scholarly journals Inference Under Random Limit Bootstrap Measures

Econometrica ◽  
2020 ◽  
Vol 88 (6) ◽  
pp. 2547-2574
Author(s):  
Giuseppe Cavaliere ◽  
Iliyan Georgiev
Keyword(s):  
Limit Distribution ◽  
Linear Models ◽  
Sufficient Conditions ◽  
Conditional Inference ◽  
Specification Tests ◽  
Inference Problems ◽  
Kolmogorov Smirnov ◽  
Distribution Of A Statistic ◽  
Random Limit ◽  
Bootstrap Distribution

Asymptotic bootstrap validity is usually understood as consistency of the distribution of a bootstrap statistic, conditional on the data, for the unconditional limit distribution of a statistic of interest. From this perspective, randomness of the limit bootstrap measure is regarded as a failure of the bootstrap. We show that such limiting randomness does not necessarily invalidate bootstrap inference if validity is understood as control over the frequency of correct inferences in large samples. We first establish sufficient conditions for asymptotic bootstrap validity in cases where the unconditional limit distribution of a statistic can be obtained by averaging a (random) limiting bootstrap distribution. Further, we provide results ensuring the asymptotic validity of the bootstrap as a tool for conditional inference, the leading case being that where a bootstrap distribution estimates consistently a conditional (and thus, random) limit distribution of a statistic. We apply our framework to several inference problems in econometrics, including linear models with possibly nonstationary regressors, CUSUM statistics, conditional Kolmogorov–Smirnov specification tests and tests for constancy of parameters in dynamic econometric models.

Bootstrap Standard Error Estimates and Inference

Econometrica ◽  
2021 ◽  
Vol 89 (4) ◽  
pp. 1963-1977 ◽  
Author(s):  
Jinyong Hahn ◽  
Zhipeng Liao
Keyword(s):  
Weak Convergence ◽  
Error Estimates ◽  
Limit Distribution ◽  
Standard Error ◽  
Asymptotic Variance ◽  
Theory And Practice ◽  
Second Moment ◽  
Theoretical Literature ◽  
Bootstrap Distribution

Asymptotic justification of the bootstrap often takes the form of weak convergence of the bootstrap distribution to some limit distribution. Theoretical literature recognized that the weak convergence does not imply consistency of the bootstrap second moment or the bootstrap variance as an estimator of the asymptotic variance, but such concern is not always reflected in the applied practice. We bridge the gap between the theory and practice by showing that such common bootstrap based standard error in fact leads to a potentially conservative inference.

A Regression Paradox for Linear Models: Sufficient Conditions and Relation to Simpson’s Paradox

2009 ◽  
Vol 63 (3) ◽  
pp. 218-225 ◽  
Author(s):  
Aiyou Chen ◽  
Thomas Bengtsson ◽  
Tin Kam Ho
Keyword(s):  
Linear Models ◽  
Sufficient Conditions ◽  
Simpson’S Paradox ◽  
Simpson's Paradox

Perceived value, satisfaction and future intentions in sport services

2019 ◽  
Vol 32 (4) ◽  
pp. 566-579 ◽  
Author(s):  
Mario Alguacil ◽  
Juan Núñez-Pomar ◽  
Carlos Pérez-Campos ◽  
Vicente Prado-Gascó
Keyword(s):  
Linear Models ◽  
Qualitative Comparative Analysis ◽  
Sufficient Conditions ◽  
Perceived Value ◽  
Hierarchical Regression ◽  
Brand Trust ◽  
Predictive Capability ◽  
Content Type ◽  
Necessary And Sufficient

Purpose The purpose of this paper is to analyze the role of brand-related variables as congruence and brand trust on the traditional model formed by perceived quality, perceived value (PV) and satisfaction, in order to compare predictive models for the variables of PV, satisfaction and future intentions of 683 users of sports services. Design/methodology/approach The analysis has been carried out using two different methodologies. First, three models have been proposed to be analyzed by hierarchical regression models, in order to subsequently propose a fuzzy-set qualitative comparative analysis (fsQCA) to verify the existence or not of necessary and sufficient conditions. Findings The results indicate that both the classic service variables and the elements related to the brand significantly predict PV, satisfaction and future intentions, in some cases with greater predictive weight being given to congruence and trust than the classic service variables. In addition, linear models have been shown to improve their predictive capability by including brand-related variables, especially the future intentions model. After the fsQCA, congruence and trust have proved to be sufficient combinations to achieve high levels of PV and future intentions, while this is not the case for satisfaction. Originality/value The importance of the aspects related to the brand, either on their own or in combination with the classic service variables, is demonstrated, contributing to the literature on brand image in sports services, which is practically non-existent.

