# Questions tagged [mathematical-statistics]

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

1,430 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
250 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 ...
71 views

127 views

### Distribution of a binary matrix times a Bernoulli vector

Suppose we have the vector $\mathbf{Y} = (Y_{1},\ldots,Y_{n})$ where $Y_{i} \sim \textrm{Bernoulli}(p_{i})$ independently. For the applications I have in mind, $n$ will typically be several thousand, ...
82 views

### Finding the minimax estimator

Suppose $x$ comes from a Bernoulli distribution $f(x, \theta) = \theta^{x}(1-\theta)^{1-x}$ where $0 \leq \theta \leq 1$. Now suppose $y$ comes from the same distribution. An estimate for the ...
283 views

### ranking based on lower confidence interval

I have a database of bridge scores from a local bridge club that effectively contains for this question, three fields: name, date...
3k views

### How to calculate 'weighted' pooled/composite statistics for two given groups given group statistics

I have two sets of independent samples from the same distribution. For each, I have calculated sample weighted mean (u1, u2) sample weighted std deviation (d1, d2) sample weighted std error (e1, e2) ...
96 views

348 views

### Measuring parameter sensitivity and variability (standard-error) in k-fold cross-validation

I mainly use k-fold cross-validation for parameter tuning and model selection for prediction problems. Now, is there a standard or if not a less-known way to measure the sensitivity of the parameters ...
108 views

1k views

### Unbiased hypothesis tests

Is there some textbook or expository account showing that the definition of "unbiased test" bears the same sort of relation to "unbiased estimator" that interval estimation generally bears to ...
91 views

### Is there any way to define a distance metric given a Hidden Markov Model?

Let's say I've gotten a HMM that describes user search strings for my e-commerce website. Let's also say that I've just received a search string from a customer that doesn't have any search results. ...
69 views

31 views

### The frog problem with negative steps

In this question The Frog Problem (puzzle in YouTube video) a frog has to jump forward from leaf to leaf with equal probability. It is computed that the expected number for the number of steps he has ...
31 views

### Regression with summary statistics

The following setting should already be familiar: Let $X$ be some space, $\mathbb R^d$ for simplicity, and let $Y\subseteq \mathbb R$. An unknown distribution $\mu$ is defined over $X\times Y$ and ...
33 views

### Intuitive explanation of scaled inverse chi-distribution

I am having a hard time understanding the scaled inverse chi-distribution. I looked for Wiki and other resources which are pretty math heavy without an intuitive ...
27 views

### Statistics books with applications in quantitative finance

I am a Pure Maths PhD. As I would like to venture myself into quantitative finance jobs, I need to pick up statistics, programming and finance. I have been reading time series analysis by Hamilton ...
17 views

### Can cross validation be applied to threshold based outlier detection model?

I have a threshold based outlier detection model. I apply PCA then calculate the distance from the centre of the features, and use the MSE to differentiate if the datapoint is a outlier. However, I ...
33 views

### Switching $H_0$ and $H_1$ by replacing $p$ with $1 - p$

I was reading the source code of tseries::adf.test, and it writes ...
38 views

### Gaussian process and its limitations

I once saw the following statement on Gaussian process, ...
39 views

25 views

### High dimensional linear regression inference

I am reading through high-dimensional literature currently but I got confused. Especially about statistical inference with LASSO, anyone can clarify me the main difference among Van De Geer(2014)ON ...
98 views

### Effect of class imbalance on logistic regression (mathematical basis)

A number of posts, and papers, state that logistic regression (LR) is robust in the face of class imbalance. Unless the imbalance is extreme (e.g., events=0.01 or less), with adequate sample sizes ...
44 views

### Help Identifying the Name of a Theorem

Recall the following theorem: Let $X$ be a random variable with probability density function $f_x(x)$ and let $g$ be monotone over the support of $f_x$. The random variable $Y=g(X)$ has density ...
### Showing that $(l'\Sigma l)\chi_p^2 = (l'S l)\frac{(n-1)p}{n-p} F_{p,n-p}$
Let $X_1,\cdots X_n$ be i.i.d. $N_p(\mu,\Sigma)$. I have that when $\mu$ and $\Sigma$ are unknown that the Scheffe type method gives $(1-\alpha)100$% confidence intervals for all linear combinations \$...