# Questions tagged [unbiased-estimator]

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 estimator of the population mean.

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### what is the issue with using sample count of unique values to estimate population count of unique values?

Let's say I am drawing a random sample of n values from a population with N values, and in the population, U of them are unique. If I observe u unique values in the sample, why can't I use that to ...
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### Unbiasedness and Variance of Predictions

Here is the problem I'm working on: I'm not quite sure if I'm showing either unbiasedness property right, and am stuck on finding the expressions for the variances. Here's what I've done so far. (a) ...
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### unbiased estimator for a parameter

1000 nodes are randomly sampled from a very large computer network and their “degree” (number of connections to other nodes) is recorded. N= 1000 Mean= 68.266 Variance= 8807.2905 maximum=1294 min= ...
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### Why is having low variance important in offline policy evaluation of reinforcement learning?

Intuitively, I understand that having an unbiased estimate of a policy is important because being biased just means that our estimate is distant from the truth value. However, I don't understand ...
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### Biased prediction (overestimation) for xgboost

I run xgboost and elastic-net on the same dataset for a classification problem, say we have ...
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### When are biased estimators with lower MSE preferred? [duplicate]

From wikipedia https://en.wikipedia.org/wiki/Bias_of_an_estimator : because a biased estimator gives a lower value of some loss function (particularly mean squared error) compared with unbiased ...
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### Does random sampling implies non-biased results?

Let's say that we want to estimate how much deforestation is done in the world considering 2 moments in time. We have a satellite that can take pictures anywhere in the world, but not of the entire ...
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### What are biased and inefficient estimators?

I’m studying statistics from Schaum’s Outline, which gives the following: ...
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### Proof of (weak) consistency for an unbiased estimator

I want to prove a theorem stating: An unbiased estimator $\hat{\theta}$ of the unknown parameter $\theta$ is consistent if $V(\hat{\theta}_n$) $\to0$ for ${n\to\infty}$. I've tried using the ...
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### cross-covariance estimation and variance reduction

Let $X,Y$ be two vector variables and $$\mathrm{Cov}(X,Y) = \mathbb{E}[(X-\mathbb{E}X)(Y-\mathbb{E}Y)^T]$$ their cross-covariance (but I think we could just pretend that's the covariance between two ...
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### Estimator with variance equal to Cramér-Rao lower bound in $N(x_i\theta,1)$-distribution

Let $Y_1,\ldots, Y_n$ be independent and $N(x_i\theta,1)$ distributed, with for each $Y_i$ a mean of $x_i\theta$ for known $x_1,\ldots,x_n$. In a previous section of this exercise I found that the ...
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### Estimator of binomial probability from poisson number of trials

I'm a lowly physicist, so I hope you will forgive me if I botch some terminology and notation here. I perform an experiment where on each trial I start with some number of particles $N$ that is ...
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### Conditional model with correlation between estimations

I am trying to estimate Click-Through-Rate (CTR) given the following two models: $$P(Click|Visible)$$ $$P(Visible)$$ The output is: $$P(Click) = P(Click|Visible)*P(Visible)$$ Unfortunately, P(...
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### What is the difference between BLUE and MVUE?

What is the difference between a Best Linear Unbiased Estimator (BLUE) and a Minimum Variance Unbiased Estimator (MVUE)? I know that "best" mean efficient, but that is also what "minimum variance" ...
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### Unbiasedness of Intrumental Variable Estimator

is instrumental variable estimator unbiased in the case of stochastic regressor X and how can i show this? (I know how to show consistency, i need to show unbiasedness)
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### When is the bias of a statistic of the form a/n + b/n^2 + c/n^3 +

In many books the bias-correction of the Jackknife resampling method is being prooved under the assumption, that the bias has a special form, namely a/n + b/n^2 + c/n^3 * ... Sometimes it's written "...
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### Do unbiased regression coefficents yield better prediction?

I ask myself if a have a omitted variables bias in my regression modell the coefficients of the model are biased so the mse growth because this coefficents are biased right? So does it mean if i ...
### Find $k \in R$ such that $P\left(\max\left\{\frac{{S_x}^2}{{S_y}^2}, \frac{{S_y}^2}{{S_x}^2}\right\} > k\right)= 0.05$
Let $\overline{X}$ and $\overline{Y}$ sample means and ${S_x}^2, {S_y}^2$ unbiased estimators for the variance of 2 independent random samples of size 7 with normal distribution with mean unknown and ...