Questions tagged [minimum-variance]
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Predicting simulated data for a known curve
I have hit a roadblock with a research problem and could really use your expertise.
I have a pre-existing curve created by extrapolating known fitted experimental data. As shown below, the x-axis is, ...
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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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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.
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UMVUE for a Uniform distribution [duplicate]
How did we derive the PDF and CDF highlighted in green?
Thanks
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Minimizing variance of sequence of independent but not identically distributed random variable
I tried to work on the problem
Let $(X_n)$ be a sequence of independent random variables with $E[X_n]=\mu$ and $Var[X_n]=n$ for every $n \in \mathbb{N}$. Find the statistic of the form $\sum_{i=1}^...
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For a given $Y$ , what is the minimum variance of a $X$ such that $E[Y|X]=X$?
Suppose $Y$ is a given (real-valued continuous) random variable. We define any variable $X$ as exogenous to $Y$ if $\forall X: E[Y|X]=X$. The question is this: For a given $Y$ , What is the minimum ...
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Foreacast Combinations: derivation of minimum MSE / variance approach
I am just despairing of the derivation of the minimum variance procedure. The method of the combination of forecasts was first established in 1969 by Bates and Granger. They also invented the minimum ...
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Finding UMVUE for exponential sample [duplicate]
Let $X_1,...,X_n$ be a random sample of i.i.d. exponential distribution with probability density function $$f(x|\theta)=\frac{1}{\theta}exp(-\frac{x}{\theta}), \ x\geq0$$
Let $S_n=\sum_{i=1}^nX_i$ and ...
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Experimental Design: Choose Data Points to Minimize Quadratic Term Variance in Multiple Regression
$\newcommand{\eps}{\varepsilon}\newcommand{\szdp}[1]{\!\left(#1\right)}
\newcommand{\szdb}[1]{\!\left[#1\right]}$
Problem Statement: Suppose that you wish to fit a model
$$Y=\beta_0+\beta_1x+\beta_2x^...
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Prove that the variance of the Generalized Least squares estimator is less than the variance of the OLS estimator
Suppose, we consider the following regression model, $$Y = X\beta + \varepsilon$$ where $\varepsilon$ ~ $N(0, \sigma^2V)$ and V is a known $n\times n$ non-singular, positive definite square matrix.
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Proof Sample Variance is Minimum Variance Unbiased Estimator for Unknown Mean
I am trying to prove that the unbiased sample variance is a minimum variance estimator. In this problem I have a Normal distribution with unknown mean (and the variance is the parameter to estimate so ...
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Error in Derivation for Control Variate Variance?
I'm trying to derive the variance for a control variate estimator, but I seem to be missing a term that allows me to end up with the covariance in the final answer.
Let $f(x)$ be my function and let $...
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How to find an minimum variance unbiased estimator for an integer parameter?
Consider multiple observations $x[n]$ for an integer parameter $A$ under White Gaussian Noise $w[n]$:
$x[n]=A+w[n]; \quad$ $n=0,1,...,N−1$ with $w[n] \sim N(0,σ^2)$.
Is it possible to have an minimum ...
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Rao-Blackwell for Minimum-Variance Unbiased Estimator
Let $X$ be an observation from a distribution with probability mass
function:$f(x;\theta) =
\left(\frac{\theta}{2}\right)^{|x|}(1-\theta)^{1-|x|}I_{\{-1,0,1\}}(x),
\, \theta \in (0,1).$ Use Rao-...
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The UMVUE of ratio of parameters for two uniform distributions,
Let $X_1,\ldots,X_m$ be i.i.d. having the uniform distribution $U(0, \theta_x)$ and $Y_1,\ldots, Y_n$ be i.i.d. having the uniform distribution $U(0, \theta_y)$. Suppose that $X_i$’s and $Y_j$’s are ...
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