Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userRedescending M-estimators and Deterministic Annealing, with Applications to Robust Regression and Tail Index Estimation
159
0
0.0
(
0
)
Added by
Wolfgang Waltenberger
Publication date
2010
fields
Mathematical Statistics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
A new type of redescending M-estimators is constructed, based on data augmentation with an unspecified outlier model. Necessary and sufficient conditions for the convergence of the resulting estimators to the Hubertype skipped mean are derived. By introducing a temperature parameter the concept of deterministic annealing can be applied, making the estimator insensitive to the starting point of the iteration. The properties of the annealing M-estimator as a function of the temperature are explored. Finally, two applications are presented. The first one is the robust estimation of interaction vertices in experimental particle physics, including outlier detection. The second one is the estimation of the tail index of a distribution from a sample using robust regression diagnostics.
rate research
Read More
A robust estimator is proposed for the parameters that characterize the linear regression problem. It is based on the notion of shrinkages, often used in Finance and previously studied for outlier detection in multivariate data. A thorough simulation study is conducted to investigate: the efficiency with normal and heavy-tailed errors, the robustness under contamination, the computational times, the affine equivariance and breakdown value of the regression estimator. Two classical data-sets often used in the literature and a real socio-economic data-set about the Living Environment Deprivation of areas in Liverpool (UK), are studied. The results from the simulations and the real data examples show the advantages of the proposed robust estimator in regression.
Fully robu
Multilevel regression and poststratification (MRP) is a flexible modeling technique that has been used in a broad range of small-area estimation problems. Traditionally, MRP studies have been focused on non-causal settings, where estimating a single population value using a nonrepresentative sample was of primary interest. In this manuscript, MRP-style estimators will be evaluated in an experimental causal inference setting. We simulate a large-scale randomized control trial with a stratified cluster sampling design, and compare traditional and nonparametric treatment effect estimation methods with MRP methodology. Using MRP-style estimators, treatment effect estimates for areas as small as 1.3$%$ of the population have lower bias and variance than standard causal inference methods, even in the presence of treatment effect heterogeneity. The design of our simulation studies also requires us to build upon a MRP variant that allows for non-census covariates to be incorporated into poststratification.
Single index models provide an effective dimension reduction tool in regression, especially for high dimensional data, by projecting a general multivariate predictor onto a direction vector. We propose a novel single-index model for regression models where metric space-valued random object responses are coupled with multivariate Euclidean predictors. The responses in this regression model include complex, non-Euclidean data, including covariance matrices, graph Laplacians of networks, and univariate probability distribution functions among other complex objects that lie in abstract metric spaces. Frechet regression has provided an approach for modeling the conditional mean of such random objects given multivariate Euclidean vectors, but it does not provide for regression parameters such as slopes or intercepts, since the metric space-valued responses are not amenable to linear operations. We show here that for the case of multivariate Euclidean predictors, the parameters that define a single index and associated projection vector can be used to substitute for the inherent absence of parameters in Frechet regression. Specifically, we derive the asymptotic consistency of suitable estimates of these parameters subject to an identifiability condition. Consistent estimation of the link function of the single index Frechet regression model is obtained through local Frechet regression. We demonstrate the finite sample performance of estimation for the proposed single index Frechet regression model through simulation studies, including the special cases of probability distributions and graph adjacency matrices. The method is also illustrated for resting-state functional Magnetic Resonance Imaging (fMRI) data from the ADNI study.
Factor models are a class of powerful statistical models that have been widely used to deal with dependent measurements that arise frequently from various applications from genomics and neuroscience to economics and finance. As data are collected at an ever-growing scale, statistical machine learning faces some new challenges: high dimensionality, strong dependence among observed variables, heavy-tailed variables and heterogeneity. High-dimensional robust factor analysis serves as a powerful toolkit to conquer these challenges. This paper gives a selective overview on recent advance on high-dimensional factor models and their applications to statistics including Factor-Adjusted Robust Model selection (FarmSelect) and Factor-Adjusted Robust Multiple testing (FarmTest). We show that classical methods, especially principal component analysis (PCA), can be tailored to many new problems and provide powerful tools for statistical estimation and inference. We highlight PCA and its connections to matrix perturbation theory, robust statistics, random projection, false discovery rate, etc., and illustrate through several applications how insights from these fields yield solutions to modern challenges. We also present far-reaching connections between factor models and popular statistical learning problems, including network analysis and low-rank matrix recovery.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
