All Questions
Tagged with estimators consistency
67
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Unbiased and consistent estimator with positive sampling variance as n approaches infinity? (Aronow & Miller) [duplicate]
In Aronow & Miller, "Foundations of Agnostic Statistics", the authors write on p105:
[A]lthough unbiased estimators are not necessarily consistent, any unbiased estimator $\widehat{\...
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523
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Asymptotic unbiasedness + asymptotic zero variance = consistency?
Here, Ben shows that an unbiased estimator $\hat\theta$ of a parameter $\theta$ that has an asymptotic variance of zero converges in probability to $\theta$. That is, $\hat\theta$ is a consistent ...
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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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Assumptions needed for consistency of plug-in estimator
Assume $X,Z$ are random variables and let $x_0$ be a fixed number. I want to estimate $A =\mathbb{E}_{X,Z}[\frac{X}{P(X=x_0|Z)}]$.
If $P(X=x_0|Z=z)$ is known for all $z$ we can apply the LLN and ...
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Mathematical Step for consistency
Let me state my problem from the beginning:
Let $i$ be an index representing countries ($i = {1,2,\ldots,N }$), and $t$ represent time, denoted as available data for country $i$ ($t = {1,2,\ldots,T_i }...
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1
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Difference between consistent and unbiased estimator [duplicate]
I have a problem where I have to think of an example to explain a practical example of consistency and unbiased. The example I thought of is the sample mean.
Consistency is when the estimator (sample ...
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1
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Is convergence in probability implied by consistency of an estimator?
Every definition of consistency I see mentions something convergence in probability-like in its explanation.
From Wikipedia's definition of consistent estimators:
having the property that as the ...
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1
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Does increasing number of observations lead to the decreasing of Mean Square Error of consistent estimators?
I know that not all weakly consistent estimators exhibit MSE-consistency : https://stats.stackexchange.com/a/610835/397467.
Anyway, does increasing the sample size leads to a reduction in their mean ...
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682
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What does the likelihood function converge to when sample size is infinite?
Let $\mathcal{L}(\theta\mid x_1,\ldots,x_n)$ be the likelihood function of parameters $\theta$ given i.i.d. samples $x_i$ with $i=1,\ldots,n$.
I know that under some regularity conditions the $\theta$ ...
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What 's the $(\Omega,\mathcal{F},P_{\theta} )$ those $T_{n}$ defined on?
Definition (Consistency)
Let $T_1,T_2,\cdots,T_{n},\cdots$ be a sequence of estimators for the parameter $g(\theta)$ where $T_{n}=T_{n}(X_1,X_2,\cdots,X_{n})$ is a function of $X_{1},X_{2},\cdots,X_{n}...
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I need to prove that $\hat\theta=\max\{X_1,...,X_n\}$ is a mean square consistent estimator for $\theta$
Let $X_1,...,X_n$ a i.i.d from a population with distribution $U[0,\theta]$, i.e.,
$f_{X_i}(x)=\frac{1}{\theta}g_{[0,\theta]}(x)$, for $i=1, \ldots, n$
where
\begin{align}
g_{[0,\theta]}(x) =
\begin{...
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142
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Consistent or inconsistent estimator
If $\hat{\theta}_n$ is an estimator for the parameter $\theta$, then the two sufficient conditions to ensure consistency of $\hat{\theta}_n$ are:
Bias($\hat{\theta}_n)\to 0$ and Var$(\hat{\theta}_n)\...
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Consistency of a simple estimator for $y_i = \beta_1 x_i + u_i$
Let $y_i = \beta_1 x_i + u_i$ for $i=1,2,..,n$. If I define $$\hat \beta_1 = \frac{y_1 + y_n}{x_1 + x_n}$$ then whether my $\hat \beta_1$ will be consistent or not in this setup?
For my estimator to ...
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Are the classical moments consistently estimated from a single realization drawn from a given PSD?
Given a sequence $\{x_k\}_{k=-N}^{N}$ having power spectral density $S(f)$, we know that that "single realization PSD"
$$
\frac{\Delta t^2}{T} \left| \sum_{k=-N}^{N} x_n \exp(-2\pi i f n \...
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Does a linear regression assume that the (unconditional) predictor data is i.i.d?
Say I have a linear, cross sectional relationship -
$y_{i}=x_{i}b+e_{i}$.
Where $E(e_{i}|X_{j})=0$ for all relevant $i,j$. Given this, one can prove that the OLS estimator is unbiased.
However, ...
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