Introduction to Robust Estimation and Hypothesis Testing

doi:10.1198/tech.2005.s334

Cited by 5 publications

(8 citation statements)

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“…This allowed for comparing the proposed Bayesian model to established classical methods. Second, we focused on methods that have been described in the psychological literature (Wilcox, 2012). While this allowed for comparing methods that would be familiar to psychologists, this decision also presented some limitations.…”

Section: Comparison To Classical Robust Methodsmentioning

confidence: 99%

“…Yuen's method requires selection of the trimming proportion γ. This can simultaneously provide non-optimal data reduction (Wilcox, 2012) and can increase researcher degrees freedom in that each value of γ will produce a different p-value (Simmons, Nelson, & Simonsohn, 2011). In contrast, the M-estimation approach quantitatively determines the degree of trimming which allows for accommodating a wider class of distributions (e.g., skewed).…”

Section: One-step M-estimatormentioning

confidence: 99%

“…The one-step M-estimator is then obtained with one iteration of the Newton-Raphson method. Importantly, one iteration provides asymptotic calibration and expected frequentist properties (e.g., type I error rates) (Wilcox, 2012). The null hypothesis test is then H 0 : µ m1 = µ m2 , with the jth group M-estimator asμ…”

Section: One-step M-estimatormentioning

confidence: 99%

“…The modified one-step M-estimator (MOM) is obtained by removing kζ(i 2 − i 1 ) from equation 11. This allows for averaging observations not determined to be outliers (Wilcox, 2012). The MOM ofμ m is given bŷ…”

Section: Modified One-step M-estimatormentioning

confidence: 99%

“…Several robust statistical methods have been developed (Wilcox, 2012). The benefits of these approaches have been thoroughly described, including in terms of improved parameter estimation (Özdemir, 2010) and optimal power (Wilcox, 2001).…”

Section: Introductionmentioning

confidence: 99%

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Rethinking Robust Statistics with Modern Bayesian Methods

Williams¹,

Martin²

2017

Preprint

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Developing robust statistical methods is an important goal for psychological science. Whereas classical methods (i.e., sampling distributions, p-values, etc.) have been thoroughly characterized, Bayesian robust methods remain relatively uncommon in practice and methodological literatures. Here we propose a robust Bayesian model (BHS t ) that accommodates heterogeneous (H) variances by predicting the scale parameter on the log scale and tail-heaviness with a Student-t likelihood (S t). Through simulations with normative and contaminated (i.e., heavy-tailed) data, we demonstrate that BHS t has consistent frequentist properties in terms of type I error, power, and mean squared error compared to three classical robust methods. With a motivating example, we illustrate Bayesian inferential methods such as approximate leave-one-out cross-validation and posterior predictive checks. We end by suggesting areas of improvement for BHS t and discussing Bayesian robust methods in practice.

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Section: Comparison To Classical Robust Methodsmentioning

confidence: 99%

Section: One-step M-estimatormentioning

confidence: 99%

Section: One-step M-estimatormentioning

confidence: 99%

Section: Modified One-step M-estimatormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Rethinking Robust Statistics with Modern Bayesian Methods

Williams¹,

Martin²

2017

Preprint

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Multiproxy dietary trait reconstruction in Pleistocene Hippopotamidae from the Mediterranean islands

Bethune

Kaiser

Schulz‐Kornas

et al. 2019

Palaeogeography, Palaeoclimatology, Palaeoecology

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Geographically isolated insular species face energetic restrictions and commonly evolve adaptations that distinguish them from their mainland ancestors. During the Pleistocene, several Mediterranean islands were inhabited by now extinct Hippopotamidae. They underwent diverse changes in locomotion, dentition and body size. Based on these differences, it is supposed that they occupied different ecological niches depending on their respective faunal complexes and available resources. In this paper, we assess the paleoecology of dwarfed hippopotami from Crete, Malta, Sicily and Cyprus using a novel dental multiproxy approach. We applied dental topography analysis (SAGA-GIS) to measure the mean slope of the dental occlusal surface, mirroring dietary adaptations, as well as 3D surface texture analysis (3DST) to quantify the surface of occlusal wear facets, which correlate with dietary abrasiveness. Low slope values were found in the larger, more hypsodont hippopotami, whilst the smaller Phanourios minor displayed the highest occlusal relief with large compression basins. Since Hippopotamus pentlandi exhibited lower mean slope values than the larger, more hypsodont Hippopotamus amphibius, we conclude that lower occlusal reliefs reflect adaptations to lower diet quality and arid environments, which are characteristic of freshwater-limited island habitats. The 3DST analysis revealed distinct ecological niches for the investigated insular hippos. Hippopotamus creutzburgi exhibited enamel surface textures analogous to those of Hippopotamus amphibius, a fresh grass grazer, thus confirming a semiaquatic lifestyle at the upland lake at Katharo, Crete. Hippopotamus pentlandi was bound to a similar niche to the extant form, probably due to the mainland character of its fauna, but experienced more dust intake. Hippopotamus melitensis had to cope with high ingestion of abrasives, seemingly on account of a more generalistic diet in its resource-limited and small habitat. Results point to either Phanourios minor broadening its dietary niche in its almost competition-free habitat, or suggest a dietary shift following a climatic change. The adopted multiproxy approach proved to be useful in identifying dental adaptations and individual foraging strategies linked to energetically restricted habitats, and therefore contributes to a better understanding of basic evolutionary and ecological principles.

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Robust Methods for Moderation Analysis with a Two-Level Regression Model

Yang

Yuan

2016

Multivariate Behavioral Research

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Moderation analysis has many applications in social sciences. Most widely used estimation methods for moderation analysis assume that errors are normally distributed and homoscedastic. When these assumptions are not met, the results from a classical moderation analysis can be misleading. For more reliable moderation analysis, this article proposes two robust methods with a two-level regression model when the predictors do not contain measurement error. One method is based on maximum likelihood with Student's t distribution and the other is based on M-estimators with Huber-type weights. An algorithm for obtaining the robust estimators is developed. Consistent estimates of standard errors of the robust estimators are provided. The robust approaches are compared against normal-distribution-based maximum likelihood (NML) with respect to power and accuracy of parameter estimates through a simulation study. Results show that the robust approaches outperform NML under various distributional conditions. Application of the robust methods is illustrated through a real data example. An R program is developed and documented to facilitate the application of the robust methods.

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Introduction to Robust Estimation and Hypothesis Testing

Cited by 5 publications

References 4 publications

Rethinking Robust Statistics with Modern Bayesian Methods

Rethinking Robust Statistics with Modern Bayesian Methods

Multiproxy dietary trait reconstruction in Pleistocene Hippopotamidae from the Mediterranean islands

Robust Methods for Moderation Analysis with a Two-Level Regression Model

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