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.
379
questions
0
votes
0
answers
8
views
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 ...
- 101
0
votes
0
answers
23
views
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 ...
- 123
7
votes
1
answer
161
views
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 $\...
- 129
2
votes
0
answers
44
views
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\...
- 171
0
votes
1
answer
53
views
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)\...
1
vote
0
answers
43
views
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 ...
- 11
0
votes
0
answers
46
views
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, ...
- 55
4
votes
1
answer
118
views
(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 ...
- 46.6k
1
vote
1
answer
39
views
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{\...
1
vote
1
answer
30
views
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}...
- 12.8k
1
vote
0
answers
28
views
*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 (...
- 711
0
votes
1
answer
72
views
Proof of consistency of OLS estimator under Heteroskedasticity
$\DeclareMathOperator{\pl}{\operatorname{plim}}$
Consider a general linear regression model with heteroskedastic errors
$$
\boldsymbol{y}=\boldsymbol{X}\boldsymbol{\beta}+\boldsymbol{u} \quad \text{...
- 1,347
0
votes
0
answers
16
views
Animal Behavior: PCA or zscoring?
Animal behavior tests usually generate multiple variables (e.g. Open Field: entries in center, time in center, total distance…). However, it is common to report only one (or few) of this variables as ...
2
votes
1
answer
207
views
What is cor.smooth(R) : Matrix was not positive definite warning Cronbach alpha in Psych?
I'm getting the warning In cor.smooth(R) : Matrix was not positive definite, smoothing was done, but what is it in this case? Can I get away with that?
code:
<...
- 611
0
votes
0
answers
7
views
Internal Consistency for single question
I have to evaluate the internal consistency for a single yes/no question. There are $N$ people answering yes or no, where only one of the answers is correct. This leaves me with a percentage correct, ...
- 1
3
votes
1
answer
48
views
Consistency of a simple estimator for $y_i = \beta_1 x_i + u_i$
Let $y_i = \beta_1 x_i + u_i$ for $i=1,2,..,n$. If I define $$\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 ...
- 43
3
votes
1
answer
130
views
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, ...
- 591
1
vote
0
answers
18
views
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 ...
- 19.5k
1
vote
1
answer
166
views
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 ...
- 13
1
vote
0
answers
27
views
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 ...
user318514
0
votes
0
answers
9
views
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?
user318514
1
vote
1
answer
90
views
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 ...
- 63
3
votes
1
answer
59
views
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).
$$
...
- 832
0
votes
0
answers
8
views
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?
user318514
1
vote
0
answers
16
views
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 ...
user318514
0
votes
0
answers
38
views
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 ...
user318514
2
votes
1
answer
141
views
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|...
- 2,204
1
vote
0
answers
45
views
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 ...
user318514
1
vote
0
answers
17
views
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 \...
- 215
1
vote
0
answers
20
views
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 ...
- 21
0
votes
0
answers
17
views
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. ...
- 1
2
votes
2
answers
181
views
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:
...
- 21
1
vote
1
answer
78
views
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 ...
- 376
3
votes
1
answer
114
views
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 ...
- 577
1
vote
1
answer
26
views
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. ...
- 31
1
vote
0
answers
29
views
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, ...
- 111
0
votes
0
answers
54
views
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: ...
- 1
0
votes
1
answer
71
views
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 ...
- 111
0
votes
0
answers
15
views
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 ...
- 11
0
votes
0
answers
20
views
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 ...
0
votes
0
answers
286
views
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.:
$$ \bar{x}_w = \sum_{i=1}^{n} w_ix_i$$
...
- 13
0
votes
1
answer
423
views
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 ...
- 3
0
votes
0
answers
72
views
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 ...
- 1
1
vote
0
answers
96
views
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 ...
- 131
1
vote
0
answers
49
views
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^{...
- 151
1
vote
1
answer
65
views
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 ...
- 890
0
votes
0
answers
23
views
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 ...
- 51
1
vote
1
answer
74
views
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 ...
- 151
1
vote
0
answers
67
views
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:
$\hat\sigma = \frac{1}{n} \sum_{i=1}^{n}|y_i-med(y_i)|$, ...
- 11
0
votes
0
answers
140
views
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 $f_\theta(x)$, ...
- 73