Unbiased Estimators and Sufficient Statistics

1975 ◽  
Vol 19 (2) ◽  
pp. 379-383 ◽  
Author(s):  
L. B. Klebanov
Keyword(s):  
Sufficient Statistics ◽  
Unbiased Estimators

scholarly journals Complete and sufficient statistics and perfect families in orthogonal and error orthogonal normal models

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Aníbal Areia ◽  
Francisco Carvalho ◽  
João T. Mexia
Keyword(s):  
Jordan Algebra ◽  
Algebraic Structure ◽  
Minimum Variance ◽  
Jordan Algebras ◽  
Symmetric Matrices ◽  
Sufficient Statistics ◽  
Unbiased Estimators

AbstractWe will discuss orthogonal models and error orthogonal models and their algebraic structure, using as background, commutative Jordan algebras. The role of perfect families of symmetric matrices will be emphasized, since they will play an important part in the construction of the estimators for the relevant parameters. Perfect families of symmetric matrices form a basis for the commutative Jordan algebra they generate. When normality is assumed, these perfect families of symmetric matrices will ensure that the models have complete and sufficient statistics. This will lead to uniformly minimum variance unbiased estimators for the relevant parameters.

Inference for the diffusion branching process

1975 ◽  
Vol 12 (3) ◽  
pp. 588-594 ◽  
Author(s):  
B. M. Brown ◽  
J. I. Hewitt
Keyword(s):  
Brownian Motion ◽  
Branching Process ◽  
Exponential Family ◽  
Minimum Variance ◽  
Sufficient Statistics ◽  
Sufficient Statistic ◽  
Unbiased Estimators ◽  
Standard Problem

For the diffusion branching process, we consider a method of inference that is essentially sequential in nature. The method allows us to simplify the natural sufficient statistics involved, and we are able to get their distributions quite easily by translating our problem into a standard problem in Brownian motion. Under certain circumstances, we are left with a complete sufficient statistic whose distribution belongs to an exponential family, and can therefore derive minimum variance unbiased estimators, etc.

Inference for the diffusion branching process

1975 ◽  
Vol 12 (03) ◽  
pp. 588-594 ◽  
Author(s):  
B. M. Brown ◽  
J. I. Hewitt
Keyword(s):  
Brownian Motion ◽  
Branching Process ◽  
Exponential Family ◽  
Minimum Variance ◽  
Sufficient Statistics ◽  
Sufficient Statistic ◽  
Unbiased Estimators ◽  
Standard Problem

For the diffusion branching process, we consider a method of inference that is essentially sequential in nature. The method allows us to simplify the natural sufficient statistics involved, and we are able to get their distributions quite easily by translating our problem into a standard problem in Brownian motion. Under certain circumstances, we are left with a complete sufficient statistic whose distribution belongs to an exponential family, and can therefore derive minimum variance unbiased estimators, etc.

scholarly journals Unbiased estimation of the solution to Zakai’s equation

2020 ◽  
Vol 26 (2) ◽  
pp. 113-129
Author(s):  
Hamza M. Ruzayqat ◽  
Ajay Jasra
Keyword(s):  
Continuous Time ◽  
Unbiased Estimation ◽  
Finite Variance ◽  
Linear Filtering ◽  
Multilevel Monte Carlo ◽  
Zakai Equation ◽  
Unbiased Estimators ◽  
First Order ◽  
Multilevel Monte Carlo Method ◽  
Filtering Problem

AbstractIn the following article, we consider the non-linear filtering problem in continuous time and in particular the solution to Zakai’s equation or the normalizing constant. We develop a methodology to produce finite variance, almost surely unbiased estimators of the solution to Zakai’s equation. That is, given access to only a first-order discretization of solution to the Zakai equation, we present a method which can remove this discretization bias. The approach, under assumptions, is proved to have finite variance and is numerically compared to using a particular multilevel Monte Carlo method.

Sufficient statistics in team control problems with a common past

1982 ◽  
Author(s):  
G. Casalino ◽  
F. Davoli ◽  
R. Minciardi ◽  
R. Zoppoli
Keyword(s):  
Control Problems ◽  
Sufficient Statistics ◽  
Team Control
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