# Questions tagged [estimator]

For questions about estimators; an estimator is an approximations of a parameter that is using the avaiable data. There could be multiple estimators for a particular parameter.

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### Showing that $\frac{\bar{X}}{10}$ is an unbiased estimator for p

Let $X_{1}, X_{2}, X_{3}, X_{4}, X_{5}$ be a random sample from a binomial distribution with $n=10$ and $p$ unknown. How do I show that $\frac{\bar{X}}{10}$ is an unbiased estimator for $p$ and then ...
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### What is Roberts's method for gradient estimation?

Graphics Gems II, chapter II.9 (Image File Compression Made Easy) says: These constraints are easily met for arithmetic prediction using Roberts’s method L.R., a “poor man’s Lapacian” (gradient ...
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### Finding unbiased estimators for the mean and variance of $X \mid Y = y$ from realizations $x$ with some belief of $Y$

I will start with some background which can be skipped. I am tracking an object in space using a sensor. The variable Y denotes some discrete property that I can track with some amount of uncertainty. ...
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### Confidence interval and moment

Suppose a random sample of size $n = 9$ is taken, where $X$ is normally distributed with unknown mean $\mu$ and unknown variance $\sigma^2$. Consider the following cases (a) Before the sample is taken,...
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### Finding the variance of MLE and comparing to MOM from a gamma distribution.

This is from Casella Berger chapter example 10 (11) part d. we have the pdf $f(x|\mu,\beta)= \frac{x^{\mu/\beta -1 e^{-x/\beta}}}{\gamma(\mu/\beta) \beta^{\mu/\beta}}$. This pdf was reparameterized ...
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### understanding the proof that the average of sum of i.i.d cauchy is not a consistent estimator of location parameter

Consider $X_1, X_2, ... ,X_n \sim_{i.i.d} Cauchy(\theta), \bar{X} = \frac{1}{n}\sum_{i=1}^n{X_i}$ To prove that it is inconsistant, consider the characteristic function of $X_i$ and $\bar{X}$, which ...
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### Compute a Monte Carlo estimate. Which of the variances (of $\hat{\theta}$ and $\hat{\theta}^{*}$) is smaller, and why?

Compute a Monte Carlo estimate $\hat{\theta}$ of $$\theta = \int_{0}^{0.5} e^{-x} dx$$ by sampling from Uniform$(0, 0.5)$, and estimate the variance of $\hat{\theta}$. Find another Monte Carlo ...
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### How to estimate population by using capture-recapture method

Recently I am studying using statistical methods to estimate animal abundance. It seems that the mark recapture method is a widely used statistical method to do it. However, there are some concepts I ...
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### understand the solution to the unbiased estimator of area of circle when given n independent radius $R$ measurement with error $\sim N(0,\sigma^2)$

$S = \pi R^2$ $E(\bar{X}^2) = Var(\bar{X})+(E(\bar{X}))^2=\sigma^2/n + R^2$ then it states thats an unbiased estimator of $\sigma^2/n = \frac{1}{n(n-1)} \sum_{i=1}^n(X_i-\bar{X})^2$. However, when i ...
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### Independence between $2$ Pearson Correlation Coefficients

Suppose that $X_1, X_2, Y$ are three scalar Gaussian distributed variables. Suppose we know that $X_1$ independent from $X_2$. However, $X_1, Y$ could be correlated. Similarly, $X_2, Y$ could be ...
Let $X = (X_{1},...,X_{n})$ be a random sample from the normal distribution with mean $\theta \in \cal{R}$ (real numbers) and variance 1. Whether the estimand $g(\theta) = |\theta|$ has an unbiased ...