We consider the problem of high-dimensional inference with the lasso estimator. Different methods including'double selection'techniques and multiple versions of the'debiased lasso'have been proposed for this task with noticeable success. However, most guarantees assume strong hypotheses on the underlying data process and the errors in the linear regression model, such as subgaussian designs and independence between errors and the data itself. We show that'standardizing'one's dataset -- a natural procedure in practical penalized regression -- leads to the same results under much weaker hypotheses, paying only a small price for not assuming light tails. The key technical point allowed by this step is exploiting the concentration properties of self-normalized processes. Importantly, we prove our results for two different methods closely related to the'debiased lasso'. The second method performs valid inference even for a misspecified linear model, under mild sparsity conditions similar to the'double selection'literature.
We consider statistical inference based on the LASSO (cf. Tibshirani (J. Roy. Statist. Soc. Ser. B, Methodol. 58 (1996) 267–288)) in high dimensional regression problems. It is well known that the LASSO produces biased estimator of the regression parameter. The bias problem is further exacerbated when the LASSO has the...
Debraj Das, A. Chatterjee, S. Lahiri· Bernoulli· 0 citations
The recent work of Sarkar and Zhang (2025) introduced Positive Tail Dependence Under the Null (PTDN) and developed Generalized Shifted Benjamini-Hochberg (BH) procedures for two-sided Gaussian $z$- and $t$-testing under known covariance structures. This paper develops further consequences of that framework. First, we d...
We introduce a flexible model for covariate-dependent multiple testing which can be encoded using a nonparametric Gaussian mixture model. Weight-localized predictive recursion (PRx), a new development in the methodology of Newton's predictive recursion algorithm, is then leveraged to estimate the components of this mix...
In real-world applications, data are often error-contaminated; naively applying conventional methods without accommodating the measurement error effects often yields inconsistent estimates. Biased results can be further exacerbated by the ultrahigh-dimensionality of covariates. Focusing on the widely used function-on-s...
A neural network is trained on simulated datasets drawn from a prior over a distribution family, using single independent draws of the root T_n - T(F) scored by the pinball loss, a proper scoring rule whose population minimizer is the posterior-predictive law of the root.
Estimating the first stage of an instrumental variables (IV) model with the least absolute shrinkage and selection operator (LASSO) requires choosing a dictionary of technical instruments and a penalty level. First-order asymptotic theory offers no guidance on these choices, as any consistent implementation yields a st...
Yu-Kun Ma, Manu Navjeevan, Bogdan Salahub· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
