New answers tagged

0 votes
Accepted

Link between mean square and variances in ANOVA

After some research, the definitions presented above for the within and between locations variance are correct. We can find these definitions in the book: Anand M. Joglekar. Statistical Methods for ...
  • 58
1 vote

Determine sample size so that it guarantees that the length of the confidence interval is less than $\frac{\sigma}{4}$

Hint: According to CLT for sample variance, if the 4th central moment of iid function exists, then sample variance converges in distribution to a normal distribution. By applying Delta method, we can ...
  • 64
0 votes

How to prove SSE and SSR are independent

To prove $(I-X(X^{T}X)^{-1}X^{T})(X(X^{T}X)^{-1}X^{T}-\frac{1}{n}J)=0$ , we only need to prove: \begin{split} \mathbf{1_n(1_n)^T} = X(X^{T}X)^{-1}X^{T}\mathbf{1_n(1_n)^T} \end{split} And $\mathbf{1_n}$...
0 votes

Question about unbiased estimators

The term "population" should not be taken too literally here. This is a question in Probability theory, which is then used in Statistics. The random variables $\{X_i\}_{i=1}^n$ (using ...
  • 19.6k
2 votes
Accepted

On $\lim\limits_{v \to \infty} \underset{\theta \in \Theta}{\operatorname{argmax}} \int_{\| \theta - z \| < \frac{1}{v}} \pi(z|x) \, {\rm d} z$

Let me impose a mild assumption that $\pi(\theta|x)$ lies in the space $C_0(\mathbb{R}^n)$ of continuous functions $f(\theta)$ on $\mathbb{R}^n$ that vanishes as $\|\theta\|\to\infty$ for each $x \in \...
0 votes

On $\lim\limits_{v \to \infty} \underset{\theta \in \Theta}{\operatorname{argmax}} \int_{\| \theta - z \| < \frac{1}{v}} \pi(z|x) \, {\rm d} z$

I understand it to be saying the following: We are integrating over the region where $||\theta - z|| < \frac{1}{\nu}$. As $\nu \to \infty$, $\frac{1}{\nu} \to 0$, so the region where $||\theta - z||...
  • 51
1 vote
Accepted

Question about definition of statistical Model in information geometry

I agree with the other answer but want to add that we should be more clear about why this is a necessary assumption that is often made in statistics. The usual definitions are: A statistical model $\...
  • 5,462
1 vote

Question about definition of statistical Model in information geometry

Short answer: My guess is that properties of the manifold will be inferred from properties of $E$ and $\xi \mapsto p(\cdot;\xi)$. In order to establish many topological properties having an injective ...
2 votes

How can I relate KL-divergence or other distances to the number of samples required to distinguish between two distributions?

An interesting case is when $p$ and $q$ are supported on a finite set, say $[n]=\{1,\ldots,n\}.$ The paper that started research along these lines in the CS literature is Batu et al see here. The ...
  • 7,507

Top 50 recent answers are included