All Questions
Tagged with sufficient-statistics references
9
questions
2
votes
0
answers
42
views
Reference request for the existence of minimal sufficient statistics
I'd like a recent paper or book that shows in what conditions we can guarantee the existence of a minimal sufficient statistic.
I know the paper "Sufficiency and Statistical Decision Functions&...
- 133
4
votes
2
answers
332
views
What is the goal of sufficient dimension reduction? Under what circumstances can it be achieved?
I have recently heard the term "sufficient dimension reduction" tossed around, although I have struggled to find material on the concept that I fully understand or that clearly explains why ...
- 687
2
votes
0
answers
54
views
Does family of sufficient $\sigma$-subalgebras depend on the reference measure?
Let $\{ P_{\gamma} \}$ be a parametric family of probability measures on $(\Omega, \mathcal{F})$, such that $P_{\gamma} \ll \mu$ for all $\gamma$, for some $\sigma$-finite $\mu$. Consider the Radon-...
- 3,348
4
votes
2
answers
1k
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Sufficient statistic for Gaussian $AR(1)$
Question Does the Gaussian $AR(1)$ model, with a fixed sample size $T$, have nontrivial sufficient statistics?
The model is given by
$$
y_t = \rho y_{t-1}, \, t = 1, \cdots, T, \; \epsilon_i
\...
- 3,348
1
vote
1
answer
222
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Gaussian sufficient statistic calculation
Consider the Gaussian model
$$
Y_i = \beta + \epsilon_i,\, i = 1, \cdots, n,\; \mbox{where}\; \epsilon_i
\stackrel{i.i.d.}{\sim} \mathcal{N}(0, \sigma^2),
$$
parametrized by $\beta$, with known $\...
- 3,348
2
votes
1
answer
99
views
Reference book for practice problems on Inference
I was wondering if there is any book which has loads of problems on statistical inference.
Desired topics are
Unbiasedness
Consistency
Sufficiency
Completeness
Rao Blackwell Theorem
etc.
11
votes
1
answer
2k
views
Proof of Pitman–Koopman–Darmois theorem
Where can I find a proof of Pitman–Koopman–Darmois theorem? I have googled for quite some time. Strangely, many notes mention this theorem yet none of them present the proof.
- 1,716
5
votes
3
answers
231
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In which case $\mathbb E[X]=\sum _ix_i P[x_i]$ can be $0$ when all $x$'s are not zero ($0$)?
Say $X$ is a random variable and $x$'s are realizations of $X$ .
Say , $\mathbb E[X]=\sum _ix_i P[x_i]=0$ . But I do not understand in which case $\mathbb E[X]=\sum _ix_i P[x_i]$ can be $0$ when all ...
- 1,705
3
votes
0
answers
146
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Kolmogorov's paper defining Bayesian sufficiency
I'm looking for a translation to either English, French or German of Kolmogorov's Russian paper
Kolmogorov, A. (1942). Sur l’estimation statistique des paramètres de la loi de Gauss. Bull. Acad. Sci. ...
- 1,443