/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

On robust estimation of the location parameter

We consider statistical inference for regression when data are grouped into clus- ters, with regression model errors independent across clusters but correlated within clusters. Examples include data on individuals with clustering on village or region or other category such as industry, and state-year dierences-in-dierences studies with clustering on state. In such settings default standard errors can greatly overstate es- timator precision. Instead, if the number of clusters is large, statistical inference after OLS should be based on cluster-robust standard errors. We outline the basic method as well as many complications that can arise in practice. These include cluster-specic �xed eects, few clusters, multi-way clustering, and estimators other than OLS.

/pdf/a-practitioner-s-guide-to-cluster-robust-inference-1xbcejtio0.pdf

A Practitioner’s Guide to Cluster-Robust Inference

Many empirical questions in economics and other social sciences depend on causal effects of programs or policies. In the last two decades, much research has been done on the econometric and statistical analysis of such causal effects. This recent theoreti- cal literature has built on, and combined features of, earlier work in both the statistics and econometrics literatures. It has by now reached a level of maturity that makes it an important tool in many areas of empirical research in economics, including labor economics, public finance, development economics, industrial organization, and other areas of empirical microeconomics. In this review, we discuss some of the recent developments. We focus primarily on practical issues for empirical research- ers, as well as provide a historical overview of the area and give references to more technical research.

/pdf/recent-developments-in-the-econometrics-of-program-42vjewfvjw.pdf

Recent developments in the econometrics of program evaluation

Suppose that a target function is monotonic, namely, weakly increasing, and an original estimate of the target function is available, which is not weakly increasing. Many common estimation methods used in statistics produce such estimates. We show that these estimates can always be improved with no harm using rearrangement techniques: The rearrangement methods, univariate and multivariate, transform the original estimate to a monotonic estimate, and the resulting estimate is closer to the true curve in common metrics than the original estimate. We illustrate the results with a computational example and an empirical example dealing with age-height growth charts.

Improving Estimates Of Monotone Functions By Rearrangement

cqiv conducts censored quantile instrumental variable (CQIV) estimation. This command can implement both censored and uncensored quantile IV estimation either under exogeneity or endogeneity. The estimator proposed by Chernozhukov, Fernandez-Val and Kowalski (2010) is used if CQIV estimation is implemented. A parametric version of the estimator proposed by Lee (2007) is used if quantile IV estimation without censoring is implemented. The estimator proposed by Chernozhukov and Hong (2002) is used if censored quantile regression (CQR) is estimated without endogeneity. Note that all the variables in the parentheses of the syntax are those involved in the first stage estimation of CQIV and QIV.

CQIV: Stata module to perform censored quantile instrumental variables regression

This paper considers inference in logistic regression models with high dimensional data. We propose new methods for estimating and constructing confidence regions for a regression parameter of primary interest α0, a parameter in front of the regressor of interest, such as the treatment variable or a policy variable. These methods allow to estimate α0 at the root-n rate when the total number p of other regressors, called controls, exceed the sample size n, using the sparsity assumptions. The sparsity assumption means that only s unknown controls are needed to accurately approximate the nuisance part of the regression function, where s is smaller than n. Importantly, the estimators and these resulting confidence regions are "honest" in the formal sense that their properties hold uniformly over s-sparse models. Moreover, these procedures do not rely on traditional "consistent model selection" arguments for their validity; in fact, they are robust with respect to "moderate" model selection mistakes in variable selection steps. Moreover, the estimators are semi-parametrically efficient in the sense of attaining the semi-parametric efficiency bounds for the class of models in t paper.

https://www.econstor.eu/bitstream/10419/97416/1/775836141.pdf

Honest confidence regions for a regression parameter in logistic regression with a large number of controls

In this paper we study post-penalized estimators which apply ordinary, unpenalized linear regression to the model selected by first-step penalized estimators, typically LASSO It is well known that LASSO can estimate the regression function at nearly the oracle rate, and is thus hard to improve upon We show that post-LASSO performs at least as well as LASSO in terms of the rate of convergence, and has the advantage of a smaller bias Remarkably, this performance occurs even if the LASSO-based model selection 'fails' in the sense of missing some components of the 'true' regression model By the 'true' model we mean here the best s-dimensional approximation to the regression function chosen by the oracle Furthermore, post-LASSO can perform strictly better than LASSO, in the sense of a strictly faster rate of convergence, if the LASSO-based model selection correctly includes all components of the 'true' model as a subset and also achieves a sufficient sparsity In the extreme case, when LASSO perfectly selects the 'true' model, the post-LASSO estimator becomes the oracle estimator An important ingredient in our analysis is a new sparsity bound on the dimension of the model selected by LASSO which guarantees that this dimension is at most of the same order as the dimension of the 'true' model Our rate results are non-asymptotic and hold in both parametric and nonparametric models Moreover, our analysis is not limited to the LASSO estimator in the first step, but also applies to other estimators, for example, the trimmed LASSO, Dantzig selector, or any other estimator with good rates and good sparsity Our analysis covers both traditional trimming and a new practical, completely data-driven trimming scheme that induces maximal sparsity subject to maintaining a certain goodness-of-fit The latter scheme has theoretical guarantees similar to those of LASSO or post-LASSO, but it dominates these procedures as well as traditional trimming in a wide variety of experiments

/pdf/post-l1-penalized-estimators-in-high-dimensional-linear-oucksgpf6o.pdf

Post-l1-penalized estimators in high-dimensional linear regression models

This paper studies a model widely used in the weak instruments literature and establishes admissibility of the weighted average power likelihood ratio tests recently derived by Andrews, Moreira, and Stock (2004, NBER Technical Working Paper 199). The class of tests covered by this admissibility result contains the Anderson and Rubin (1949, Annals of Mathematical Statistics 20, 46–63) test. Thus, there is no conventional statistical sense in which the Anderson and Rubin (1949) test “wastes degrees of freedom.” In addition, it is shown that the test proposed by Moreira (2003, Econometrica 71, 1027–1048) belongs to the closure of (i.e., can be interpreted as a limiting case of) the class of tests covered by our admissibility result.

Victor Chernozhukov

Papers

Improving Estimates Of Monotone Functions By Rearrangement

CQIV: Stata module to perform censored quantile instrumental variables regression

Honest confidence regions for a regression parameter in logistic regression with a large number of controls

Post-l1-penalized estimators in high-dimensional linear regression models

Admissible invariant similar tests for instrumental variables regression