All Questions
Tagged with estimators point-estimation
24
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What is the difference between unbiasedness, consistency and efficiency of estimators? How are these interrelated among themselves? [duplicate]
!Efficiency(https://stackoverflow.com/20240427_193105.jpg). Given snapshot of the book states that among the class of consistent estimators, in general, more than one consistent estimator of a ...
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What is the variance decomposition method?
For $i = 1, \ldots, m$ and $j = 1, \ldots , n$ we have observations $x_{ij}$. We can assume that
$$
x_{ij} = y_{i} + z_{ij}, \qquad y_{i} \sim \mathcal{N}(\mu_{y},\sigma_{y}^{2}), \quad z_{ij} \sim \...
- 101
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Forming a consistent estimator for the area under the regression line
I am trying to solve the following problem:
Take the following simple linear regression model, where $x_i \in \mathbb R$:
$y_i=\beta_0 + x_i \beta_1 + \epsilon_i$
Given that:
$\mathbb E[\epsilon_i]=...
- 145
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Winsorized mean - trimming furthest points instead of both endpoints
I'm wondering if the Winsorized mean can be improved by trimming the 5% farthest points from the mean instead of trimming 5% on each endpoint. Concretely:
Consider the Winsorized mean, where we ...
- 6,688
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Trimmed, weighted mean
The trimmed mean (or truncated mean) is a robust version of the mean, designed to be robust to outliers. I am wondering what is the right trimmed version of a weighted average.
If I have a sample ...
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1
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50
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Mean-square convergence of maximum likelihood estimators: Examples?
From what I've gleaned from the literature, Cràmer, in his 1947 monograph Methods of Mathematical Statistics, proved convergence in probability of an MLE under certain regularity conditions. ...
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Is there a term for an estimator's probability of estimating an impossible estimand value?
This is similar to Mean Squared Error and Mean Absolute Error but in this case the loss function assigns estimates to $0$ when they are a possible estimand and $1$ when they are impossible.
As a ...
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What's the advantage of a point estimate over an interval estimate?
A point estimate is :
A single numerical value that is used to estimate the corresponding population parameter.
Whereas an interval estimate is :
An estimate that consists of two numerical values ...
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1
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1
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1k
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Most Efficient Estimator and Uniformly minimum variance unbiased estimator
I am studying Estimation theory from "Introduction to theory of statistics" by "Mood and Graybill".
After completing I thought I understood UMVUE (uniformly minimum variance ...
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97
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Taking Expectation Over Inverse Sum of Indicator Functions?
I'm working with a zero inflated Poisson distribution that has the following pmf:
$$f(y|w,\lambda)=wI[y=0]+(1-w)\frac{e^{-\lambda}\lambda^{y}}{y!}$$
I would like to find the expectation of the ...
- 154
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Variance Estimator Change if we know Population Mean? (Normal dist. example)
For a normal distribution $N(\mu, \sigma^2)$ a commonly used unbiased and consistent estimator of variance is
$$\hat \sigma^2=\frac{\sum_ix_i^2 + n(\bar x)^2}{n-1}=\frac{\sum_i(x_i-\bar x)^2}{n-1}$$
...
- 154
2
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373
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What is an intuitive of definition of "point identification" (point identified parameter) in econometrics?
I've recently come across the notion of point identification in several econometric papers.
See, e.g., https://scholar.harvard.edu/files/tamer/files/pie.pdf, who mentions point identification ...
- 153
2
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1
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266
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How to interpret a sampling distribution from a Frequentist and Bayesian perspective
I've read multiple of the threads about Bayesian vs Frequentist interpretations of probability, but I'm having trouble trying to reconcile them with the idea of the sampling distribution when ...
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nonexistence of a sufficient statistic
Let $X_1,X_2,\dots,X_n$ be a random sample from a $\Gamma(\theta,\theta)$ distribution. Then
$$
\prod_{i=1}^n f(x_i;\theta) = \frac{1}{\Gamma(\theta)^n\theta^n}(\prod_{i=1}^n x_i)^{\theta-1}e^{-\frac{...
- 220
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When can't Cramer-Rao lower bound be reached?
The Cramer-Rao lower bound (CRLB) gives the minimum variance of an unbiased estimator. One sentence in the wiki page says "However, in some cases, no unbiased technique exists which achieves the bound....
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