We develop uniformly valid confidence regions for regression coefficients in a highdimensional sparse median regression model with homoscedastic errors. Our methods are based on a moment equation ...that is immunized against nonregular estimation of the nuisance part of the median regression function by using Neyman's orthogonalization. We establish that the resulting instrumental median regression estimator of a target regression coefficient is asymptotically normally distributed uniformly with respect to the underlying sparse model and is semiparametrically efficient. We also generalize our method to a general nonsmooth Z-estimation framework where the number of target parameters is possibly much larger than the sample size. We extend Huber's results on asymptotic normality to this setting, demonstrating uniform asymptotic normality of the proposed estimators over rectangles, constructing simultaneous confidence bands on all of the target parameters, and establishing asymptotic validity of the bands uniformly over underlying approximately sparse models.
We propose robust methods for inference about the effect of a treatment variable on a scalar outcome in the presence of very many regressors in a model with possibly non-Gaussian and heteroscedastic ...disturbances. We allow for the number of regressors to be larger than the sample size. To make informative inference feasible, we require the model to be approximately sparse; that is, we require that the effect of confounding factors can be controlled for up to a small approximation error by including a relatively small number of variables whose identities are unknown. The latter condition makes it possible to estimate the treatment effect by selecting approximately the right set of regressors. We develop a novel estimation and uniformly valid inference method for the treatment effect in this setting, called the "post-double-selection" method. The main attractive feature of our method is that it allows for imperfect selection of the controls and provides confidence intervals that are valid uniformly across a large class of models. In contrast, standard post-model selection estimators fail to provide uniform inference even in simple cases with a small, fixed number of controls. Thus, our method resolves the problem of uniform inference after model selection for a large, interesting class of models. We also present a generalization of our method to a fully heterogeneous model with a binary treatment variable. We illustrate the use of the developed methods with numerical simulations and an application that considers the effect of abortion on crime rates.
We develop results for the use of Lasso and post-Lasso methods to form first-stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments, p. ...Our results apply even when p is much larger than the sample size, n. We show that the IV estimator based on using Lasso or post-Lasso in the first stage is root-n consistent and asymptotically normal when the first stage is approximately sparse, that is, when the conditional expectation of the endogenous variables given the instruments can be well-approximated by a relatively small set of variables whose identities may be unknown. We also show that the estimator is semiparametrically efficient when the structural error is homoscedastic. Notably, our results allow for imperfect model selection, and do not rely upon the unrealistic "beta-min" conditions that are widely used to establish validity of inference following model selection (see also Belloni, Chernozhukov, and Hansen (2011b)). In simulation experiments, the Lasso-based IV estimator with a data-driven penalty performs well compared to recently advocated many-instrument robust procedures. In an empirical example dealing with the effect of judicial eminent domain decisions on economic outcomes, the Lasso-based IV estimator outperforms an intuitive benchmark. Optimal instruments are conditional expectations. In developing the IV results, we establish a series of new results for Lasso and post-Lasso estimators of nonparametric conditional expectation functions which are of independent theoretical and practical interest. We construct a modification of Lasso designed to deal with non-Gaussian, heteroscedastic disturbances that uses a data-weighted 𝓁₁-penalty function. By innovatively using moderate deviation theory for self-normalized sums, we provide convergence rates for the resulting Lasso and post-Lasso estimators that are as sharp as the corresponding rates in the homoscedastic Gaussian case under the condition that log p = o(n 1/3 ). We also provide a data-driven method for choosing the penalty level that must be specified in obtaining Lasso and post-Lasso estimates and establish its asymptotic validity under non-Gaussian, heteroscedastic disturbances.
In this paper, we provide efficient estimators and honest confidence bands for a variety of treatment effects including local average (LATE) and local quantile treatment effects (LQTE) in data-rich ...environments. We can handle very many control variables, endogenous receipt of treatment, heterogeneous treatment effects, and function-valued outcomes. Our framework covers the special case of exogenous receipt of treatment, either conditional on controls or unconditionally as in randomized control trials. In the latter case, our approach produces efficient estimators and honest bands for (functional) average treatment effects (ATE) and quantile treatment effects (QTE). To make informative inference possible, we assume that key reduced-form predictive relationships are approximately sparse. This assumption allows the use of regularization and selection methods to estimate those relations, and we provide methods for postregularization and post-selection inference that are uniformly valid (honest) across a wide range of models. We show that a key ingredient enabling honest inference is the use of orthogonal or doubly robust moment conditions in estimating certain reducedform functional parameters. We illustrate the use of the proposed methods with an application to estimating the effect of 401(k) eligibility and participation on accumulated assets. The results on program evaluation are obtained as a consequence of more general results on honest inference in a general moment-condition framework, which arises from structural equation models in econometrics. Here, too, the crucial ingredient is the use of orthogonal moment conditions, which can be constructed from the initial moment conditions. We provide results on honest inference for (function-valued) parameters within this general framework where any high-quality, machine learning methods (e.g., boosted trees, deep neural networks, random forest, and their aggregated and hybrid versions) can be used to learn the nonparametric/high-dimensional components of the model. These include a number of supporting auxiliary results that are of major independent interest: namely, we (1) prove uniform validity of a multiplier bootstrap, (2) offer a uniformly valid functional delta method, and (3) provide results for sparsitybased estimation of regression functions for function-valued outcomes.
