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Bandwidth choice is crucial in spatial kernel estimation in exploring non‐Gaussian complex spatial data. The paper investigates the choice of adaptive and non‐adaptive bandwidths for density estimation given data on a spatial lattice. An adaptive bandwidth depends on local data and hence adaptively conforms with local features of the spatial data. We propose a spatial cross‐validation (SCV) choice...
Adaptive enrichment designs involve preplanned rules for modifying enrolment criteria based on accruing data in a randomized trial. We focus on designs where the overall population is partitioned into two predefined subpopulations, e.g. based on a biomarker or risk score measured at baseline. The goal is to learn which populations benefit from an experimental treatment. Two critical components of...
Mediation analysis in causal inference has traditionally focused on binary exposures and deterministic interventions, and a decomposition of the average treatment effect in terms of direct and indirect effects. We present an analogous decomposition of the population intervention effect, defined through stochastic interventions on the exposure. Population intervention effects provide a generalized...
We provide a new computationally efficient class of estimators for risk minimization. We show that these estimators are robust for general statistical models, under varied robustness settings, including in the classical Huber ε‐contamination model, and in heavy‐tailed settings. Our workhorse is a novel robust variant of gradient descent, and we provide conditions under which our gradient descent variant...
Markov chain Monte Carlo (MCMC) methods provide consistent approximations of integrals as the number of iterations goes to ∞. MCMC estimators are generally biased after any fixed number of iterations. We propose to remove this bias by using couplings of Markov chains together with a telescopic sum argument of Glynn and Rhee. The resulting unbiased estimators can be computed independently in parallel...
In observational studies, potential confounders may distort the causal relationship between an exposure and an outcome. However, under some conditions, a causal dose–response curve can be recovered by using the G‐computation formula. Most classical methods for estimating such curves when the exposure is continuous rely on restrictive parametric assumptions, which carry significant risk of model misspecification...
Generalized linear models are often misspecified because of overdispersion, heteroscedasticity and ignored nuisance variables. Existing quasi‐likelihood methods for testing in misspecified models often do not provide satisfactory type I error rate control. We provide a novel semiparametric test, based on sign flipping individual score contributions. The parameter tested is allowed to be multi‐dimensional...
Hypothesis testing in the linear regression model is a fundamental statistical problem. We consider linear regression in the high dimensional regime where the number of parameters exceeds the number of samples (p>n). To make informative inference, we assume that the model is approximately sparse, i.e. the effect of covariates on the response can be well approximated by conditioning on a relatively...
Two‐stage sampling designs are commonly used for household and health surveys. To produce reliable estimators with associated confidence intervals, some basic statistical properties like consistency and asymptotic normality of the Horvitz–Thompson estimator are desirable, along with the consistency of associated variance estimators. These properties have been mainly studied for single‐stage sampling...
We propose a family of tests to assess the goodness of fit of a high dimensional generalized linear model. Our framework is flexible and may be used to construct an omnibus test or directed against testing specific non‐linearities and interaction effects, or for testing the significance of groups of variables. The methodology is based on extracting left‐over signal in the residuals from an initial...
We develop methodology for testing relevant hypotheses about functional time series in a tuning‐free way. Instead of testing for exact equality, e.g. for the equality of two mean functions from two independent time series, we propose to test the null hypothesis of no relevant deviation. In the two‐sample problem this means that an ‐distance between the two mean functions is smaller than a prespecified...
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