Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userDo we need to estimate the variance in robust mean estimation?
160
0
0.0
(
0
)
Added by
Qiang Sun
Publication date
2021
fields
Mathematical Statistics
and research's language is
English
Authors
Qiang Sun
Ask ChatGPT about the research
No Arabic abstract
This paper studies robust mean estimators for distributions with only finite variances. We propose a new loss function that is a function of the mean parameter and a robustification parameter. By simultaneously optimizing the empirical loss with respect to both parameters, we show that the resulting estimator for the robustification parameter can automatically adapt to the data and the unknown variance. Thus the resulting mean estimator can achieve near-optimal finite-sample performance. Compared with prior work, our method is computationally efficient and user-friendly. It does not need cross-validation to tune the robustification parameter.
rate research
Read More
The variance of noise plays an important role in many change-point detection procedures and the associated inferences. Most commonly used variance estimators require strong assumptions on the true mean structure or normality of the error distribution, which may not hold in applications. More importantly, the qualities of these estimators have not been discussed systematically in the literature. In this paper, we introduce a framework of equivariant variance estimation for multiple change-point models. In particular, we characterize the set of all equivariant unbiased quadratic variance estimators for a family of change-point model classes, and develop a minimax theory for such estimators.
We study variance estimation and associated confidence intervals for parameters characterizing genetic effects from genome-wide association studies (GWAS) misspecified mixed model analysis. Previous studies have shown that, in spite of the model misspecification, certain quantities of genetic interests are estimable, and consistent estimators of these quantities can be obtained using the restricted maximum likelihood (REML) method under a misspecified linear mixed model. However, the asymptotic variance of such a REML estimator is complicated and not ready to be implemented for practical use. In this paper, we develop practical and computationally convenient methods for estimating such asymptotic variances and constructing the associated confidence intervals. Performance of the proposed methods is evaluated empirically based on Monte-Carlo simulations and real-data application.
Propensity score methods have been shown to be powerful in obtaining efficient estimators of average treatment effect (ATE) from observational data, especially under the existence of confounding factors. When estimating, deciding which type of covariates need to be included in the propensity score function is important, since incorporating some unnecessary covariates may amplify both bias and variance of estimators of ATE. In this paper, we show that including additional instrumental variables that satisfy the exclusion restriction for outcome will do harm to the statistical efficiency. Also, we prove that, controlling for covariates that appear as outcome predictors, i.e. predict the outcomes and are irrelevant to the exposures, can help reduce the asymptotic variance of ATE estimation. We also note that, efficiently estimating the ATE by non-parametric or semi-parametric methods require the estimated propensity score function, as described in Hirano et al. (2003)cite{Hirano2003}. Such estimation procedure usually asks for many regularity conditions, Rothe (2016)cite{Rothe2016} also illustrated this point and proposed a known propensity score (KPS) estimator that requires mild regularity conditions and is still fully efficient. In addition, we introduce a linearly modified (LM) estimator that is nearly efficient in most general settings and need not estimation of the propensity score function, hence convenient to calculate. The construction of this estimator borrows idea from the interaction estimator of Lin (2013)cite{Lin2013}, in which regression adjustment with interaction terms are applied to deal with data arising from a completely randomized experiment. As its name suggests, the LM estimator can be viewed as a linear modification on the IPW estimator using known propensity scores. We will also investigate its statistical properties both analytically and numerically.
Missing data and confounding are two problems researchers face in observational studies for comparative effectiveness. Williamson et al. (2012) recently proposed a unified approach to handle both issues concurrently using a multiply-robust (MR) methodology under the assumption that confounders are missing at random. Their approach considers a union of models in which any submodel has a parametric component while the remaining models are unrestricted. We show that while their estimating function is MR in theory, the possibility for multiply robust inference is complicated by the fact that parametric models for different components of the union model are not variation independent and therefore the MR property is unlikely to hold in practice. To address this, we propose an alternative transparent parametrization of the likelihood function, which makes explicit the model dependencies between various nuisance functions needed to evaluate the MR efficient score. The proposed method is genuinely doubly-robust (DR) in that it is consistent and asymptotic normal if one of two sets of modeling assumptions holds. We evaluate the performance and doubly robust property of the DR method via a simulation study.
We examine the possibility of soft cosmology, namely small deviations from the usual framework due to the effective appearance of soft-matter properties in the Universe sectors. One effect of such a case would be the dark energy to exhibit a different equation-of-state parameter at large scales (which determine the universe expansion) and at intermediate scales (which determine the sub-horizon clustering and the large scale structure formation). Concerning soft dark matter, we show that it can effectively arise due to the dark-energy clustering, even if dark energy is not soft. We propose a novel parametrization introducing the softness parameters of the dark sectors. As we see, although the background evolution remains unaffected, due to the extreme sensitivity and significant effects on the global properties even a slightly non-trivial softness parameter can improve the clustering behavior and alleviate e.g. the $fsigma_8$ tension. Lastly, an extension of the cosmological perturbation theory and a detailed statistical mechanical analysis, in order to incorporate complexity and estimate the scale-dependent behavior from first principles, is necessary and would provide a robust argumentation in favour of soft cosmology.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
