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.
385 questions
1 vote
0 answers
12 views
Asymptotic bias when misspecifying ARMA-X type model
Consider the following model: $$y_t = c_0 + \phi y_{t-1} + \beta x_{t} + u_t,$$ where $u_t$ follows an MA(1) process: $u_t = \varepsilon_t + \theta\varepsilon_{t-1},$ where $\varepsilon_t$ is white ...
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2 votes
0 answers
19 views
Lasso consistency with linearly dependent features
I know that the Lasso can be used for subset selection and there exists theoretical results on the consistency of the Lasso, in particular the sign consistency. One of the assumptions to prove the ...
1 vote
0 answers
26 views
How can we empirically test semantic field constraints and self-consistency in high-dimensional embedding spaces?
I'm exploring a new hypothesis for AI reasoning: the "Asymmetric Self-Consistency Hypothesis", as described in this public preprint. The core idea is that, in high-dimensional semantic ...
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3 votes
2 answers
250 views
Is the intercept of the LASSO linear regression consistent to its population OLS counterpart?
Suppose the population OLS regression: $y=\beta_0+\boldsymbol{\beta}^\prime \boldsymbol{x}+\epsilon$, where the $y$ and $\boldsymbol{x}$ are not standardized (the mean can be nonzero). The solution of ...
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0 votes
1 answer
65 views
Consistency of classical estimation of hyper-parameters from multiple samples
Let $\sigma>0$. Suppose we observe $N$ samples of sizes $T_1,\dots,T_n$ that are each generated by the following data generating process: $\theta_n$ is drawn from the distribution $\mathrm{N}(0,\...
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1 vote
1 answer
79 views
Conditions of M-estimator to be consistent
I read from Asymptotic Statistics (Van der Vaart, 1998) Theorem 5.7 that, to let the M-estimator $\hat{\theta}_n$ converge in probability to $\theta_0$, two conditions need to be satisfied, one of ...
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0 votes
0 answers
97 views
What does consistency mean in high-dimensional settings?
In some papers about $\mathcal{l}_1$-penalized regression, $$ \hat{\beta}=\underset{\beta\in\mathbb{R}^{p}}{\operatorname{\arg\min}}\|Y-X\beta\|_2^2+\lambda\|\beta\|_1, $$ the authors say that they ...
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2 votes
0 answers
94 views
Showing that an estimator is consistent and asymptotically normal
I have the following exercise and i am kind of stuck. Consider a random sample $X_1, \ldots, X_n$ of $n$ observations from a $\operatorname{POISS}(\mu)$-distribution. Use $\left(1-\frac{1}{n}\right)^{...
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