Compactness of infinite dimensional parameter spaces

Freyberger, Joachim; Masten, Matthew A.

doi:10.1920/wp.cem.2016.0116

Cited by 11 publications

(5 citation statements)

References 42 publications

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“…The Hölder classes have been used for instance by Chen and Pouzo (2015) in the context of nonparametric quantile instrumental variable models. For more details on the use of (weighted-)nonparametric smoothness classes in econometrics, we refer to Chen (2007) and Freyberger and Masten (2015).…”

Section: Discussionmentioning

confidence: 99%

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Asymptotic results under multiway clustering

Davezies,

D'Haultfoeuille,

Guyonvarch

2018

Preprint

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If multiway cluster-robust standard errors are used routinely in applied economics, surprisingly few theoretical results justify this practice. This paper aims to fill this gap. We first prove, under nearly the same conditions as with i.i.d. data, the weak convergence of empirical processes under multiway clustering. This result implies central limit theorems for sample averages but is also key for showing the asymptotic normality of nonlinear estimators such as GMM estimators. We then establish consistency of various asymptotic variance estimators, including that of Cameron et al. (2011) but also a new estimator that is positive by construction. Next, we show the general consistency, for linear and nonlinear estimators, of the pigeonhole bootstrap, a resampling scheme adapted to multiway clustering. Monte Carlo simulations suggest that inference based on our two preferred methods may be accurate even with very few clusters, and significantly improve upon inference based on Cameron et al. (2011).

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Section: Discussionmentioning

confidence: 99%

“…When β < 0, the norm ||•|| ∞,β is convenient for classes of smooth but unbounded functions that diverge in the tails at an appropriate rate. When β > 0, ||•|| ∞,β is useful when the class F consists of uniformly bounded functions decaying sufficiently fast in the tails (see e.g Freyberger and Masten, 2015,. for more details).…”

mentioning

confidence: 99%

Asymptotic results under multiway clustering

Davezies,

D'Haultfoeuille,

Guyonvarch

2018

Preprint

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“…Thus, Q 0 (•) is continuous with respect to d c . Note that since the parameter space of the finite-dimensional parameter ψ, Ψ, is assumed to be compact in Assumption 8, the original parameter space Θ is compact under the d c , by Theorems 1 and 2 in Freyberger and Masten (2015), and thus the conditions (ii) and (iii) are satisfied with the specified parameter space and the norm. Since the condition (iv) is directly imposed, we have d( θn , θ 0 ) = o p (1) by Proposition B.1.…”

Section: B26 Directional Derivatives Of the Log-likelihood Functionmentioning

confidence: 99%

“…In our setting, the Hölder norm is the strong norm and || • ||c is the consistency norm. Related to this issue,Freyberger and Masten (2015) recently extend the idea to more cases and present compactness results for several parameter spaces.11 See the online appendix for details.…”

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confidence: 99%

Estimation in a generalization of bivariate probit models with dummy endogenous regressors

Han

Lee

2019

J of Applied Econometrics

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Summary The purpose of this paper is to provide guidelines for empirical researchers who use a class of bivariate threshold crossing models with dummy endogenous variables. A common practice employed by the researchers is the specification of the joint distribution of unobservables as a bivariate normal distribution, which results in a bivariate probit model. To address the problem of misspecification in this practice, we propose an easy‐to‐implement semiparametric estimation framework with parametric copula and nonparametric marginal distributions. We establish asymptotic theory, including root‐n normality, for the sieve maximum likelihood estimators that can be used to conduct inference on the individual structural parameters and the average treatment effect (ATE). In order to show the practical relevance of the proposed framework, we conduct a sensitivity analysis via extensive Monte Carlo simulation exercises. The results suggest that estimates of the parameters, especially the ATE, are sensitive to parametric specification, while semiparametric estimation exhibits robustness to underlying data‐generating processes. We then provide an empirical illustration where we estimate the effect of health insurance on doctor visits. In this paper, we also show that the absence of excluded instruments may result in identification failure, in contrast to what some practitioners believe.

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“…Let's first note that the space Θ is || • || L 2 (P ) -compact as shown in Freyberger & Masten (2015).…”

Section: A Proofsmentioning

confidence: 99%

Significance Tests for Neural Networks

Horel¹,

Giesecke²

2019

Preprint

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Neural networks underpin many of the best-performing AI systems. Their success is largely due to their strong approximation properties, superior predictive performance, and scalability. However, a major caveat is explainability: neural networks are often perceived as black boxes that permit little insight into how predictions are being made. We tackle this issue by developing a pivotal test to assess the statistical significance of the feature variables of a neural network. We propose a gradient-based test statistic and study its asymptotics using nonparametric techniques. The limiting distribution is given by a mixture of chi-square distributions. The tests enable one to discern the impact of individual variables on the prediction of a neural network. The test statistic can be used to rank variables according to their influence. Simulation results illustrate the computational efficiency and the performance of the test. An empirical application to house price valuation highlights the behavior of the test using actual data.

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Compactness of infinite dimensional parameter spaces

Cited by 11 publications

References 42 publications

Asymptotic results under multiway clustering

Asymptotic results under multiway clustering

Estimation in a generalization of bivariate probit models with dummy endogenous regressors

Significance Tests for Neural Networks

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