# Tag Info

Accepted

### Why do we not care about completeness, sufficiency of an estimator as much anymore?

We still care. However, a large part of statistics is now based on a data-driven approach where these concepts may not be essential or there are many other important concepts. With computation power ...
• 1,462
Accepted

### Likelihood Function is Minimal Sufficient

Consider an observable data vector $\mathbf{x} = (x_1,...,x_n) \in \mathscr{X}$ with a joint-distribution that is indexed by the parameter $\theta \in \Theta$. It is possible to establish that "...
• 128k
Accepted

### How can a statistician who has the data for a non-normal distribution guess better than one who only has the mean?

For a uniform distribution between $0$ and $2 \mu$, the player who guesses the sample mean would do worse than one which guesses $\frac{3}{5} \max(x_i)$ (the sample maximum is a sufficient statistic ...
• 26.3k
Accepted

### What is "Likelihood Principle"?

The concept of the likelihood principle (LP) is that the entire inference should be based on the likelihood function and solely on the likelihood function. Informally, the likelihood function is ...
• 106k
Accepted

### Solution to German Tank Problem

Likelihood Common problems in probability theory refer to the probability of observations $x_1, x_2, ... , x_n$ given a certain model and given the parameters (let's call them $\theta$) involved. For ...
• 81.5k

### Why do we not care about completeness, sufficiency of an estimator as much anymore?

We do care but usually either the issue is taken care of, or we're not making a specific distributional assumption with which we could apply those considerations. Many of the usual estimators for ...
• 285k

• 106k
Accepted

### Sufficient statistic for bivariate or multivariate normal

As W. Huber tried to lead you to conclude, the sufficiency is a simple consequence of looking at the likelihood: \begin{align*} f(\mathbf{x}_1,\ldots,\mathbf{x}_n|\boldsymbol{\mu},\boldsymbol{\Sigma}) ...
• 106k

### Is there a difference between Bayesian and Classical sufficiency?

Here is one example of differentiation between classical and Bayesian statistics: when comparing two models $\mathcal{M}_1$ and $\mathcal{M}_2$, a statistic $S(\cdot)$ may be sufficient for both ...
• 106k

### Why is the weak likelihood principle not a theorem?

Fermat's Last Theorem is a proposition of Number Theory, so you'd want to prove it from Peano's axioms; the parallel postulate, of Euclidean geometry, so from Euclid's other four postulates: but the ...

• 106k

### When using the likelihood function, where does the indicator function come from?

Most families of distributions $f_\theta$ have a fixed support, $$\text{supp}(f_\theta)=\{x\in\mathcal{X};\ f_\theta(x)>0\}$$ like the Normal or Binomial distributions, but some have a parameter ...
• 106k
Accepted

### Sufficient order statistics

Your confusion stems from the loose notations I presume: when writing $$f(\mathbf{x}) = \prod_{i=1}^n f(x_i) = \prod_{i=1}^n f(x_{(i)}),$$ George Casella and Roger Berger first use $f$ for the density ...
• 106k
Here is an experiment in a non-standard case, the location Cauchy problem, where non-standard means that there is no uniformly best unbiased estimator. Let us consider $(X_1,\ldots,X_N)$ a sample from ...