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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Cronbach's alpha on discrete multiple-choice responses

Suppose you want to calculate the Cronbach's alpha for a test whose responses are multiple-choice, e.g. 1, 2, 3, 4. These responses are nominal and not ordinal, in they do not have any type of natural ...
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Are the Grenander conditions on the explanatory variable to ensure OLS has consistent treatment effect estimates applicable to GLM/GLMM?

Are the Grenander conditions on the explanatory variable to ensure OLS has consistent treatment effect estimates applicable to GLM/GLMM where you have count,binary data? If you don't know what ...
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Posterior consistency for scale-mixture shrinkage priors in low dimension?

Consider the model [1] $$y_n=X_n\beta_n+\epsilon_n$$ $$\beta_i|\sigma^2,v_i \sim \mathcal{N}(0,\sigma^2 v_i), i=1,\ldots,p$$ $$v_i \sim \beta^\prime(a,b)$$ $$\sigma^2 \sim \mathcal{IG}(c,d)$$ where $\...
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Why is posterior consistency research focuses only high-dimensionality?

I have notice that most literature (especially recently) about posterior consistency as $n\rightarrow \infty$ only focuses on areas of high dimensionality i.e. on $p_n\rightarrow \infty$ as $n\...
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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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Methods describe the temporal consistency of kernel density data

I am working on a spatial time series analysis project. The task is to study the spatial distribution of point features (e.g., crime events, traffic accidents) over time. I aim to find the places with ...
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Trouble understanding expected value (does it assume infinite sample size?) and bias vs consistent

This might be a dumb question.. but I was wondering if someone can help me out with the concept expectation. This question started from trying to understand bias vs consistent. So when we roll a dice, ...
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(Why) is a logistic regression maximum likelihood estimator consistent?

A nice property of maximum likelihood estimators is that, while they can be biased, they are consistent for $iid$ observations. In a logistic regression, unless the conditional distributions all have ...
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Proving estimator consistency

I have the following estimator: $\hat{\sigma}^2_N = \frac{1}{h^2}\sum\limits_{i=1}^{N}x^2_i$, where $x_i \sim i.i.d. \; \mathcal{N}(\mu\frac{h}{N}, \sigma^2\frac{h}{N})$. We can show that $E[\hat{\...
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are the marginals of boosted trees consistent if we can assume unconfoundedness?

given outcome $y$ and data $X$ with data generating process $y = f(X)+\epsilon$ where $\epsilon$ independent of $X$ and gradient boosted trees as the algorithm approximating $f$, does $\partial \hat{y}...
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*When* are mixed models with a lagged dependent variable inconsistent/biased?

Suppose panel data where multiple observations are made of units over time. Regressing a dependent variable measured at each time point on lag of the dependent variable and a unit-specific intercept (...
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Proof of consistency of OLS estimator under Heteroskedasticity

$\DeclareMathOperator{\pl}{\operatorname{plim}}$ Consider a general linear regression model with heteroskedastic errors $$ \boldsymbol{y}=\boldsymbol{X}\boldsymbol{\beta}+\boldsymbol{u} \quad \text{...
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Animal Behavior: PCA or zscoring?

Animal behavior tests usually generate multiple variables (e.g. Open Field: entries in center, time in center, total distance…). However, it is common to report only one (or few) of this variables as ...
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What is cor.smooth(R) : Matrix was not positive definite warning Cronbach alpha in Psych?

I'm getting the warning In cor.smooth(R) : Matrix was not positive definite, smoothing was done, but what is it in this case? Can I get away with that? code: <...
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Internal Consistency for single question

I have to evaluate the internal consistency for a single yes/no question. There are $N$ people answering yes or no, where only one of the answers is correct. This leaves me with a percentage correct, ...
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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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For Instrumental Variables, Why can we show that it is unbiased by taking E(Y|X,Z)?

My understanding is that instrumentals variables regressions estimator is consistent, but not unbiased, for identifying the causal effect of a variable x and y. I understand that for an instrument,z, ...
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Is there a natural equivalent of consistency for the case of prediction?

