# Questions tagged [mathematical-statistics]

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

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### A possible typo in the textbook?

On page 74 of Lehmann's Testing Statistical Hypothesis, the author writes Let $P_0$ and $P_1$ be probability distributions possessing densities $p_0$ and $p_1$ respectively w.r.t. a measure $\mu$ ...
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### Maximizing a computationally expensive function

Let $f:[0,1]^{80} \rightarrow [0,1]$ be some function, and say I have a computationally expensive way to calculate $f(x)$ for each $x \in [0,1]^{80}$ (expensive = 40s per query). The goal is to ...
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### Confused about the realizability assumption and equations of upper bound

I'm reading the the first chapter of Understanding machine learning from theory to algorithms and they said that: Let be the set of "bad" hypotheses, that is (e is the accuracy ...
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### Finding the Cauchy Principal Value Mean of the pdf for $Z=XY$ where $\mathbb{E}[Y]$ does not exist

Let's first define the Cauchy Principal Value Mean (PVM). For a continuous random variable $V$ with pdf $f_{V}(v)$, the PVM of $f_{V}$ is \mathrm{PV}(\mathbb{E}[V])=\lim_{a\to\infty}\...
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### Generalized univariate normal distribution with $k+1$ parameters

Final update on 11/28/2019: I have worked on this a bit more, and wrote an article summarizing all the main findings. You can read it here. The goal here is to obtain a highly generic family of ...
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### Why are these 2 ARIMA formulations equivalent?

In the "Understanding constants in R" section of his book, Hyndman & Athanasopoulos textbook "Forecasting: Principles and Practice" claims that the following AR processes equations are equivalent: ...