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Mathematical theory of statistics, concerned with formal definitions and general results.

2
votes
0answers
I am considering a model that includes a covariance matrix which is a function of model's parameters: $$ \mathbf \Sigma = \Sigma(\mathbf \theta), $$ where $\mathbf \theta$ is $p$-dimensional, $\mathbf …
asked Feb 3 '14 by Matteo Fasiolo
4
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0answers
At page 85-86 of Young and Smith "Essentials of Statistical Inference" there is an interesting result. If $X$ is a r.v. distributed according to the exponential family and $\phi(x)$ is a bounded (but …
asked Nov 18 '12 by Matteo Fasiolo
3
votes
1answer
I have encountered the following integral: $$ \int_{- \infty}^{+ \infty} X(\theta) \frac{\exp \big \{-\frac{\theta^2}{2\sigma^2} \big \}}{\sigma\sqrt{2 \pi}}d\theta $$ where, for fixed $\theta = \thet …
asked Jan 2 '14 by Matteo Fasiolo
15
votes
Here I expand upon kjetil's answer, and I focus on those situations where the Cumulant Generating Function (CGF) is unknown, but it can be estimated from the data $x_1,\dots,x_n$, where $x\in R^d$. Th …
answered Jan 25 '16 by Matteo Fasiolo