We propose a pivotal method for estimating high-dimensional sparse linear regression models, where the overall number of regressors p is large, possibly much larger than n, but only s regressors are ...significant. The method is a modification of the lasso, called the square-root lasso. The method is pivotal in that it neither relies on the knowledge of the standard deviation σ nor does it need to pre-estimate σ. Moreover, the method does not rely on normality or sub-Gaussianity of noise. It achieves near-oracle performance, attaining the convergence rate σ{(s/n) log p} 1/2 in the prediction norm, and thus matching the performance of the lasso with known σ. These performance results are valid for both Gaussian and non-Gaussian errors, under some mild moment restrictions. We formulate the square-root lasso as a solution to a convex conic programming problem, which allows us to implement the estimator using efficient algorithmic methods, such as interior-point and first-order methods.
Summary
The current COVID‐19 pandemic is caused by the SARS‐CoV‐2 coronavirus. The initial recognized symptoms were respiratory, sometimes culminating in severe respiratory distress requiring ...ventilation, and causing death in a percentage of those infected. As time has passed, other symptoms have been recognized. The initial reports of cutaneous manifestations were from Italian dermatologists, probably because Italy was the first European country to be heavily affected by the pandemic. The overall clinical presentation, course and outcome of SARS‐CoV‐2 infection in children differ from those in adults as do the cutaneous manifestations of childhood. In this review, we summarize the current knowledge on the cutaneous manifestations of COVID‐19 in children after thorough and critical review of articles published in the literature and from the personal experience of a large panel of paediatric dermatologists in Europe. In Part 1, we discuss one of the first and most widespread cutaneous manifestation of COVID‐19, chilblain‐like lesions. In Part 2, we review other manifestations, including erythema multiforme, urticaria and Kawasaki disease‐like inflammatory multisystemic syndrome, while in Part 3, we discuss the histological findings of COVID‐19 manifestations, and the testing and management of infected children, for both COVID‐19 and any other pre‐existing conditions.
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Skin manifestations of COVID‐19 in children: Part 2 Andina, D.; Belloni‐Fortina, A.; Bodemer, C. ...
Clinical and experimental dermatology,
April 2021, 2021-Apr, 2021-04-00, 20210401, 2021-04, Letnik:
46, Številka:
3
Journal Article
Recenzirano
Odprti dostop
Summary
The current COVID‐19 pandemic is caused by the SARS‐CoV‐2 coronavirus. The initial recognized symptoms were respiratory, sometimes culminating in severe respiratory distress requiring ...ventilation, and causing death in a percentage of those infected. As time has passed, other symptoms have been recognized. The initial reports of cutaneous manifestations were from Italian dermatologists, probably because Italy was the first European country to be heavily affected by the pandemic. The overall clinical presentation, course and outcome of SARS‐CoV‐2 infection in children differ from those in adults, as do the cutaneous manifestations of childhood. In this review, we summarize the current knowledge on the cutaneous manifestations of COVID‐19 in children after thorough and critical review of articles published in the literature and from the personal experience of a large panel of paediatric dermatologists in Europe. In Part 1, we discussed one of the first and most widespread cutaneous manifestations of COVID‐19, chilblain‐like lesions. In this part of the review, we describe other manifestations, including erythema multiforme, urticaria and Kawasaki disease‐like inflammatory multisystemic syndrome. In Part 3, we discuss the histological findings of COVID‐19 manifestations, and the testing and management of infected children for both COVID‐19 and any other pre‐existing conditions.
Click here for the corresponding questions to this CME article.
Summary
The current COVID‐19 pandemic is caused by the SARS‐CoV‐2 coronavirus. The initial recognized symptoms were respiratory, sometimes culminating in severe respiratory distress requiring ...ventilation, and causing death in a percentage of those infected. As time has passed, other symptoms have been recognized. The initial reports of cutaneous manifestations were from Italian dermatologists, probably because Italy was the first European country to be heavily affected by the pandemic. The overall clinical presentation, course and outcome of SARS‐CoV‐2 infection in children differ from those in adults as do the cutaneous manifestations of childhood. In this review, we summarize the current knowledge on the cutaneous manifestations of COVID‐19 in children after thorough and critical review of articles published in the literature and from the personal experience of a large panel of paediatric dermatologists in Europe. In Part 1, we discuss one of the first and most widespread cutaneous manifestations of COVID‐19, chilblain‐like lesions, and in Part 2 we expanded to other manifestations, including erythema multiforme, urticaria and Kawasaki disease‐like inflammatory multisystemic syndrome. In this part of the review, we discuss the histological findings of COVID‐19 manifestations, and the testing and management of infected children for both COVID‐19 and any other pre‐existing conditions.
Click here for the corresponding questions to this CME article.
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