# Tagged Questions

Any statistical process which seeks to approximate an unknown value, such as a distribution, a point estimate (e.g. mean), or confidence interval.

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### Why is sample standard deviation a biased estimator of $\sigma$?

According to the Wikipedia article on unbiased estimation of standard deviation the sample SD $$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i - \overline{x})^2}$$ is a biased estimator of the SD of the ...
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### Practical thoughts on explanatory vs predictive modeling [duplicate]

Possible Duplicate: Practical thoughts on explanatory vs. predictive modeling This question has been bugging me for some time, and I was going to write a blog post about it. However, I ...
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### Calculating required sample size, precision of variance estimate?

Background I have a variable with an unknown distribution. I have 500 samples, but I would like demonstrate the precision with which I can calculate variance, e.g. to argue that a sample size of 500 ...
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### Can the empirical Hessian of an M-estimator be indefinite?

Jeffrey Wooldridge in his Econometric Analysis of Cross Section and Panel Data (page 357) says that the empirical Hessian "is not guaranteed to be positive definite, or even positive semidefinite, for ...
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### What is an unbiased estimate of population R-square?

I am interested in getting an unbiased estimate of $R^2$ in a multiple linear regression. On reflection, I can think of two different values that an unbiased estimate of $R^2$ might be trying to ...
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### How to find confidence intervals for ratings?

Evan Miller's "How Not to Sort by Average Rating" proposes using the lower bound of a confidence interval to get a sensible aggregate "score" for rated items. However, it's working with a Bernoulli ...
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### Variance of the reciprocal II

Background I've recently read the paper Leo A. Goodman, On the Exact Variance of Products Journal of the American Statistical Association Vol. 55, No. 292 (Dec., 1960), pp. 708-713 from where I ...
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### Internal vs external cross-validation and model selection

My understanding is that with cross validation and model selection we try to address two things: P1. Estimate the expected loss on the population when training with our sample P2. Measure and report ...
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### Unbiased estimation of covariance matrix for multiply censored data

Chemical analyses of environmental samples are often censored below at reporting limits or various detection/quantitation limits. The latter can vary, usually in proportion to the values of other ...
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### What are complete sufficient statistics?

I have some trouble understanding complete sufficient statistics? Let $T=\Sigma x_i$ be a sufficient statistic. If $E[g(T)]=0$ with probability 1, for some function $g$, then it is a complete ...
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### Calculating the parameters of a Beta distribution using the mean and variance

How can I calculate the $\alpha$ and $\beta$ parameters for a Beta distribution if I know the mean and variance that I want the distribution to have? Examples of an R command to do this would be most ...
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### What is the difference between estimation and prediction?

For example, I have historical loss data and I am calculating extreme quantiles (Value-at-Risk or Probable Maximum Loss). The results obtained is for estimating the loss or predicting them? Where can ...
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### How to calculate Zipf's law coefficient from a set of top frequencies?

I have several query frequencies, and I need to estimate the coefficient of Zipf's law. These are the top frequencies: ...
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At many question-and-answer sites, like StackExchange, people can upvote or downvote each answer. These sites also typically try to use the votes to sort answers, so the answers that are most likely ...
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### Why squared residuals instead of absolute residuals in OLS estimation?

Why are we using the squared residuals instead of the absolute residuals in OLS estimation? My idea was that we use the square of the error values, so that residuals below the fitted line (which are ...
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### Bias correction in weighted variance

For unweighted variance $$\text{Var}(X):=\frac{1}{n}\sum_i(x_i - \mu)^2$$ there exists the bias corrected sample variance, when the mean was estimated from the same data: ...
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### Estimating parameters of a normal distribution: median instead of mean?

The common approach for estimating the parameters of a normal distribution is to use the mean and the sample standard deviation / variance. However, if there are some outliers, the median and the ...
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### How to get confidence interval on population r-square change

For sake of a simple example assume that there are two linear regression models Model 1 has three predictors, x1a, x2b, and ...
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### References on numerical optimization for statisticians

I'm looking for a solid reference (or references) on numerical optimization techniques aimed at statisticians, that is, it would apply these methods to some standard inferential problems (eg MAP/MLE ...
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### Dynamic calculation of number of samples required to estimate the mean

I am trying to estimate the mean of a more-or-less Gaussian distribution via sampling. I have no prior knowledge about its mean or its variance. Each sample is expensive to obtain. How do I ...
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### Estimation of exponential model

An exponential model is a model described by following equation: $$\hat{y_{i}}=\beta_{0}\cdot e^{\beta_{1}x_{1i}+\ldots+\beta_{k}x_{ki}}$$ The most common approach used to estimate such model is ...
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### Delta method and correlated variables

I have been reading about the delta method in regards to auto regressive distributed lag models. This is very new to me, so excuse any beginner mistakes. The problem is as follows: We have a model ...
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### How to do estimation, when only summary statistics are available?

This is in part motivated by the following question and the discussion following it. Suppose the iid sample is observed, $X_i\sim F(x,\theta)$. The goal is to estimate $\theta$. But original sample ...
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### How can I estimate unique occurrence counts from a random sampling of data?

Let's say I have a large set of $S$ values which sometimes repeat. I wish to estimate the total number of unique values in the large set. If I take a random sample of $T$ values, and determine that ...
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### How to evaluate quality of probability estimator for Bernoulli experiments?

Given that I have a set of bernoulli experiments, each with a different and unkown probability $p_i$ and an outcome $x_i$, and an estimator that for each experiment gives a prediction of the ...
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### Estimating beta-binomial distribution

Suppose that I culture cancer cells in n different dishes g₁, g₂, … , gn and observe the number of cells ni in each dish that look different than normal. The total number of cells in dish gi is ti. ...
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### Robust parameter estimation for shifted log normal distribution

I have a data set which fits a logNormal distribution quite well. (From a theoretical point of view, it is some hard-to-tackle quotient distribution). However, the data is quite dirty, so parameter ...
Population r-square $\rho^2$ can be defined assuming fixed scores or random scores: Fixed scores: The sample size and the particular values of the predictors are held fixed. Thus, $\rho^2_f$ is the ...
Consider a Poisson process with unknown parameter $\lambda$. We perform a sequence of $n$ observations at intervals $\overline{t}=t_1,\,t_2,\,\dots,\,t_n$. Each observation is a binary variable $x_i$ ...