Robust Estimation for Generalized Additive Models

Wong, Raymond K. W.; Yao, Fang; Lee, Thomas C.

doi:10.1080/10618600.2012.756816

Cited by 28 publications

(36 citation statements)

References 22 publications

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“…To obtain the smooth estimator of the univariate components, the techniques for additive models will be able to be used (see Wong et al (2014)). For estimating the bivariate components, on the other hand, we expect to use the proposed method of this paper.…”

Section: Discussionmentioning

confidence: 99%

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Nonlinear surface regression with dimension reduction method

Yoshida

2016

AStA Adv Stat Anal

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This paper considers nonlinear regression analysis with a scalar response and multiple predictors. An unknown regression function is approximated by radial basis function models. The coefficients are estimated in the context of M-estimation. It is known that ordinary M-estimation leads to overfitting in nonlinear regression. The purpose of this paper is to construct a smooth estimator. The proposed method in this paper is conducted by a two-step procedure. First, the sufficient dimension reduction methods are applied to the response and radial basis functions for transforming the large number of radial bases to a small number of linear combinations of the radial bases without loss of information. In the second step, a multiple linear regression model between a response and the transformed radial bases is assumed and the ordinary Mestimation is applied. Thus, the final estimator is also obtained as a linear combination of radial bases. The validity and an asymptotic study of the proposed method are explored. A simulation and data example are addressed to confirm the behavior of the proposed method.

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Section: Discussionmentioning

confidence: 99%

“…On the other hand, the ordinary M-estimation, minimizing n i=1 ρ(Y i − S(x i )), leads to a wiggly curve. Alimadad and Salibian-Barrera (2011) and Wong et al (2014) studied the M-estimation but their methods are limited to additive models. We wish to constrain c to overcome the undersmoothed fits in general multiple regression.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear surface regression with dimension reduction method

Yoshida

2016

AStA Adv Stat Anal

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“…Similarly, mean prediction standard errors (MPSE) were calculated from the testing set prediction variances. The MAPE and MPSE values of the different methods from the tenfold cross validation were compared using paired t tests (Wong et al, ). These were corrected for multiple comparisons using the Bonferroni procedure (Bretz et al, ).…”

Section: Methodsmentioning

confidence: 99%

Evaluation of Nonparametric and Parametric Statistical Procedures for Modeling and Prediction of Cluster‐Correlated Hydroclimatic Data

Singh

Abebe

Srivastava

2018

Water Resources Research

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Climate and hydrologic variables such as temperature, precipitation, streamflow, and baseflow generally do not follow Gaussian distribution due to the presence of outliers and heavy tails. Therefore, they are usually analyzed using the nonparametric Wilcoxon rank sum test rather than parametric methods like classical t tests and analysis of variance. Furthermore, in addition to having a non‐Gaussian distribution, these data exhibit monthly/seasonal variability, which leads to within month/season cluster correlation. In this study, a nonparametric procedure, called joint rank fit (JRFit), for analyzing cluster‐correlated data was implemented and compared against traditional methods such as restricted maximum likelihood, least absolute deviations, and rank‐based fit (a model‐based extension of Wilcoxon rank sum) for studying the coupled effect of the phases of El Niño–Southern Oscillation and Atlantic Multidecadal Oscillation on baseflow levels. The results from a large Monte Carlo simulation experiment showed that JRFit was more efficient than the other three methods for data with (i) high variability, (ii) outliers due to contamination, or (iii) strong monthly/seasonal correlation. The efficiency gain of JRFit was up to 50% compared to restricted maximum likelihood for heavy‐tailed and highly correlated data. Predictive performance evaluated using the mean absolute prediction error and mean prediction standard error from an out‐of‐sample cross‐validation study showed JRFit to be optimal for providing predictions of baseflow on the basis of the phases of El Niño–Southern Oscillation and Atlantic Multidecadal Oscillation. Thus, it is recommended that JRFit be implemented in hydroclimatic studies to provide powerful inference when there is evidence of clustering in the data.

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“…Consistency and asymptotic normality were established. Wong et al (2014) used M-type estimators to estimate generalized additive models in the presence of aberrant observations. Asymptotic properties served as the motivation in decomposing the overall M-type estimation problem into a sequence of conventional additive model fitting.…”

Section: Robustness and Nonparametric Methodsmentioning

confidence: 99%

Robustness, Data Analysis, and Statistical Modeling: The First 50 Years and Beyond

Barrios

2015

CSAM

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We present a survey of contributions that defined the nature and extent of robust statistics for the last 50 years. From the pioneering work of Tukey, Huber, and Hampel that focused on robust location parameter estimation, we presented various generalizations of these estimation procedures that cover a wide variety of models and data analysis methods. Among these extensions, we present linear models, clustered and dependent observations, times series data, binary and discrete data, models for spatial data, nonparametric methods, and forward search methods for outliers. We also present the current interest in robust statistics and conclude with suggestions on the possible future direction of this area for statistical science.

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Robust Estimation for Generalized Additive Models

Cited by 28 publications

References 22 publications

Nonlinear surface regression with dimension reduction method

Nonlinear surface regression with dimension reduction method

Evaluation of Nonparametric and Parametric Statistical Procedures for Modeling and Prediction of Cluster‐Correlated Hydroclimatic Data

Robustness, Data Analysis, and Statistical Modeling: The First 50 Years and Beyond

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