# Questions tagged [estimators]

A rule for calculating an estimate of a given quantity based on observed data [Wikipedia].

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### How to find asymptotically normal estimator if I know probability density function [closed]

I have $X_1, X_2,\ldots,X_n$ be a random sample of size n from a distribution with probability density function: $$p(x) = \theta^2xe^{-\theta x}I (x > 0).$$ How can I find an asymptotically normal ...
1 vote
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### Show that $T=\sum_{i=1}^n X_i$ is a sufficient statistic for $p$ [duplicate]

I try to use the definition of sufficient statistic to prove that Suppose that $X_1,\dots, X_n$ is an iid random sample from $X\sim \mathrm{Bernoulli}(p)$. Show that $T=\sum_{i=1}^n X_i$ is a ...
• 557
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### Compare variance estimators in complex sampling designs by simulations

I need to find the best variance estimator of my parameter $\theta$ using complex sampling data. My survey data with dimension N are drawn with a two-stages stratified sampling. I thus began from my ...
1 vote
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### Understanding Wilson confidence interval for estimating precision of ML model

Two related questions from statistics noob. Can someone recommend a good statistics textbook that covers Wilson confidence interval? The reason why I'm looking for Wilson CI specifically is that I am ...
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### Let $X_1,\dots, X_n$ be random sample from $Bernoulli(p)$. Which estimator is better?

Let $X_1,\dots, X_n$ be random sample from $Bernoulli(p)$. Compare the risks of the squared loss of two estimators of $p$: $$\hat{p}_1=\bar{X}, \, \hat{p}_2=\frac{n\bar{X}+\alpha}{\alpha+\beta+n}$$...
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### Estimating a light field from diffracted images

I am a physicist, and the following problem has arisen in my research: Given functions $G_j:\mathbb{R}^2\rightarrow\mathbb{R}$ and parameters $\alpha_j\in\mathbb{R}$, for $j=1,2,\dots, N$, find two ...
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