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

Correspondence analysis, The method or technique for displaying the relatio...

The method or technique for displaying the relationships between categorical variables in a type of the scatter plot diagram. For two this type of variables displayed in the form o

Cluster analysis, Cluster analysis : A set of methods or techniques for con...

Cluster analysis : A set of methods or techniques for constructing a sensible and informative classi?cation of an initially unclassi?ed set of data, using variable values observed

Exponential family, A family of the probability distributions of the form g...

A family of the probability distributions of the form given as   here θ is the parameter and a, b, c, d are the known functions. It includes the gamma distribution, normal dis

Quantitative Methods, After graduating from Tech Julia was unable to find r...

After graduating from Tech Julia was unable to find regular employment and approached the Director of Athletics at Tech to request that she remain a vendor of the following year.

Weathervane plot, Weathervane plot is the graphical display of the multiva...

Weathervane plot is the graphical display of the multivariate data based on bubble plot. The latter is enhanced by the addiction of the lines whose lengths and directions code the

Zero-inflated poisson regression, Zero-inflated Poisson regression is  the...

Zero-inflated Poisson regression is  the model for count data with the excess zeros. It supposes that with probability p the only possible observation is 0 and with the probabilit

Data monitoring committees (dmc), Committees to monitor the accumulating da...

Committees to monitor the accumulating data from the clinical trials. Such committees have chief responsibilities for ensuring the continuing safety of the trial participants, rele

Assignment, Different approaches to the study of early indian history

Different approaches to the study of early indian history

Statistically modeling, A comprehensive regression analysis of the case stu...

A comprehensive regression analysis of the case study London has been carried out to test the 4 assumptions of regression: 1. Variables are normally distributed 2. Linear rel

Cross-sectional study, A study not involving the passing of time. All infor...

A study not involving the passing of time. All information is collected at the same time and subjects are contacted only once. Many surveys are of this type. The temporal sequence

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