# 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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### For an ideal Kalman filter, I have that the NEES test passes but NIS test does not?

Sorry if this is more of a debugging question, but I have been stuck on this supposedly simple NIS test for a very long while. If anyone knows any sources which cover the theory or implementation of ...
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### Granular regression with repeating dependent variable within group

I am estimating a standard OLS regression model where the unit of observation is inventor-firm-year level. The dependent variable I am interested in is patent count (a measure of inventor productivity)...
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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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### Consistency of IV Estimator

I have a quick question about the proof of the consistency of the IV estimator. I following the Davidson and MacKinnon (1st ed.) text where, as one of their assumptions, they state the following ...
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### Stochastic boundedness in consistency proof

I'm reading Knight and Fu (2000), Asymptotics for Lasso-Type Estimators and I don't understand why (6) and (7) imply consistency in Theorem 1 (copied and pasted below). I'm familiar with the standard ...
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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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### Example of non-consistency of M-estimators in case of pointwise converging criterion functions

When one wants to establish consistency of an M-estimator $\widehat{\theta}_n$, one typically requires uniform convergence of the criterion function $\theta \mapsto M_n(\theta)$. That is, one requires ...
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### What's the relationship between "bias-variance tradeoff" and "consistent model selection"?

I'm very confused about the relationship between "bias-variance tradeoff" and "consistent model selection". Based on my current interpretation, the ultimate goal of taking care of ...
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### Asymptotic normality implies consistency

I'm trying without success to solve the following exercise in my econometric textbook: Show that $\sqrt{N}\left(\widehat{\beta_1} - \beta_1 \right) \xrightarrow{d} \mathcal{N}(0,a^2)$, where $a^2$ is ...
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### Are sample quantiles consistent with population quantiles?

The Wikipedia page about quantiles describes two approaches to the definition of quantiles: population quantiles, and sample quantiles. The section on sample quantiles lists nine different flavors of ...
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### Demonstration of Convergence in Probability of the Average Prediction Error for a Consistent Machine Learning Algorithm

I'm quite new to this topic, but I've set myself the task of understanding how to demonstrate that the average of prediction errors in the sample for a machine learning algorithm, which consistently ...
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### Bias vs consistency in instrumental variable estimation

So in Mostly Harmless Econometrics, page 154, they analyse the bias of instrumental variables: They consider the case of one endogenous variable $x$, multiple instruments $Z$, and $\eta$ is the ...
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### Calculating MLE under restriction on coefficients

Consider the following simple linear regression model: $y_i = a + b \cdot x_i + \epsilon_i \space\space\space\space\space\space\space where \space i= 1, 2, 3, \cdots , n$ here $\epsilon_i \space's$ ...
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### Proof of Variable Selection Consistency for LASSO in Zhao & Yu, 2006

I'm going through the proof of Proposition 1 in Zhao & Yu, 2006 (https://www.jmlr.org/papers/volume7/zhao06a/zhao06a.pdf), titled On Model Selection Consistency of LASSO. The proof is in Appendix ...
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### Questions about efficiency of estimators with longitudinal data

I'm modelling data with repeated observations; I'm reading up on options and pitfalls, and have a few questions. Coefficient estimates are still unbiased and consistent in the presence of ...
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### Why are lags of the dependent variable a no-no in traditional random effects models?

This post says: Lagged versions of the dependent variable are a no-no in traditional random effects models. The problem is that they are correlated with the random intercept and produce inconsistent ...
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