# Questions tagged [estimation]

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### estimating transformation of linear function non-parametrically

Suppose I have a regression model as follows $$Y_i = f(X_i + \varepsilon_i),$$ where $\varepsilon_i$ is standard normally distributed. I want to estimate function $f(\cdot)$ non parmetrically. I ...
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### Is it harder to estimate the variance of a Gaussian compared to its mean?

In various ML talks I keep hearing that variance estimation is harder than mean estimation but I never really get why the above statement is correct. Is there a theoretical argument or a published ...
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### Determine probability of an event using maximum likelihood estimation

Problem I have a bag of many red and green balls. To find out the ratio between the two, I randomly picked balls with replacement. Out of the 100 outcomes, 60 were red balls and 40 were green balls. ...
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### Involving data length as a decision variable in a optimization for parameter estimation

Consider I have $N$ historical data as outputs from a unknown time-varying system. Assuming within any small time interval $T$, the time-varying system can be approximated by a linear time invariant (...
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### How do I choose between regression methods for inference?

Suppose my goal is to understand the relationship between variable $y$ and covariates $X$. Let's say $y$ is a rate, the number of success in $n$ trials, therefore bounded between $0$ and $1$. Now I ...
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### Why do OLS and logistic regression coefficients have opposite sign?

I have data $y$ which is the rate of success in $n$ trials. I also have covariates $X$ that I want to regress against $y$ to understand the relationship between them. I tried 2 different approaches. ...
1answer
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### Where plus 1 came from in variance estimation [duplicate]

While $$\mathrm{E}(\tilde{\mathrm{y}})=\alpha+\beta \tilde{\mathrm{x}}$$ Subject is Regression Analysis and this formula is from the "Features of Estimation ". and y is a neutral variable. ...
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### How are the number of actual rape cases estimated?

I see in news articles of number of rapes reported and an estimate for actual number of rape cases. I am interested in knowing about statistical techniques used for making such estimations. Also, are ...
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### Practical method to do MLE for natural parameters in exponential family

I encountered the following question in my research and I hope this is the correct place to post it. I'm following the notation in this lecture note by Michael I. Jordan. Assume random vector $X$ ...
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### estimating the total number of balls (n) after 2 draws of k balls

The problem is predicting the total number of balls (n) after 2 draws of k balls. After the first draw of k balls, we have marked them so we can see if we had them before. The balls are returns and we ...
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### Is the mundlak estimator equal to the within estimator?

Mundlak has proposed to estimate the following correlated random effects model:  y_{i t}=\boldsymbol{x}_{i t}^{\prime} \boldsymbol{\beta}+\overline{\boldsymbol{x}}_{i}^{\prime} \gamma+\omega_{i}+u_{...
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### Giving a job lecture on “minimax statistical estimation”. What kind of questions to expect?

As part of a job application process, I am giving a short "mock lecture" for students on minimax estimation in statistics. I will introduce the basic concept and give an example. I am able ...