cient. The points

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd