# 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.

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### sufficient, minimal, complete

Are all complete statistics functions of each other? For example if I have T and S complete statistics Can you always write T in terms of S and S in terms of T?
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### sufficient statistics for bernoulli distribution

Let Y1, . . . , Yn be a random sample of size n where each Yi ~ Bernoulli(p), and let Y = $\sum$ Yi for i = 1, . . . , n. The estimator is W= (Y+1)/(n+2) Is the estimator a sufficient statistics for ...
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### Sufficient statistic $\sum_{j=1}^{n} |x_{j}|$ for laplace distribution

Let be $X_{1},\ldots , X_{n}$ random variables independent and identically distributed with density function: $$f_{\theta}(x)=\dfrac{1}{2}e^{-|x-\mu|}, \quad x,\mu \in \mathbb{R}$$ Find the joint ...
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### What are the "Dangers" of using "Non-Sufficient" Statistics?

I was reading one of the answers listed on this previous Stackoverflow question about the importance of sufficient statistics (Generalized Linear Models - What's special about the exponential ...
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### Distribution of unbiased estimator given the sufficient statistic

Let T be a sufficient statistic for parameter a, and W be an unbiased estimator of a, then will the distribution of W|T always be independent of parameter a? I understand that T being sufficient for ...
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### Did I show sufficiency and minimal sufficiency correctly?

I am currently trying to show that the statistic $\sum\limits_{y = 1}^n Y_i^2$ is minimal sufficient for $\mu$ where $Y_1, \dots, Y_n$ is a random sample from $N(\mu,\mu)$ for $\mu > 0$. The ...
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### Why does this theorem for minimal sufficient from the "All of Statistics" textbook by Wasserman have these exponents of $n$?

In the textbook All of Statistics: A Concise Course in Statistical Inference by Larry Wasserman, the definition of minimal sufficient is given as follows: 9.35 Definition. A statistic $T$ is minimal ...
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### How do I proceed from here for factorization of likelihood / joint normal density for finding sufficient statistics?

I'm trying to show that the statistic $\left(\sum_{i = 1}^n Y_i, \sum_{i = 1}^n Y_i^2 \right)$ is sufficient for $\mu$ where $(Y_1, \dots, Y_n)$ is a random sample from $N(\mu, \mu)$ for $\mu > 0$. ...
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