# Questions tagged [self-study]

A routine exercise designed to test one's knowledge; often from a textbook, course, or test used for a class or self-study. This community's policy is to "provide helpful hints" for such questions rather than complete answers.

8,150 questions
Filter by
Sorted by
Tagged with
9 views

### Have I constructed the Neyman-orthogonal score correctly?

I am trying to construct a Neyman-orthogonal score for the Poisson m-estimator, using section 2.2 of Chernozhukov et al. (2018). Have I done this correctly? If so, can somebody please help me show/...
1 vote
46 views

### Rao-Blackwell Theorem

I'm having problems on understanding the Rao-Blackwell theorem. In particular I don't understand why the resulting estimator is the one with minimum variance between ALL unbiased estimators of the ...
44 views

### No Existence of Efficient estimator

I need to prove that given $(X_1,...,X_n)$ from the density $$\frac{1}{\theta}x^{\frac{1}{\theta}-1}1_{(0,1)}$$ no efficient estimator exists for $g(\theta)$=$\frac{1}{{\theta}+1}$. I have shown that ...
20 views

• 51
82 views

### How to find probability from $E[X^n]$?

It is given that $E[X^n] = \frac{2}{5}(-1)^n + \frac{2^{n+1}}{5}+\frac{1}{5}$, where $n=1,2,3,\ldots.$ I need to find $P(|X-\frac{1}{2}| > 1)$. What my approach is : I have opened the modulus ...
1 vote
47 views

### Interpretation of incidence rate ratio

The incidence rate ratio (and 95% confidence interval) of rotavirus gastroenteritis for the vaccine group compared to the placebo group is $0.67 (0.55, 0.82)$. I want to know approximately how many ...
89 views

### Posterior Distribution using Jeffreys prior

I'm trying to show that if $X_1, \cdots, X_n \stackrel{iid}{\sim} N(\mu, \sigma^2)$ with unknown $\mu$, $\sigma$ and the prior $\pi(\mu, \sigma^2) \propto 1/\sigma^2$ then the posterior distribution ...
• 183
59 views

### Hastie "statistical learning" 2.28. Least squares and covariance

In Hasties book "statistical learning", just above equation 2.28, it says that $\mathbf{X}^T\mathbf{X} \rightarrow NCov(X)$ (when $N$ is large and $E(X)=0$). Why is this true? $Cov(X)$ is ...
25 views

### PDF of difference of uniform distributions [duplicate]

Main questions are in bold but feel free to correct me if I'm wrong somewhere else. As far as possible, I need both intuition and formal explanation. Let $X \sim Uniform(a,b)$ and $Y \sim Uniform(c,d)$...
1 vote
43 views

• 87
52 views

### Two-proportion hypothesis test with variances unknown

"A group of test subjects are split into two groups. 1000 people are given a vaccine, and 15 of them get the disease. 800 people are given a placebo, and 60 of them get the disease. Test the ...
• 207