# Tagged Questions

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 ...

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### use corrected or uncorrected variance when calculating skewness & kurtosis?

In several online sources, e.g. NIST engineering statistics handbook I have read that for the calculation of skewness & kurtosis I should use N in the denominator instead of (N-1) when calculating ...
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### Unbiased estimate for treatment effect in block randomized experiment where probability of treatment varies by block

I want to analyze the results of a block randomized experiment. Within each block, units are randomized to treatment and control as if that block were a completely randomized experiment. Specifically, ...
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### Understanding the derivation of the unbiased expectation estimate

For context, I am reading David Barber's Bayesian Reasoning and Machine Learning book, section 27.1. He presents the following derivation that shows why monte carlo estimates of expectations are ...
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### The projection matrix and proof of an unbiased estimator for sigma-squared

Hi, given this information we are meant to prove that the above estimator is unbiased. I understand the proof for the most part (below). What I do not understand is the intuitive reason why the ...
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### If $X \sim \mathcal{P}(u)$, show that $S=(-1)^X$ is the UMVUE of $e^{2u}$

If $X \sim \mathcal{P}(u)$, show that $S=(-1)^X$ is the UMVUE of $e^{2u}$. I can't figure this out, finding UMVUE always confuses me. Any help is greatly appreciated
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### What is the intuition behind defining completeness in a statistic as being impossible to form an unbiased estimator of $0$ from it?

In classical statistics, there is a definition that a statistic $T$ of a set of data $y_1, \ldots, y_n$ is defined to be complete for a parameter $\theta$ it is impossible to form an unbiased ...
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### Cramer-Rao Lower Bound for the estimation of Pearson correlation

Given a bivariate Gaussian distribution $\mathcal{N}\left(0,\begin{pmatrix} 1 & \rho \\ \rho & 1 \end{pmatrix}\right)$, I am looking for information on the distribution of $\hat{\rho}$ ...
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### How to Prove Unbiased Estimator

I'm unsure of how to convince myself that $$\hat{\beta} = \frac{\sum X_i Y_i}{\sum X_i^2}$$ is an unbiased estimator when the regression model $$Y_i = \beta X_i + \epsilon_i$$ follows basic OLS ...
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### Estimating variance or coefficient of variation for population given total and count for four segments of population

My goal is to estimate the coefficient of variation for a population, but the data we have been given is very limited. All we have is the total and count for four segments of the population. The ...
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### If given statistic is unbiased estimator?

I am having trouble finding out and verifying estimators properties ( like unbiased, consistency sufficiency, efficiency ) but in this particular problem given below I have to find a constant such ...
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### Regression method if dependent variable is the absolute value of a continous variable [duplicate]

Suppose we have a dependent variable $Y$ that has normal distribution with a mean of $0$. If I run a regression model using the absolute value of $Y$, $|Y|$, i.e. $|Y| = b_1 + b_2 X + u$, my dependent ...
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Consider a consumption model with bivariate data points $(Y_i,X_i)$, $i=1,...,n$, with $Y_i$ consumption and $X_i$ income. The univariate model is $$Y_i=\beta X_i+u_i,$$ where $E(u_i|X_i)=0, \textrm{... 0answers 37 views ### Bias of an estimated Gaussian density I have an iid sample,$X_1,\dots,X_N \in R^d$, from a multivariate normal density with mean$\mu$and covariance matrix$\Sigma$. I am estimating the density$p(y) = N(y| \mu, \Sigma)$, using$\hat{...
I was wondering if the the following is an example of the law of iterated expectations. Say we observe the entire population of the random variable $X$. Call the mean of the population $\mu$ . ...