Refers generally to a property of a statistical procedure to go to the "right" place as the sample size tends to infinity, primarily referring to estimators converging to the true parameter value as the sample sizes diverges.
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23 views
Consistent estimator with var=0
I'm trying to think of an example of a consistent estimator with var=0 but I'm having a hard time.
I pretty sure it exists but I'm unable to find one.
Any help\hints would be much appreciated.
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15 views
How to test inconsistency / within-subject variance across time?
I have this dataset where I have DV measured over 5 time points for every subject (over about 30 subjects).
If I graph the values of individual subjects over time and look at them, there are no ...
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31 views
counterexample for the sufficient condition required for consistency
We know that if an estimator is an unbiased estimator of theta and if its variance tends to 0 as n tends to infinity then it is a consistent estimator for theta. But this is a sufficient and not a ...
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74 views
Consistency of sample quantile
I'm new to statistics and recently I learnt about non-parametric estimation. On the estimation of empirical quantiles, many notes talk about the asymptotic behavior of sample quantiles. The proof is ...
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1answer
79 views
Is optimizing α for partitions of a scale a sensible method for factor analysis? (was: relation between consistency and unidimensionality)
Cluelessness Disclaimer
I'm a statistics noob so if at all possible, please don't stone me. Also write slowly and in simple terms.
I'm wondering what the relation between the internal ...
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45 views
Assessing the consistency of an estimator of the average path length of a large network
I have found the following in a network-science article and would like clarification of what the authors are claiming:
We observe that the root mean square of the difference between the empirical ...
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1answer
61 views
Conditions in law of large numbers
The (Strong) Law of large numbers states that
$ \frac{1}{N}\sum_{k=1}^N h(X_k) \rightarrow \mathbb{E}\left[h(X)\right]$
a.s in $\mu$ as $N\rightarrow \infty$.
but I can't find any conditions on ...
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71 views
Inference on original population based on sample - estimating sampling probability
In my research I am working on some data (let’s call it sales data), however we almost have no information on the original sample. My goal is to come up with possible explanations on how it could be ...
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135 views
Asymptotic normality of MLE in exponential with higher-power x
Given the distribution:
$f(x;\theta) = \frac{3}{\theta}x^2e^{-x^3/\theta}$ if $x>0$
the MLE for $\theta$ is $\frac{1}{n}\sum_{i=1}^n x_i^3$. It's an unbiased estimator with variance $\theta^2/n$. ...
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0answers
100 views
Consistency of estimator
Regression: Wage=b0+b1collegegrad, where collegegrad is a dummy variable. Suppose you want to estimate the wage ratio between college graduates and non-college graduates. Is the estimator theta=b0/b1 ...
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86 views
Measures of internal consistency of survey items
I have a question on a survey that asks students how useful a feature of the software was that they used for learning. I then have three questions that assess in what way the feature was useful. The ...
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391 views
Are inconsistent estimators ever preferable?
Consistency is obviously a natural and important property estimators, but are there situations where it may be better to use an inconsistent estimator rather than a consistent one?
More specifically, ...
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4k views
What is the difference between a consistent estimator and an unbiased estimator?
I'm really surprised that nobody appears to have asked this already...
When discussing estimators, two terms frequently used are "consistent" and "unbiased". My question is simple: what's the ...
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1answer
188 views
Consistent estimator for probability density function at a given point
I am trying to conduct a simulation study on a variation of the kernel density estimator. In that experiment, there is a parameter in one of my formulas that involves the value of the unknown pdf at a ...
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1answer
128 views
Convex cost functions and Fisher consistency
In Section 4.2 of the paper by Boucheron et al., the authors argue that the minimizer $f^*$ of the cost functional
$$A(f) = \mathbb{E}\{\phi(-Yf(X))\}$$
is such that the classifier $g^*$, constructed ...
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0answers
102 views
How does one derive the Fisher-consistency correction factor for Rousseeuw and Croux's $S_n$ (and $Q_n$)?
In "Alternatives to the Median Absolute Deviation" (Rousseeuw and Croux, J. Amer. Statistical Assoc, 88(424), 1993, pp.1273–1283) and a few other papers from the same authors published in ...
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3k views
How to show that an estimator is consistent?
Is it to show that MSE = 0 as $n\rightarrow\infty$? I also read in my notes something about plim. How do I find plim and use it to show that the estimator is consistent?
