# Questions tagged [consistency]

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. Use also for Fisher consistency, the property that an estimator when applied to the complete population gives the right answer.

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### Show that bias term involving an indicator function convergences to zero

Assume that we have $N$ observations of i.i.d. data $(Y_i,X_i)_{i=1}^{N}$. We want to learn the model given by $Y=f(X)+\epsilon$. We use the data to estimate $\hat{f}$ using any machine learning ...
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### Consistency of estimators vs sample size

I understand that consistency of an estimator is large sample property, but does it make sense to talk about consistency in small samples as well? Can I say about the estimator that it is consistent ...
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### Unbiasedness and consistency of OLS

Does unbiasedness of OLS in a linear regression model automatically imply consistency? Edit: I am asking specifically about the assumptions for unbiasedness and consistency of OLS. If the assumptions ...
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### Consistency of least absolute deviation estimator (LAD) vs OLS

If we know that OLS estimator of beta in linear regression model is unbiased and consistent and we don't have any further assumptions (on errors or anything), will LAD estimator of beta be also ...
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### Quantile regression estimator - conditions for consistency and efficiency

What are the conditions for consistency and efficiency of Quantile regression estimator (for example LAD) in a linear regression model?
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### Let $X\sim\text{Rayleigh}(\theta^{2})$. Prove that $T_{n}$ is consistent, given that $T_{n}(\textbf{X}) = \frac{1}{2n}\sum_{i=1}^{n}x^{2}_{i}$

Let $X\sim\text{Rayleigh}(\theta^{2})$. Prove that $T_{n}$ is consistent, given that $$T_{n}(\textbf{X}) = \frac{1}{2n}\sum_{i=1}^{n}x^{2}_{i}$$ MY ATTEMPT To begin with, let us notice that \begin{...
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### Consistency test

I have data that consists of 7 characteristics for each participant. There are about 170 participants. The test was repeated in some time and the same 7 characteristics were acquired. I need to find ...
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### Cronbach's alpha for different items?

Can I perform a Cronbach's alpha test when the questions or items are completely different to each other as opposed to having similar questions written differently as a consistency measure?
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### Lagged dependent variables, bias and consistency

I am working through Christopher Dougherty's Introduction to Econometrics, and am struggling to fully grasp the consequences of lagged dependent variables in terms of bias and consistency. The key ...
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### Consistent estimation and valid inference when performing regressions on data with differing levels of granularity

Imagine that a dataset has a combination of variables of differing levels of granularity (e.g. an international sample of firms containing both firm-level and country level information). There are $K$ ...
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### Endogeneity and Consistency

So I learned about the endogeneity problem of linear regression in class today, where E[XU] and Cov[X,U] isn't equal to zero but some random constant c times a standard basis k-element vector with 1 ...
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### Consistent estimator and distribution function

a general question: If the distribution function $F_n$ of some estimator $T_n$ suffices \lim_{n \rightarrow \infty} F_n(x) = 1 \text{ or } 0 \forall x}. Does that imply that $T_n$ is consistent? I ...
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### first factor saturation vs. general factor saturation

a simple explanation between these two in the context of reliability analysis, specifically Cronbach's alpha.
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### Can any unbiased estimator be changed into a consistent estimator when estimating functions of the mean [closed]

For an i.i.d sequence of Random Variables $X_1, \dots, X_n$, each with mean $\mu = \mathbb E[X]$, the goal is to estimate some continuous function $f$ evaluated at the mean, $f[\mathbb E[X]]$. If ...
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### Chronbach's Alpha of Likert Item

My questionnaire is consists of ten 5-point scaled likert items. If the likert items have a good chronbach alpha, is it ok to take the average score of 10 items?