A functional equation technique for obtaining wiener process probabilities associated with theorems of Kolmogorov-Smirnov type

1959 ◽  
Vol 55 (4) ◽  
pp. 328-332 ◽  
Author(s):  
J. Kiefer ◽  
D. V. Lindley
Keyword(s):  
Functional Equation ◽  
Distribution Function ◽  
Wiener Process ◽  
Limit Distribution ◽  
Sample Distribution ◽  
Probabilistic Computation ◽  
Limit Distributions ◽  
Kolmogorov Smirnov

1. Introduction. Since the first proofs by Kolmogorov (13) and Smirnov ((14), (15)) of their well-known results on the limit distribution of the deviations of the sample distribution function, many alternative proofs of these results have been given. For example, we may cite the various approaches of Feller (4), Doob (3), Kac (8), Gnedenko and Korolyuk(7), and Anderson and Darling (1). The approaches of (3), (8) and (1) rest on a probabilistic computation regarding the Wiener process, and are justified by the paper of Donsker (2) (see also (11)). Of all these approaches, only those of (8) and (1) can be extended to obtain the limit distributions of the ‘k–sample’ generalizations of the Kolmogorov-Smirnov statistics suggested in (9), and the author ((9), (10)) and Gihman(6) carried out such proofs.

scholarly journals Conditional sampling for spectrally discrete max-stable random fields

2011 ◽  
Vol 43 (2) ◽  
pp. 461-483 ◽  
Author(s):  
Yizao Wang ◽  
Stilian A. Stoev
Keyword(s):  
Random Fields ◽  
Linear Models ◽  
Conditional Sampling ◽  
Prediction Problem ◽  
Conditional Distributions ◽  
Spatial Extremes ◽  
Inference Problems ◽  
New Perspective ◽  
Stable Random Fields ◽  
Computational Solution

Max-stable random fields play a central role in modeling extreme value phenomena. We obtain an explicit formula for the conditional probability in general max-linear models, which include a large class of max-stable random fields. As a consequence, we develop an algorithm for efficient and exact sampling from the conditional distributions. Our method provides a computational solution to the prediction problem for spectrally discrete max-stable random fields. This work offers new tools and a new perspective to many statistical inference problems for spatial extremes, arising, for example, in meteorology, geology, and environmental applications.

scholarly journals Technical Note—Sufficient Conditions for Insensitivity in Linear Models

1976 ◽  
Vol 24 (1) ◽  
pp. 183-188
Author(s):  
Robert W. Rosenthal
Keyword(s):  
Linear Models ◽  
Sufficient Conditions ◽  
Technical Note

scholarly journals A Second-Order Sufficient Optimality Condition for Risk-Neutral Bi-level Stochastic Linear Programs

2020 ◽  
Author(s):  
Matthias Claus
Keyword(s):  
Optimality Condition ◽  
Linear Models ◽  
Sufficient Conditions ◽  
Strong Stability ◽  
Second Order ◽  
Linear Programs ◽  
Sufficient Optimality Condition ◽  
Lipschitz Continuous ◽  
Risk Neutral ◽  
Stochastic Linear Programs

Abstract The expectation functionals, which arise in risk-neutral bi-level stochastic linear models with random lower-level right-hand side, are known to be continuously differentiable, if the underlying probability measure has a Lebesgue density. We show that the gradient may fail to be local Lipschitz continuous under this assumption. Our main result provides sufficient conditions for Lipschitz continuity of the gradient of the expectation functional and paves the way for a second-order optimality condition in terms of generalized Hessians. Moreover, we study geometric properties of regions of strong stability and derive representation results, which may facilitate the computation of gradients.

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