# Questions tagged [sufficient-statistics]

A sufficient statistic is a lower dimensional function of the data which contains all relevant information about a certain parameter in itself.

278 questions
Filter by
Sorted by
Tagged with
62 views

### Sufficient statistic vector of single parameter?

Can the sufficient statistic for a single parameter be a vector? In my case, I am finding the sufficient statistics for the Poisson parameter in a HMM mixture. The parameter enters my log likelihood ...
134 views

### How does one can guarantee that any unbiased estimator is MVUE due to it containing a minimal sufficient statistic?

Sufficiency is okay. But I don't really get it why the fact guarantees it has minimal variance? Can anyone explain to me somewhat intuitively?
560 views

1k views

### Basu's Theorem Proof

I am having trouble with the proof of Basu's theorem... specifically, I'm not sure about the $\theta$s in the expectations below: Let $T$ be a complete sufficient statistic. Let $V$ be an ancillary ...
80 views

### Sufficiency - Knowns and Unknowns

I have a self-study question that goes as follows: Let $X$ be one observation from a $N\sim(0, \sigma^2)$ population. Is $|X|$ a sufficient statistic? My question is - since you KNOW the $\mu$ ...
975 views

### Basic intuition about minimal sufficient statistic

As stated by Wikipedia: A sufficient statistic is minimal sufficient if it can be represented as a function of any other sufficient statistic. In other words, $S(X)$ is minimal sufficient if and ...
90 views

### Puzzling Sufficient Statistic

If $X_1\sim U(0,\theta)$ then $X_1$ is a sufficient statistic for $\theta$. Also when $X_2\sim U(0,\theta + 1)$ then $X_2$ is a sufficient statistic for $\theta$. Is that right? Now if $X_1, X_2$ ...
956 views

### Find the unique MVUE

This question is from Robert Hogg's Introduction to Mathematical Statistics 6th Version problem 7.4.9 at page 388. Let $X_1,...,X_n$ be iid with pdf $f(x;\theta)=1/3\theta,-\theta<x<2\theta,$ ...
1k views

770 views

### Understanding a characterization of minimal sufficient statistics

I have some questions regarding the proof of the theorem below. First we need a definition: A statistic $T$ is minimal sufficient iff $T$ is a function of any other sufficient statistic. That is, ...
2k views

638 views

### Minimum dimension of sufficient statistics

Suppose that we have a parameter of $k$-dimensions. Say, for example, for $N(u,\theta)$ both unknown then the parameter is of two dimensions, and $n$ i.i.d. observations. Is it possible to find a ...
462 views

195 views

### Unbiased estimator and sufficient statistics [closed]

Let $X_1,..,X_n$ be a random sample of $f(x;\theta)=\theta x^{\theta-1}I_{[0,1]}(x)$ Find a sufficient statistic for $\theta$ and construct a unbiased estimator for $\theta$ as a function of ...
276 views

### Sufficient statistics and UMVUE for joint poisson, bernoulli

Given a pair $(X,Y)$ of r.v.s such that: $$X \sim \text{Poisson}(\lambda)\quad \text{and}\quad Y \sim B(\frac{\lambda}{1+\lambda})$$ with $X,Y$ independent, determine a one-dimensional sufficient ...