Statistics and Data Science Seminar
Bikas Sinha
ISI
Coverage Probability and Exact Inference
Abstract: Abstract : With reference to 'point estimation' of a real-valued parameter $\theta$ involved in the distribution of a
real-valued random variable $X$, we consider a sample size $n$ and an underlying exact-sense unbiased
estimator ${\hat{\theta}}_n$ of $\theta$ for every $n = k, k+1, k+2, ...\ldots$ where $k$ is the minimum sample
size for existence of an exact-sense unbiased estimator of $\theta$. We wish to investigate exact small sample
properties of the sequence of estimators considered here. This we study by considering what is termed as
'Coverage Probability (CP)' and defined as $CP(n, c)=P[-c < {\hat{\theta}}_n - \theta < c]$. It is desired that the
sequence $[CP(n, c); n=k, k+1, k+2, ...\ldots]$ behaves like an increasing sequence for every $c>0$. We may
note that we are asking for a property beyond 'consistency' of a sequence of estimators. In this presentation we
will discuss several interesting features of the behavior of the $CP(n, c)$.
TBA
Wednesday September 14, 2016 at 4:00 PM in SEO 636