Consistency is generally understood to be a pretty basic requirement for a decent estimator of a model parameter or other population quantity. If your estimator isn't consistent, then it won't ...
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Quantile Regression proof

I'm interested in understanding the formal proof of why Quantile Regression works. That is, show me in which conditions the pinball/quantile loss provides asymptotic consistent estimations of the ...
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Do unbiased L2 consistent, consistent in probability, or almost sure consistent estimator have a asymptotic variance equal to rao-cramer or better?

Does a L2 consistent, consistent in probability, or almost sure consistent estimator have a asymptotic variance equal to rao-cramer or better? With almost-sure consistency, why doesn't the estimator ...
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Many crossed-random effects increase multicollinearity, decreases efficiency or consistency or introduces bias?

Many crossed-random effects increases multicollinearity, decreases efficiency or consistency or introduces bias? What are the trade-offs of using many random-effects?
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When the sample mean converges to the population mean, does the probability that the sample mean is equal to the population mean tend to 0?

Let $y_1, y_2, \ldots , y_N$ be arbitrary real numbers and suppose a process of simple random sampling without replacement that selects $n$ out of $N$ elements. Then suppose that these $N$ elements ...
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Does a misspecified model always have lower likelihood value than the correct model?

Suppose the true dgp is $$ x_i \sim d_1(\theta_1), \quad i=1,\ldots,N $$ where $d_1$ is some probability distribution with parameter(s) $\theta_1$, but I wrongly assume $$ x_i \sim d_2(\theta_2). $$ ...
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Is instrumental variables estimator applicable when a covariate is Spearman $\rho>0$ but not Pearson correlated with the residuals?

Is instrumental variables estimator applicable when a covariate is Spearman but not Pearson correlated with the residuals? Does Spearman non-zero correlation with residuals imply loss of consistency?
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Do covariates correlated with residuals in generalized linear models make estimates not consistent or other problems? [closed]

Do covariates correlated with residuals in generalized linear models make estimates not consistent or make other problems? Economists raise an issue about endogenous variables in OLS and do some 2SLS ...
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Are generalized estimating equations estimates affected by endogenous covariates (covariates correlated with model residuals)?

Are generalized estimating equations consistent or still okay with endogenous variables? The authors of GEE say here that their estimates remain consistent without any qualifications about endogeneity ...
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For the logit model, how is the maximum likelihood and minimum distance estimator related?

Suppose I have data $\{y_i,x_i\}_{i=1}^N$, where $x_i\in\{s_1,...,s_K\}$ and follows a discrete uniform distribution. For each realized $x_i$, $y_i$ is generated by the logit model, i.e., $Pr(Y_i=1|...
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Does a Heteroskedasticity and Autocorrelation Consistent Estimator for generalized linear (mixed/non-mixed) models exist?

Does a Heteroskedasticity and Autocorrelation Consistent Estimator for generalized linear models exist? That would make GEEs outdated unless no-free lunch theorem suggests otherwise. I am only aware ...
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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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Eckart–Young–Mirsky theorem for $n \gg m$

It has been proven that the best reconstruction error in the $k$ rank matrix estimation problem in terms of Frobenius or $L2$ norm is given by the $k$-truncated SVD as shown here. I've read in ...
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Using time as a variable to calculate consistency

How can I use time as a factor in calculating consistency/reliability. Given a simplified scenario : I am trying to rank researcher based on how often they publish a paper by giving them a score. ...
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Cronbach’s alpha not equal to ICC 3,k

I am calculating ICC over 16 items rated by 41 raters, using the ICC function from the psych package. The output is: ...
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Internal consistency of correlation [duplicate]

I have this question below , and I am unable to understand what is internal consistency, can anyone please tell the concept , I have read its wiki page but I couldn't understand how to solve a ...
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Can I say that $T_n$ is a consistent estimator of $\theta$ by Monte Carlo simulation under this setting?

