Unanswered Questions
2,010 questions with no upvoted or accepted answers
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Concentration of maximum of subexponential random variables
I'm looking for a concentration bound on the maximum of a collection of sub-exponential random variables, which are not necessarily independent. More specifically, I have the following collection:
\...
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Exercise on Borel Cantelli Lemma ($\limsup X_n/ \ln(n) =1$ a.s.) help required to rigorously write the statement
I hope this question is within the scope of this site. Please note that I have solved this Exercise, I do have doubts about my presentation though and about how to rigorously empathize on the ...
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Question 10.9 from Bayesian Data Analysis, what does accuracy mean here?
I'm doing an independent study in Bayesian Statistics following some chapters from BDA3. When solving the first question from Ch 10 I got stuck. It says:
[If] a scalar variable $\theta$ is ...
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Why does MLE tend to normal distribution
We have $X_1,\dots, X_n$ are iid (the distribution can be of any type, e.g. Bernoulli (p), normal ($\mu, \sigma^2$), Poisson ($\lambda$).
If we use MLE $\hat \theta$ to estimate any parameter $\theta$ ...
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French website Providing Instruction/Tutorials on Statistical Theory
This is somewhat of an odd question for CV, but since it's a question about statistical education, I think it falls within the scope of CV. Several years ago I stumbled across a French website that ...
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Dealing with auxiliary random variables for Mean-Field Variational Inference in Bayesian Poisson factorization
I am studying as a part of a class assignment a recent paper on Poisson factorization. Some points of the paper regarding the usage of some auxiliary variables are not clear to me. I would like to ...
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Linear Regression - Confidence interval for mean response vs prediction interval
I understand the concept of a confidence interval for the mean response (fitted line) for simple linear regression $y$ = $\beta_{0}$+$\beta_{1}$$X_{i}$. It is that taken over many times, with 95% ...
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Deriving the maximum likelihood for a generative classification model for K classes
In Christopher Bishop's book "Pattern Recognition and Machine learning", there is the following question:
Consider a generative classification model for $K$ classes defined by the prior class ...
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Conjugate of Weibull with shape known
This isn't exactly a homework problem but rather a self-selected problem I'm doing to prepare for a midterm.
I can see from Wikipedia that it is an inverse gamma but I am unable to reach the ...
CommunityBot
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Asymptotic properties of functional models
When working in Functional Data Analysis, a classical "preprocessing" step is to represent the "observations" using a B-spline expansion:
$$
X_i(t) \approx \sum_{j=1}^J \lambda_{ij}...
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How to show a UMVUE exists only if $g(p)$ is a polynomial of degree at most $n$?
Let $X\sim Bin(n,p)$. The problem is to show that a UMVUE can exist for $g(p)$ only if $g(p)$ is a polynomial in $p$ of degree at most $n$.
For the case when $g(p) = \frac{1}{p}$ we can show that it ...
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Minimum-variance unbiased estimator to estimate quantiles when the errors are normal distributed
What is the minimum-variance unbiased estimator to estimate quantiles when the errors are normal distributed?
median
When we wish to estimate the median, $\mu$, of a normal distributed variable then ...
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Partitioned regression model: estimator of beta 1
below is an exercise that is really giving me a hard time, I believe that there is a simple way around it but I can not find it:
Assume the correct regression model is
Y = X$\beta$ + $\epsilon$
for E(...
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Does Cross-Validation Really Work?
This question was taken from "The Elements of Statistical Learning" by Friedman, Hastie and Tibshirani (question 7.10)
Consider a scenario with N = 20 samples in two equal-sized classes, and p = 500 ...
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Variance of quotient of Poisson random variable and sum of the Poisson sample
Let
$$Y_1\sim \operatorname{Poisson}(\lambda_1)\\Y_2\sim \operatorname{Poisson}(\lambda_2),$$ where $Y_1$ and $Y_2$ are independent, and $\lambda_1, \lambda_2>0$.
What is the variance of $$\frac{...
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