Thin plate spline model under skew-normal random errors: estimation and diagnostic analysis for spatial data

Cavieres, Joaquin; Ibacache-Pulgar, Germán; Contreras-Reyes, Javier E.

doi:10.1080/00949655.2022.2090564

Cited by 4 publications

(4 citation statements)

References 23 publications

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“…The EM algorithm (Dempster et al 1977) and some of its extraordinary variants such as the expectation conditional maximization (ECM) algorithm (Meng and Rubin 1993) and the expectation-conditional maximization either (ECME) algorithm (Liu and Rubin 1994) are broadly applicable methods to carry out ML estimation for mixture distributions and variety of incomplete-data problems (Aitkin and Wilson 1980;McLachlan and Krishnan 2007;Redner and Walker 1984). Mahdavi et al (2021aMahdavi et al ( , 2021b and Cavieres et al (2022) developed novel EM-based procedures designed under the selection mechanism to compute the ML estimates of scale-shape mixtures of flexible generalized skew-normal and multivariate flexible skew-symmetric-normal distributions. Here, we develop a novel EM-based procedure designed under the selection mechanism to compute the ML estimates of the proposed model.…”

Section: Maximum Likelihood Estimation Via Em Algorithmmentioning

confidence: 99%

On the Contaminated Weighted Exponential Distribution: Applications to Modeling Insurance Claim Data

Mahdavi

Kharazmi

Contreras-Reyes

2022

JRFM

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Deriving loss distribution from insurance data is a challenging task, as loss distribution is strongly skewed with heavy tails with some levels of outliers. This paper extends the weighted exponential (WE) family to the contaminated WE (CWE) family, which offers many flexible features, including bimodality and a wide range of skewness and kurtosis. We adopt Expectation-Maximization (EM) and Bayesian approaches to estimate the model, providing the likelihood and the priors for all unknown parameters. Finally, two sets of claims data are analyzed to illustrate the efficiency of the proposed method in detecting outliers.

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Section: Maximum Likelihood Estimation Via Em Algorithmmentioning

confidence: 99%

On the Contaminated Weighted Exponential Distribution: Applications to Modeling Insurance Claim Data

Mahdavi

Kharazmi

Contreras-Reyes

2022

JRFM

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“…Ibacache-Pulgar et al [27] developed the local influence method within the context of semiparametric additive beta regression models. Meanwhile, Cavieres et al [28] calculated the normal curvature to assess the sensitivity of estimators in a thin-plate spline model that incorporates skew normal random errors. Jeldes et al [29] applied the partially coefficient-varying model with symmetric random errors to air pollution data from the cities of Santiago, Chile, and Lima, Peru.…”

Section: Introductionmentioning

confidence: 99%

Local Influence for the Thin-Plate Spline Generalized Linear Model

Ibacache-Pulgar,

Pacheco,

Nicolis

et al. 2024

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Thin-Plate Spline Generalized Linear Models (TPS-GLMs) are an extension of Semiparametric Generalized Linear Models (SGLMs), because they allow a smoothing spline to be extended to two or more dimensions. This class of models allows modeling a set of data in which it is desired to incorporate the non-linear joint effects of some covariates to explain the variability of a certain variable of interest. In the spatial context, these models are quite useful, since they allow the effects of locations to be included, both in trend and dispersion, using a smooth surface. In this work, we extend the local influence technique for the TPS-GLM model in order to evaluate the sensitivity of the maximum penalized likelihood estimators against small perturbations in the model and data. We fit our model through a joint iterative process based on Fisher Scoring and weighted backfitting algorithms. In addition, we obtained the normal curvature for the case-weight perturbation and response variable additive perturbation schemes, in order to detect influential observations on the model fit. Finally, two data sets from different areas (agronomy and environment) were used to illustrate the methodology proposed here.

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“…For instance, Tang et al [24] proposed semiparametric mixed-effects submodels for multivariate longitudinal breast cancer data; Refs. [12,[25][26][27] proposed semiparametric mixture Tobit, partially linear mixed-effects, and quantile regression models, respectively, for HIV/AIDS dynamics; and Cavieres et al [28] modelled a spatial data semiparametrically with a smoothing tin plate for spatial coordinates.…”

Section: Introductionmentioning

confidence: 99%

“…In recent years, skew distributions have gained popularity as a useful tool for dealing with asymmetric longitudinal data in many applications. The most commonly used skew-elliptical distributions in the literature are multivariate skew-normal [27,28,32,33] and multivariate skew-t [8,12,26,29] distributions.…”

Section: Introductionmentioning

confidence: 99%

A Semiparametric Bayesian Joint Modelling of Skewed Longitudinal and Competing Risks Failure Time Data: With Application to Chronic Kidney Disease

et al. 2022

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In clinical and epidemiological studies, when the time-to-event(s) and the longitudinal outcomes are associated, modelling them separately may give biased estimates. A joint modelling approach is required to obtain unbiased results and to evaluate their association. In the joint model, a subject may be exposed to more than one type of failure event (competing risks). Considering the competing event as an independent censoring of the time-to-event process may underestimate the true survival probability and give biased results. Within the joint model, longitudinal outcomes may have nonlinear (irregular) trajectories over time and exhibit skewness with heavy tails. Accordingly, fully parametric mixed-effect models may not be flexible enough to model this type of complex longitudinal data. In addition, assuming a Gaussian distribution for model errors may be too restrictive to adequately represent within-individual variations and may lack robustness against deviation from distributional assumptions. To simultaneously overcome these issues, in this paper, we presented semiparametric joint models for competing risks failure time and skewed-longitudinal data by using a smoothing spline approach and a multivariate skew-t distribution. We also considered different parameterization approaches in the formulation of joint models and used a Bayesian approach to make the statistical inference. We illustrated the proposed methods by analyzing real data on a chronic kidney disease. To evaluate the performance of the methods, we also carried out simulation studies. The results of both the application and simulation studies revealed that the joint modelling approach proposed in this study performed well when the semiparametric, random-effects parameterization, and skew-t distribution specifications were taken into account.

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Thin plate spline model under skew-normal random errors: estimation and diagnostic analysis for spatial data

Cited by 4 publications

References 23 publications

On the Contaminated Weighted Exponential Distribution: Applications to Modeling Insurance Claim Data

On the Contaminated Weighted Exponential Distribution: Applications to Modeling Insurance Claim Data

Local Influence for the Thin-Plate Spline Generalized Linear Model

A Semiparametric Bayesian Joint Modelling of Skewed Longitudinal and Competing Risks Failure Time Data: With Application to Chronic Kidney Disease

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