# Questions tagged [minimax]

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### Do shrinkage estimators solve the Neyman-Scott paradox?

I read the following SE question: What problem do shrinkage methods solve? And I wondered if shrinkage estimators provide a consistent estimator of the sample variance in a "mixed-effects" model using ...
112 views

### The difference of normal means is also minimax?

Let $X_i \sim N(\xi, \sigma^2)$ and $Y_i \sim N(\eta, \tau^2)$ for known $\sigma^2$ and $\tau^2$. I know that $\bar{X}$ and $\bar{Y}$ are minimax under squared error loss since their variance is ...
86 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 ...
190 views

### Question about foundations of the uniform shrinkage prior

I am collecting papers about the uniform shrinkage prior for hierarchical Bayesian model. In "A prior for the variance in hierarchical models" of Michael J. Daniels it is stated at the end of page two ...
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### Space-filling design algorithms from a discrete domain

Given $S = (X_1, \ldots, X_n)$, where each $X_i \in \mathbb{R}^2$, are there algorithms that produce $(X_{(1)}, \ldots, X_{(m)})$, where $m << n$ and the $X_{(i)}$ are sampled from $S$ to fill ...
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### Auxiliary random experiment

This question is from Robert Hogg's Introduction to Mathematical Statistic 6th version exercise 8.5.2 page 461. The question is: Let $X_1, X_2,...,X_{10}$ be a random sample of size 10 from a Poisson ...
64 views

### Minimax estimators in Bayesian analysis

I got recently introduced to minimax methods in statistical decision theory. Is there an analogue in Bayesian analysis and some resources related to this?
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### Optimizing Hyperparameters with just a Score Function

I'm trying to create artificial intelligence for the popular game "2048" using this page as a reference: https://stackoverflow.com/questions/22342854/what-is-the-optimal-algorithm-for-the-game-2048/...
11 views

### minimax estimator in applications

In the applications, does it really matter if the estimator is minimax or not if, say, we are interested in forecasting and with current non-minimax estimator we have better out-of-sample scores?
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### Detection Theory minimax with non differentiable interior

The minimax is used in detection theory and decision theory for minimizing the overall average risk for the worst case prior.  \min_{\delta} \max_{\pi_0} r(\pi_0,\delta) = \max_{\pi_0} \min_{\delta}...
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### Finding and presenting solution for optimized supplier portfolio

I am trying to find the best solution to create a "model" and presentation of the following challenge: I have several products which shall be bought from as few suppliers as possible. For each ...
Let $X_1,...,X_n$ be independent r.v.'s from the poisson $P(\theta)$ ,$\theta \in (0,\infty)$. and consider loss function $L(\theta ; \delta ) =\frac{[\theta - \delta(x_1,...,x_n)]^2}{\theta}$. then ...