Given a iid random samples $X\sim N(\theta,1)$, we have a unknown parameter $\theta$ and its estimator $T_n=T_n(X_1,\dots,X_n)$. If we have strictly proved that $T_n$ is a consistent estimator, can ...
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Checking consistency of answers within groups (e.g. household) in R

I got some survey data, in which the respondents answered various questions about environmental conditions on a 1-5 Likert scale. The respondents are also assigend to a household by an household ID. ...
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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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Confusion about consistency of time series model parameter

Can someone clear this confusion. Lets say I have a time series model: $$X_t \text{ follows Poisson}(\lambda_t)$$ $$\lambda_t=a*X_{t-1}+b*\lambda_{t-1}$$ Then I find estimators for $a$ and $b$ called: ...
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root n consistency of parameter in mixture distribution

We have iid observations $\{X_i\}_{i=1}^n$ from CDF $\theta G + (1- \theta)H$ where $\theta \in (0,1)$ is unknown. Find a $\sqrt{n}$ consistent estimator for $\theta$ using the observations. Note that ...
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Testing Data Consistency and its effect on Multilevel Modeling Multivariate Inference

I have a MLM model looking at the effect of demographics of a few cities on a region wide outcome variable as follows: RegionalProgress = β0j + β1j * Demographics + u0j + e0ij The data used in this ...
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Using IV when regressor is not endogenous

Suppose I have a single regressor model and the regressor itself is uncorrelated with the error term. If I were to use IV estimation to estimate the coefficient, would the estimate be incorrect, and ...
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Weighted average estimator - unbiased and consistent

Take an estimator that produces a weighted average of all n observations in an i.i.d sample from a population with mean $\mu$ and variance $\sigma^2$. I.e.: $$ \bar{x}_w = \sum_{i=1}^{n} w_ix_i$$ ...
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What is the variance of $s^2$?

I am trying to calculate the variance of $s^2=\frac{1}{n-1}\sum (x_i-\bar x)^2$. So what I want to find is $ Var(s^2)$. I have seen different posts, but many of them seem to make the assumption that ...
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Proportion data: Logistic with MLE vs. OLS with logit-transformed response

This is an expansion of @Beethoven_90's comment on this question. Suppose I have proportion data $Y_i$ computed from a binomial; $Y_i = \frac{S_i}{N_i}$ where $S_i \sim Bin(N_i, p_i)$ and $p_i$ is the ...
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Sample skewness consistency

Is sample skewness a consistent estimator of (moment coefficient) skewness? I have ran some experiments and it seems this is not the case, but I cannot find any definite answer online. Here is an ...
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Marginal Distribution of a Stochastic Block Model?

Let us say I have a Stochastic Block Model i.e. a random vector $X^{(n)} = [x_1,...,x_n]$ where $P(x_i = c) = P_{c}$, where $c \in \{1,...,u\}$, and a random simple undirected graph represented by $Y^{...
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consistency of maximum likelihood estimator

For population with n size and following density function $$f(y, a)= (1/6a^4)y^3e^{-y/a}$$ For that, I have found the maximum likelihood estimator of a which is $\hat{a}= \bar{y}/4$ I have also shon ...
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Statistical test for questionnaire with various components

I was asked to analyze a research questionnaire that consists of a Likert scale, a checklist, and questions with yes, no, and don't know as response, as part of the pilot testing. I was struggling ...
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Would decision tree propagate error?

Given a regression dataset $X,Y$. Suppose there are two different decision tree (CART) $T_1, T_2$ fitted from it. Each using different feature encoding method. And we get two different tree. And there ...
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consistency of mle of double exponential distribution ( not advanced)

Let $y_i\sim DE(\mu, \sigma), $ $i=1,2,...,n, \ i.i.d.$ Where DE represents the double exponential distribution. The the MLE of \sigma is: $\hat\sigma = \frac{1}{n} \sum_{i=1}^{n}|y_i-med(y_i)|$, ...
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Consistency of Posterior

I have a conceptual question regarding the definition of the consistency of a Bayesian posterior. I found this definition on the web: Given the i.i.d. data $x_1,...,x_n$ and the model $f_\theta(x)$, ...
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