Questions tagged [unbiased-estimator]

Refers to an estimator of a population parameter that "hits the true value" on average. That is, a function of the observed data $\hat{\theta}$ is an unbiased estimator of a parameter $\theta$ if $E(\hat{\theta}) = \theta$. The simplest example of an unbiased estimator is the sample mean as an estimator of the population mean.

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Unbiased estimator of the reversed regression

Suppose I have random variables $X$ and $Y$. I am interested in an unbiased estimator of $\mathbb{E}[Y | X]$, but I performed regression the other way and have $\mathbb{E}[X |Y]$. Under what data ...
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Unbiased estimate of success probability

Typically we assume independence to estimate the probability of success i.e. probability of head in a coin tossing example. Means we toss a coin $n$ times and see how many times we get ...
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Unbiased Estimator of Nugget Effect

Question: I am trying the measure the nugget effect, which is parameterized by $(1-\lambda)$ in the following variance-covariance used to describe the multivariate normal distribution of my n-...
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Unbiased estimator of mean divided by square root of second moment [closed]

Let $X$ be some random variable. Assume that $$\mu = \mathbb{E}X,\,\delta = \sqrt{\mathbb{E}X^2}$$ are well defined and finite (in other words $X$ has first two moments). Now suppose that $X_1,...,X_n$...
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What estimator and R package can be used for staggered difference-in-difference with (non-panel) cross-sectional data, controls and interactions

I am trying to run a difference-in-difference analysis in R. My data is non-panel, so I am reliant on a TWFE model where I have groups of individuals who are ...
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Question on nonlinear least squares

Consider the following equation for $Y>0$: $$(1) \quad \log(Y)=\log(\gamma)+\log(\alpha+\beta X)+\epsilon.$$ Assume that $E(\epsilon| X)=c\neq 0$. What are the consequences of this assumption on ...
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Proving an Estimator of the sample variance to be MVUE

Question: Prove that $\hat{\sigma}_x^2=\displaystyle\frac{1}{N-1}\sum_{i=1}^N(X_i-\overline{X})^2$, with $\overline{X}=\frac{1}{N}\sum_{i=1}^N X_i$ is an unbiased, minimum variance estimator of the ...
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Degrees of freedom for biased sample autocorrelation function

I want to find the expression for the a biased estimate of the autocorrelation function for a time series $X$, and am doing this from the biased estimated autocovariance function for lag $k$, divided ...
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How to compute the bias of the auto-normalized importance sampling estimator

A preceding post has compared auto-normalized importance sampling with ordinal importance sampling. Beginner readers shall be directed there, but I will remind the readers of just enough elements for ...
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Why weighted importance sampling is a biased estimator?

By simple math, we can have $$E_P[f(X)] = \sum_X f(x)p(x) = \sum_X f(x)\frac{p(x)}{q(x)}q(x) = E_Q[f(X)\frac{P(X)}{Q(X)}],$$ which can be approximated by Monte Carlo sampling in two ways. 1. Normal (...
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When to calculate the bias corrected geometric mean

Most sources give a simple equation to compute the geometric mean (GeoMean) of data samples from a lognormal distribution. GeoMean = exp(m) where m is the mean of ...
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On unbiasedness of an optimal forecast

Diebold "Forecasting in Economics, Business, Finance and Beyond" (v. 1 August 2017) section 10.1 lists absolute standards for point forecasts, with the first one being unbiasedness: Optimal ...
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Unbiased estimator for mean

The question: Given a random sample $X_1,...,X_n$ show that $\frac{1}{n}\sum_{i=1}^n X_i$ is an unbiased estimator for $E(X_1)$. My confusion: Given a statistical model $(\Omega,\Sigma,p_{\theta})$, ...
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Covariance of Best Linear Unbiased Estimators and arbitrary LUE

I'm working on a problem involving two linear unbiased estimators $T$ and $T'$ of a parameter $\theta$, defined from a sample $\{X_1, \dots, X_n\}$ with mean $\theta$ and finite variance. I aim to ...
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Why does not this underlying hypergeometric distribution lead to unbiased estimators?

This example is take from Lippman's "Elements of probability and statistics". Let N be the number of fish in a lake the warden wants to estimate. He catches 100 fish, tags them and releases ...
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Do you change the mean / standard deviation when calculating the unbiased normalised autocorrelation function?

I am trying to calculate the unbiased normalised autocorrelation function. I think this field is a little complicated as different sources appear to use different nomenclature to describe the same ...
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How to estimate the age of players correctly?

I have the data of players active on a gaming console and the playtime hours corresponding to the games they have played and their age. I want to analyze the top (say 10) games that the people between ...
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Consider the population $R^2$: $$\rho^2 = 1- \frac{\sigma^{2}_u}{\sigma^{2}_y}$$ This equation describes the proportion of the variation in $y$ in the population explained ...
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What are the uniformly minimum variance unbiased estimators (UMVUE) for the minimum and maximum parameters of a PERT distribution?

I believe the answers to this question are the sample minimum and the sample maximum, but I have not been able to find a reference or proof of this.