Biometrika

Journal: Biometrika

Abbreviation

Biometrika

Publisher

Oxford University Press

ISSN

0006-3444
1464-3510

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Publications 1 - 10 of 15

Characterizing M-estimators
Dimitriadis, Timo; Fissler, Tobias; Ziegel, Johanna (2024)
Biometrika
We characterize the full classes of M-estimators for semiparametric models of general functionals by formally connecting the theory of consistent loss functions from forecast evaluation with the theory of M-estimation. This novel characterization result allows us to leverage existing results on loss functions known from the literature on forecast evaluation in estimation theory. We exemplify advantageous implications for the fields of robust, efficient, equivariant and Pareto-optimal M-estimation.
Systematic sampling with errors in sample locations
Ziegel, Johanna; Baddeley, Adrian; Dorph-Petersen, Karl-Anton; et al. (2010)
Biometrika
Honest calibration assessment for binary outcome predictions
Dimitriadis, Timo; Dümbgen, Lutz; Henzi, Alexander; et al. (2023)
Biometrika
Probability predictions from binary regressions or machine learning methods ought to be calibrated: if an event is predicted to occur with probability x, it should materialize with approximately that frequency, which means that the so-called calibration curvep(middot) should equal the identity, i.e., p(x) = x for all x in the unit interval. We propose honest calibration assessment based on novel confidence bands for the calibration curve, which are valid subject to only the natural assumption of isotonicity. Besides testing the classical goodness-of-fit null hypothesis of perfect calibration, our bands facilitate inverted goodness-of-fit tests whose rejection allows for the sought-after conclusion of a sufficiently well-specified model. We show that our bands have a finite-sample coverage guarantee, are narrower than those of existing approaches, and adapt to the local smoothness of the calibration curve p and the local variance of the binary observations. In an application to modelling predictions of an infant having low birth weight, the bounds give informative insights into model calibration.
Markov models for accumulating mutations
Beerenwinkel, Niko; Sullivant, Seth (2009)
Biometrika
Graphical tools for selecting conditional instrumental sets
Henckel, Leonard; Buttenschoen, Martin; Maathuis, Marloes H. (2024)
Biometrika
We consider the efficient estimation of total causal effects in the presence of unmeasured confounding using conditional instrumental sets. Specifically, we consider the two-stage least-squares estimator in the setting of a linear structural equation model with correlated errors that is compatible with a known acyclic directed mixed graph. To set the stage for our results, we characterize the class of linearly valid conditional instrumental sets that yield consistent two-stage least-squares estimators for the target total effect and derive a new asymptotic variance formula for these estimators. Equipped with these results, we provide three graphical tools for selecting more efficient linearly valid conditional instrumental sets: first, a graphical criterion that, for certain pairs of linearly valid conditional instrumental sets, identifies which of the two corresponding estimators has the smaller asymptotic variance second, an algorithm that greedily adds covariates that reduce the asymptotic variance to a given linearly valid conditional instrumental set and, third, a linearly valid conditional instrumental set for which the corresponding estimator has the smallest asymptotic variance that can be ensured with a graphical criterion.
Variable selection in high-dimensional linear models
Bühlmann, Peter; Kalisch, Markus; Maathuis, Marloes H. (2010)
Biometrika
Symmetric rank covariances: a generalized framework for nonparametric measures of dependence
Weihs, Luca; Drton, Mathias; Meinshausen, Nicolai (2018)
Biometrika
The need to test whether two random vectors are independent has spawned many competing measures of dependence. We focus on nonparametric measures that are invariant under strictly increasing transformations, such as Kendall’s tau, Hoeffding’s D, and the Bergsma–Dassios sign covariance. Each exhibits symmetries that are not readily apparent from their definitions. Making these symmetries explicit, we define a new class of multivariate nonparametric measures of dependence that we call symmetric rank covariances. This new class generalizes the above measures and leads naturally to multivariate extensions of the Bergsma–Dassios sign covariance. Symmetric rank covariances may be estimated unbiasedly using U-statistics, for which we prove results on computational efficiency and large-sample behaviour. The algorithms we develop for their computation include, to the best of our knowledge, the first efficient algorithms for Hoeffding’s D statistic in the multivariate setting.
Lower bounds for the number of false null hypotheses for multiple testing of associations under general dependence structures
Meinshausen, Nicolai; Bühlmann, Peter (2005)
Biometrika
Ancestor regression in linear structural equation models
Schultheiss, Christoph; Bühlmann, Peter (2023)
Biometrika
We present a new method for causal discovery in linear structural equation models. We propose a simple technique based on statistical testing in linear models that can distinguish between ancestors and non-ancestors of any given variable. Naturally, this approach can then be extended to estimating the causal order among all variables. Unlike with many methods, it is possible to provide explicit error control for false causal discovery, at least asymptotically. This holds even under Gaussianity where various methods fail because of nonidentifiable structures. These Type I error guarantees come at the cost of reduced power. Additionally, we provide an asymptotically valid goodness-of-fit p-value for assessing whether multivariate data stem from a linear structural equation model.
A Rank-Based Sequential Test of Independence
Henzi, Alexander; Law, Michael (2024)
Biometrika
We consider the problem of independence testing for two univariate random variables in a sequential setting. By leveraging recent developments on safe, anytime-valid inference, we propose a test with time-uniform type I error control and derive explicit bounds on the finite sample performance of the test. We demonstrate the empirical performance of the procedure in comparison to existing sequential and non-sequential independence tests. Furthermore, since the proposed test is distribution free under the null hypothesis, we empirically simulate the gap due to Ville’s inequality–the supermartingale analogue of Markov’s inequality–that is commonly applied to control type I error in anytime-valid inference, and apply this to construct a truncated sequential test.

Publications 1 - 10 of 15

Journal: Biometrika

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