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Results tagged with unbiased-estimator
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user 11887
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.
40
votes
Accepted
What is the intuition behind defining completeness in a statistic as being impossible to for...
I will try to add to the other answer. First, completeness is a technical condition which is justified mainly by the theorems that use it. So let us start with some related concepts and theorems where …
- 82.8k
12
votes
Questions about unbiased sample variance
Many misunderstandings here. It would be easier to answer if you defined your terms and included some formulas. But:
1) NO, it is not correct to say that an unbiased estimator is necessarily close …
- 82.8k
11
votes
Best estimator of the mean of a normal distribution based only on box-plot statistics
An exact answer will be difficult, so first I will look at asymptotic theory. Answers from that could be tested by simulation, comparing it to a maximum likelihood estimator computed by maximizing an …
- 82.8k
7
votes
Accepted
Variance of unbiased estimator for the shape parameter of Pareto distribution
I will write the standard Pareto distribution with density
$$
f(x;\alpha,x_m)=\frac{\alpha x_m^\alpha}{x^{\alpha+1}}\cdot I(x > x_m),
$$ for some $\alpha>0, x_m>0$. Then the loglikelihood function …
- 82.8k
7
votes
Accepted
Is the sample mean always an unbiased estimator of the expected value?
Answered in comments: The first question is answered immediately using the linearity of expectation. The second conclusion is true only when the underlying distribution has finite variance, in whi …
- 82.8k
6
votes
Accepted
Where does linear regression fit into the bias-variance tradeoff?
OLS is an unbiased estimator assuming the model is true, which is to say,
Effects are exactly linear
All variables with non-zero effects are included
All interactions are included
no non-linear effe …
- 82.8k
5
votes
Accepted
Unbiased Estimator of Largest Mean of Two Normal Distributions
Finding an exactly unbiased estimator is probably impossible, so a practical solution is bootstrapping. I will here show nonparametric bootstrap, but small modification give a parametric bootstrap. S …
- 82.8k
5
votes
Accepted
Is the sample mean an unbiased estimator of population mean in the presence of autocorrelation?
Yes, autocorrelation (or spatial correlation or ...) do not destroy the unbiasedness of the sample mean as an estimator of population mean.
Expectation is a linear operator, so when you calculate the …
- 82.8k
5
votes
Ratio of Unbiased Estimators
No, it will not be unbiased (unless the estimator of the denominator have zero variance.) And it will not help if the numerator and denominator are independent. In general, if $\hat{\theta}$ is an un …
- 82.8k
4
votes
Is an WLS estimator unbiased, when wrong weights are used?
It is unbiased, let's see: Let the linear model be $Y=X\beta +e$, in matrix form, with $E e=0$ and the variance-covariance matrix of the errors $e$ be $\Omega$. We use for weights the matrix $W$. Th …
- 82.8k
4
votes
Accepted
Estimating ratio of regression coefficients
Reformulate the problem and maybe use nonlinear regression. If your regression model is
$$ y_i=\beta_0 + \beta_1 x_{i1} + \beta_2 x_{i2} + \epsilon_i $$ and the interest parameter is $\theta =\frac{\b …
- 82.8k
3
votes
Accepted
What is an "unbiased forecast"?
We can write your predictor for $Y_h$ as
$$
\widehat{Y_h}=T\left(W(x,y),X_h\right)
$$
Then $\widehat{Y_h}$ is unbiased as a predictor for $Y_h$ if
$$ \DeclareMathOperator{\E}{\mathbb{E}}
\E \{\wideh …
- 82.8k
3
votes
Empirical Implications of Unbiased Estimators
if we repeat an experiment under identical conditions many times, the average value of the estimate will be close to the true value
was said, and the following figure from Understanding "variance" i …
- 82.8k
2
votes
Unbiased estimators of the log odds
For the case $g(p)=1/p$, a more rigorous proof for nonexistence of unbiased estimators is For the binomial distribution, why does no unbiased estimator exist for $1/p$?. With $g(p)=\log\frac{p}{1-p}$ …
- 82.8k
2
votes
Accepted
What is the problem in the Neyman-Scott problem?
Partially answered in comments:
The problem has nothing to do with the fact that the bias can be corrected. It's that a particular procedure--namely, the Maximum Likelihood estimator--does not enjoy a …
- 82.8k