arXiv subjects

Christian E. Galarza

Publications and source records attributed to Christian E. Galarza.

7 recordsLinked to original sources

arXiv2026

Parametric modal regression for right-censored positive responses

We present a unified parametric framework for modal regression applicable to continuous positive distributions, with explicit support for right-censored observations. The key contribution is a systematic analytical reparameterization of density parameters as direct functions of the conditional mode. This closed-form mapping is derived for the Gamma, Beta, Weibull, Lognormal, and Inverse Gaussian distributions, directly linking the mode to a linear predictor. Maximum likelihood estimation is performed using the censored log-likelihood, with asymptotic inference based on the observed Fisher information matrix. A Monte Carlo simulation study across multiple distributions, sample sizes, and censoring levels confirms consistent parameter recovery. Empirical bias and RMSE decrease as expected, and Wald confidence intervals achieve nominal coverage. Finally, the proposed methodology is illustrated through an application to real-world reliability data. All methodology is implemented in the open-source R package ModalCens.

stat.ME↗

arXiv2022

Censored autoregressive regression models with Student-$t$ innovations

The Student-$t$ distribution is widely used in statistical modeling of datasets involving outliers since its longer-than-normal tails provide a robust approach to hand such data. Furthermore, data collected over time may contain censored or missing observations, making it impossible to use standard statistical procedures. This paper proposes an algorithm to estimate the parameters of a censored linear regression model when the regression errors are autocorrelated and the innovations follow a Student-$t$ distribution. To fit the proposed model, maximum likelihood estimates are obtained throughout the SAEM algorithm, which is a stochastic approximation of the EM algorithm useful for models in which the E-step does not have an analytic form. The methods are illustrated by the analysis of a real dataset that has left-censored and missing observations. We also conducted two simulations studies to examine the asymptotic properties of the estimates and the robustness of the model.

stat.ME↗

arXiv2021

Moments and random number generation for the truncated elliptical family of distributions

This paper proposes an algorithm to generate random numbers from any member of the truncated multivariate elliptical family of distributions with a strictly decreasing density generating function. Based on Neal (2003) and Ho et al. (2012), we construct an efficient sampling method by means of a slice sampling algorithm with Gibbs sampler steps. We also provide a faster approach to approximate the first and the second moment for the truncated multivariate elliptical distributions where Monte Carlo integration is used for the truncated partition, and explicit expressions for the non-truncated part (Galarza et al., 2020). Examples and an application to environmental spatial data illustrate its usefulness. Methods are available for free in the new R library elliptical.

stat.CO↗

arXiv2021

Spatial Censored Regression Models in R: The CensSpatial package

CensSpatial is an R package for analyzing spatial censored data through linear models. It offers a set of tools for simulating, estimating, making predictions, and performing local influence diagnostics for outlier detection. The package provides four algorithms for estimation and prediction. One of them is based on the stochastic approximation of the EM (SAEM) algorithm, which allows easy and fast estimation of the parameters of linear spatial models when censoring is present. The package provides worthy measures to perform diagnostic analysis using the Hessian matrix of the completed log-likelihood function. This work is divided into two parts. The first part discusses and illustrates the utilities that the package offers for estimating and predicting spatial censored data. The second one describes the valuable tools to perform diagnostic analysis. Several examples in spatial environmental data are also provided.

stat.ME↗

arXiv2020

On moments of folded and doubly truncated multivariate extended skew-normal distributions

This paper develops recurrence relations for integrals that relate the density of multivariate extended skew-normal (ESN) distribution, including the well-known skew-normal (SN) distribution introduced by Azzalini and Dalla-Valle (1996) and the popular multivariate normal distribution. These recursions offer a fast computation of arbitrary order product moments of the multivariate truncated extended skew-normal and multivariate folded extended skew-normal distributions with the product moments as a byproduct. In addition to the recurrence approach, we realized that any arbitrary moment of the truncated multivariate extended skew-normal distribution can be computed using a corresponding moment of a truncated multivariate normal distribution, pointing the way to a faster algorithm since a less number of integrals is required for its computation which result much simpler to evaluate. Since there are several methods available to calculate the first two moments of a multivariate truncated normal distribution, we propose an optimized method that offers a better performance in terms of time and accuracy, in addition to consider extreme cases in which other methods fail. The R MomTrunc package provides these new efficient methods for practitioners.

math.ST↗

arXiv2020

Finite mixture modeling of censored and missing data using the multivariate skew-normal distribution

Finite mixture models have been widely used to model and analyze data from a heterogeneous populations. Moreover, data of this kind can be missing or subject to some upper and/or lower detection limits because of the restriction of experimental apparatuses. Another complication arises when measures of each population depart significantly from normality, for instance, asymmetric behavior. For such data structures, we propose a robust model for censored and/or missing data based on finite mixtures of multivariate skew-normal distributions. This approach allows us to model data with great flexibility, accommodating multimodality and skewness, simultaneously, depending on the structure of the mixture components. We develop an analytically simple, yet efficient, EM- type algorithm for conducting maximum likelihood estimation of the parameters. The algorithm has closed-form expressions at the E-step that rely on formulas for the mean and variance of the truncated multivariate skew-normal distributions. Furthermore, a general information-based method for approximating the asymptotic covariance matrix of the estimators is also presented. Results obtained from the analysis of both simulated and real datasets are reported to demonstrate the effectiveness of the proposed method. The proposed algorithm and method are implemented in the new R package CensMFM.

stat.ME↗

arXiv2020

Moments of the doubly truncated selection elliptical distributions with emphasis on the unified multivariate skew-$t$ distribution

In this paper, we compute doubly truncated moments for the selection elliptical (SE) class of distributions, which includes some multivariate asymmetric versions of well-known elliptical distributions, such as, the normal, Student's t, slash, among others. We address the moments for doubly truncated members of this family, establishing neat formulation for high order moments as well as for its first two moments. We establish sufficient and necessary conditions for the existence of these truncated moments. Further, we propose optimized methods able to deal with extreme setting of the parameters, partitions with almost zero volume or no truncation which are validated with a brief numerical study. Finally, we present some results useful in interval censoring models. All results has been particularized to the unified skew-t (SUT) distribution, a complex multivariate asymmetric heavy-tailed distribution which includes the extended skew-t (EST), extended skew-normal (ESN), skew-t (ST) and skew-normal (SN) distributions as particular and limiting cases.

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