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作者：Chan, K. W.; Yau, C. Y.
作者单位：Chinese University of Hong Kong
摘要：Estimation of the time-average variance constant is important for statistical analyses involving dependent data. This problem is difficult as it relies on a bandwidth parameter. Specifically, the optimal choices of the bandwidths of all existing estimators depend on the estimand itself and another unknown parameter that is very difficult to estimate. Thus, optimal variance estimation is unachievable. In this paper, we introduce a concept of converging flat-top kernels for constructing variance...
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作者：[Anonymous]
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作者：Henckel, L.; Buttenschoen, M.; Maathuis, M. H.
作者单位：University College Dublin; University of Oxford; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：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 es...
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作者：Singh, R.; Xu, L.; Gretton, A.
作者单位：Massachusetts Institute of Technology (MIT); University of London; University College London
摘要：We propose estimators based on kernel ridge regression for nonparametric causal functions such as dose, heterogeneous and incremental response curves. The treatment and covariates may be discrete or continuous in general spaces. Because of a decomposition property specific to the reproducing kernel Hilbert space, our estimators have simple closed-form solutions. We prove uniform consistency with finite sample rates via an original analysis of generalized kernel ridge regression. We extend our ...
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作者：Bing, Xin; Wegkamp, Marten
作者单位：University of Toronto; Cornell University
摘要：This paper considers binary classification of high-dimensional features under a postulated model with a low-dimensional latent Gaussian mixture structure and nonvanishing noise. A generalized least-squares estimator is used to estimate the direction of the optimal separating hyperplane. The estimated hyperplane is shown to interpolate on the training data. While the direction vector can be consistently estimated, as could be expected from recent results in linear regression, a naive plug-in es...
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作者：Fan, Yixuan; Jiao, Zhanyi; Wang, Ruodu
作者单位：Tianjin University; Illinois State University; University of Waterloo
摘要：We address the problem of testing the conditional mean and conditional variance for nonstationary data. We build e-values and p-values for four types of nonparametric composite hypothesis with specified mean and variance as well as other conditions on the shape of the data-generating distribution. These shape conditions include symmetry, unimodality and their combination. Using the obtained e-values and p-values, we construct tests via e-processes, also known as testing by betting, as well as ...
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作者：Huang, Melody; Pimentel, Samuel D.
作者单位：Yale University; University of California System; University of California Berkeley
摘要：Weighting methods are popular tools for estimating causal effects, and assessing their robustness under unobserved confounding is important in practice. Current approaches to sensitivity analyses rely on bounding a worst-case error from omitting a confounder. In this paper, we introduce a new sensitivity model called the variance-based sensitivity model, which instead bounds the distributional differences that arise in the weights from omitting a confounder. The variance-based sensitivity mode...
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作者：Dette, H.; Kroll, M.
作者单位：Ruhr University Bochum
摘要：We prove that an m-out-of-n bootstrap procedure for Chatterjee's rank correlation is consistent whenever asymptotic normality of Chatterjee's rank correlation can be established. In particular, we prove that m-out-of-n bootstrap works for continuous as well as discrete data with independent coordinates; furthermore, simulations indicate that it also performs well for discrete data with dependent coordinates, and that it outperforms alternative estimation methods. Consistency of the bootstrap i...
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作者：Bao, Yajie; Huo, Yuyang; Ren, Haojie; Zou, Changliang
作者单位：Shanghai Jiao Tong University; Nankai University
摘要：Conformal inference is a popular tool for constructing prediction intervals. We consider here the scenario of post-selection/selective conformal inference, that is, prediction intervals are reported only for individuals selected from unlabelled test data. To account for multiplicity, we develop a general split conformal framework to construct selective prediction intervals with the false coverage-statement rate control. We first investigate the false coverage rate-adjusted method of in the pre...
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作者：Dimitriadis, Timo; Fissler, Tobias; Ziegel, Johanna
作者单位：Ruprecht Karls University Heidelberg; Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Bern
摘要：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-estimat...
