Now showing 1 - 10 of 16
  • Publication
    Consistency of p-norm based tests in high dimensions: characterization, monotonicity, domination
    ( 2023)
    Kock, Anders Bredahl
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    Many commonly used test statistics are based on a norm measuring the evidence against the null hypothesis. To understand how the choice of a norm affects power properties of tests in high dimensions, we study the consistency sets of p-norm based tests in the prototypical framework of sequence models with unrestricted parameter spaces, the null hypothesis being that all observations have zero mean. The consistency set of a test is here defined as the set of all arrays of alternatives the test is consistent against as the dimension of the parameter space diverges. We characterize the consistency sets of p-norm based tests and find, in particular, that the consistency against an array of alternatives cannot be determined solely in terms of the p-norm of the alternative. Our characterization also reveals an unexpected monotonicity result: namely that the consistency set is strictly increasing in p∈(0,∞), such that tests based on higher p strictly dominate those based on lower p in terms of consistency. This monotonicity allows us to construct novel tests that dominate, with respect to their consistency behavior, all p-norm based tests without sacrificing size.
  • Publication
    How Reliable are Bootstrap-Based Heteroskedasticity Robust Tests?
    ( 2023)
    Pötscher, Benedikt M.
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    We develop theoretical finite-sample results concerning the size of wild bootstrap-based heteroskedasticity robust tests in linear regression models. In particular, these results provide an efficient diagnostic check, which can be used to weed out tests that are unreliable for a given testing problem in the sense that they overreject substantially. This allows us to assess the reliability of a large variety of wild bootstrap-based tests in an extensive numerical study.
    Scopus© Citations 1
  • Publication
    Functional sequential treatment allocation
    ( 2022)
    Kock, Anders Bredahl
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    Veliyev, Bezirgen
    Consider a setting in which a policy maker assigns subjects to treatments, observing each outcome before the next subject arrives. Initially, it is unknown which treatment is best, but the sequential nature of the problem permits learning about the effectiveness of the treatments. While the multi-armed-bandit literature has shed much light on the situation when the policy maker compares the effectiveness of the treatments through their mean, much less is known about other targets. This is restrictive, because a cautious decision maker may prefer to target a robust location measure such as a quantile or a trimmed mean. Furthermore, socio-economic decision making often requires targeting purpose specific characteristics of the outcome distribution, such as its inherent degree of inequality, welfare or poverty. In the present article, we introduce and study sequential learning algorithms when the distributional characteristic of interest is a general functional of the outcome distribution. Minimax expected regret optimality results are obtained within the subclass of explore-then-commit policies, and for the unrestricted class of all policies. Supplementary materials for this article are available online.
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  • Publication
    Uniformly valid confidence intervals post-model-selection
    (Institute of Mathematical Statistics, 2020)
    Bachoc, François
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    Steinberger, Lukas
    We suggest general methods to construct asymptotically uniformly valid confidence intervals post-model-selection. The constructions are based on principles recently proposed by Berk et al. (Ann. Statist. 41 (2013) 802–837). In particular, the candidate models used can be misspecified, the target of inference is model-specific, and coverage is guaranteed for any data-driven model selection procedure. After developing a general theory, we apply our methods to practically important situations where the candidate set of models, from which a working model is selected, consists of fixed design homoskedastic or heteroskedastic linear models, or of binary regression models with general link functions. In an extensive simulation study, we find that the proposed confidence intervals perform remarkably well, even when compared to existing methods that are tailored only for specific model selection procedures.
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  • Publication
    Power in high-dimensional testing problems
    ( 2019)
    Kock, Anders Bredahl
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    Fan, Liao, and Yao (2015) recently introduced a remarkable method for increasing the asymptotic power of tests in high-dimensional testing problems. If applicable to a given test, their power enhancement principle leads to an improved test that has the same asymptotic size, has uniformly non-inferior asymptotic power, and is consistent against a strictly broader range of alternatives than the initially given test. We study under which conditions this method can be applied and show the following: In asymptotic regimes where the dimensionality of the parameter space is fixed as sample size increases, there often exist tests that cannot be further improved with the power enhancement principle. However, when the dimensionality of the parameter space increases sufficiently slowly with sample size and a marginal local asymptotic normality (LAN) condition is satisfied, every test with asymptotic size smaller than 1 can be improved with the power enhancement principle. While the marginal LAN condition alone does not allow one to extend the latter statement to all rates at which the dimensionality increases with sample size, we give sufficient conditions under which this is the case.
    Scopus© Citations 9
  • Publication
    Further results on size and power of heteroskedasticity and autocorrelation robust tests, with an application to trend testing
    (Institute of Mathematical Statistics and Bernoulli Society, 2019)
    Pötscher, Benedikt M.
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  • Publication
  • Publication
    Finite sample properties of tests based on prewhitened nonparametric covariance estimators
    (Institute of Mathematical Statistics and Bernoulli Society, 2017)
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  • Publication
    On the power of invariant tests for hypotheses on a covariance matrix
    (Cambridge University Press, 2017) ;
    Pöscher, Benedikt M.
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  • Publication
    On size and power of heteroskedasticity and autocorrelation robust tests
    (Cambridge University Press, 2016) ;
    Pötscher, Benedikt M.
    Testing restrictions on regression coefficients in linear models often requires correcting the conventional F-test for potential heteroskedasticity or autocorrelation amongst the disturbances, leading to so-called heteroskedasticity and autocorrelation robust test procedures. These procedures have been developed with the purpose of attenuating size distortions and power deficiencies present for the uncorrected F-test. We develop a general theory to establish positive as well as negative finite-sample results concerning the size and power properties of a large class of heteroskedasticity and autocorrelation robust tests. Using these results we show that nonparametrically as well as parametrically corrected F-type tests in time series regression models with stationary disturbances have either size equal to one or nuisance-infimal power equal to zero under very weak assumptions on the covariance model and under generic conditions on the design matrix. In addition we suggest an adjustment procedure based on artificial regressors. This adjustment resolves the problem in many cases in that the so-adjusted tests do not suffer from size distortions. At the same time their power function is bounded away from zero. As a second application we discuss the case of heteroskedastic disturbances.
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