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Questions tagged [estimators]

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

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Looking for unbiased estimators for Poisson probabilities

I am looking for unbiased estimators for Poisson probabilities. That is, some estimator $\hat{g}(k)$ such that $E( \hat{g}(k) ) = \text{Poisson}(k|\lambda)$ I discovered one in this old paper: ...
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How does one calculate Fisher-consistency factor for Rousseeuw and Croux's $S_n$ for empirical distribution?

In "Alternatives to the Median Absolute Deviation" (Rousseeuw and Croux, J. Amer. Statistical Assoc, 88(424), 1993, pp.1273–1283), the authors described an estimator of SD better than median absolute ...
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How to estimate an activity based on self reported activity in a social network

I help run a social network for rock climbers who self report what they have climbed on a specific day, and optionally who they climbed it with. These climbers who self report are a perfect lower ...
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Comparison of GMM and ML estimators for regression with correlated errors

Consider a linear model with normally distributed, autocorrelated errors \begin{aligned} y&=X\beta+\varepsilon \\ \varepsilon&\sim N(0,\sigma^2_{\varepsilon}) \text{ and autocorrelated.} \end{...
260 views

Sample mean is always an optimal estimator of the mean?

Suppose we have $T_i,i=1..n$ i.i.d. with unknown distribution and we want to estimate $E[T]$. Note that in this setting we are not estimating E[T] as a parameter of a parameter-dependent family of ...
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Are there differentiable estimators for Entropy?

I have recently came across a paper on estimation of Information theoretic measure such as Entropy, Mutual Information and divergence, using a Mean Nearest Neighbor approach. Since, the estimator is ...
497 views

Why do we divide by the degree of freedom?

This might be trivial and vague question, but I still don't understand why when creating test statistics or estimators we always divide by the degree of freedom. Just to give examples of what I'm ...
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Principled way comparing and evaluating learned features/variables of estimators?

Does anyone know of any principled ways to compare and evaluate estimators based on what features have they learned. Basically I am interested in showing what features have these estimators picked up ...
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variance estimator for a symmetrical two-sides censored normal distribution

Suppose to draw a sample of $n$ observations from $X \sim \mathcal{N}(0,\sigma)$, with observations outside the interval $(-c,+c)$ censored; $c$ is known and one can conveniently set $c=1$, for ...
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Policy evaluation in contextual bandit setting

I am currently reading a paper whose links is (Exploration Scavenging) http://delivery.acm.org/10.1145/1400000/1390223/p528-langford.pdf?ip=128.135.98.49&id=1390223&acc=ACTIVE%20SERVICE&...
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(contextual bandit problem) What does 'identical draw' mean here?

I am currently reading a paper (Learning from Logged Implicit Exploration Data) whose link is below. https://arxiv.org/pdf/1003.0120.pdf The paper supposes we have a set of possibly deterministic ...
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Bias of Pearson correlation estimator of two Bernoulli variables

Crossposting link: https://math.stackexchange.com/questions/3312349/bias-of-pearson-correlation-estimator-of-two-bernoulli-variables Suppose we have two correlated Bernoulli random variables, $X_j$ ...
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quick questions about a contextual bandit problem

I am currently reading the paper "Learning from Logged Implicit Exploration Data" https://arxiv.org/pdf/1003.0120.pdf. But I believe the questions I have can be answered without reading the whole ...
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Expected value without complete sample space

The book way: Suppose, we have a bag with 8 balls numbered 1-8, we want to estimate the population parameter mean. we note down the entire sample space. (1,1)(1,2).. (8,8) calculate mean of each ...
717 views

Huber M-Estimator calculation

I found out that we can calculate some estimator depends on the objective function. Where if we want to minimize the least square $\sum (x_i - \theta)^2$ the best estimator is the mean. And if we want ...
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Mean Squared Error as quantifier of the Bias-Variance tradeoff

I have acquired the impression that many of the people doing statistical work, will prefer a biased estimator $\hat b$ to an unbiased one $\hat \beta$, if the former has lower Mean Squared Error. This ...