arXiv subjects

Jacobo de Uña-Álvarez

Publications and source records attributed to Jacobo de Uña-Álvarez.

9 recordsLinked to original sources

arXiv2026

Goodness-of-Fit Tests for Censored and Truncated Data: Maximum Mean Discrepancy Over Regular Functionals

We develop a systematic, omnibus approach to goodness-of-fit testing for parametric distributional models when the variable of interest is only partially observed due to censoring and/or truncation. In many such designs, tests based on the nonparametric maximum likelihood estimator are hindered by nonexistence, computational instability, or convergence rates too slow to support reliable calibration under composite nulls. We avoid these difficulties by constructing a regular (pathwise differentiable) Neyman-orthogonal score process indexed by test functions, and aggregating it over a reproducing kernel Hilbert space ball. This yields a maximum-mean-discrepancy-type supremum statistic with a convenient quadratic-form representation. Critical values are obtained via a multiplier bootstrap that keeps nuisance estimates fixed. We establish asymptotic validity under the null and local alternatives and provide concrete constructions for left-truncated right-censored data, current status data, and random double truncation; in particular, to the best of our knowledge, we give the first omnibus goodness-of-fit test for a parametric family under random double truncation in the composite-hypothesis case. Simulations and an empirical illustration demonstrate size control and power in practically relevant incomplete-data designs.

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arXiv2026

Smoothing spline density estimation from doubly truncated data

In Astronomy, Survival Analysis and Epidemiology, among many other fields, doubly truncated data often appear. Double truncation generally induces a sampling bias, so ordinary estimators may be inconsistent. In this paper, smoothing spline density estimation from doubly truncated data is investigated. For this purpose, an appropriate correction of the penalized likelihood that accounts for the sampling bias is considered. The theoretical properties of the estimator are discussed, and its practical performance is evaluated through simulations. Two real datasets are analyzed using the proposed method for illustrative purposes. Comparison to kernel density smoothing is included.

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arXiv2024

Logistic regression with missing responses and predictors: a review of existing approaches and a case study

In this work logistic regression when both the response and the predictor variables may be missing is considered. Several existing approaches are reviewed, including complete case analysis, inverse probability weighting, multiple imputation and maximum likelihood. The methods are compared in a simulation study, which serves to evaluate the bias, the variance and the mean squared error of the estimators for the regression coefficients. In the simulations, the maximum likelihood methodology is the one that presents the best results, followed by multiple imputation with five imputations, which is the second best. The methods are applied to a case study on the obesity for schoolchildren in the municipality of Viana do Castelo, North Portugal, where a logistic regression model is used to predict the International Obesity Task Force (IOTF) indicator from physical examinations and the past values of the obesity status. All the variables in the case study are potentially missing, with gender as the only exception. The results provided by the several methods are in well agreement, indicating the relevance of the past values of IOTF and physical scores for the prediction of obesity. Practical recommendations are given.

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arXiv2023

Controlling the number of significant effects in multiple testing

In multiple testing several criteria to control for type I errors exist. The false discovery rate, which evaluates the expected proportion of false discoveries among the rejected null hypotheses, has become the standard approach in this setting. However, false discovery rate control may be too conservative when the effects are weak. In this paper we alternatively propose to control the number of significant effects, where 'significant' refers to a pre-specified threshold $γ$. This means that a $(1-α)$-lower confidence bound $L$ for the number of non-true null hypothesis with p-values below $γ$ is provided. When one rejects the nulls corresponding to the $L$ smallest p-values, the probability that the number of false positives exceeds the number of false negatives among the significant effects is bounded by $α$. Relative merits of the proposed criterion are discussed. Procedures to control for the number of significant effects in practice are introduced and investigated both theoretically and through simulations. Illustrative real data applications are given.

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arXiv2023

Testing for an ignorable sampling bias under random double truncation

In clinical and epidemiological research doubly truncated data often appear. This is the case, for instance, when the data registry is formed by interval sampling. Double truncation generally induces a sampling bias on the target variable, so proper corrections of ordinary estimation and inference procedures must be used. Unfortunately, the nonparametric maximum likelihood estimator of a doubly truncated distribution has several drawbacks, like potential non-existence and non-uniqueness issues, or large estimation variance. Interestingly, no correction for double truncation is needed when the sampling bias is ignorable, which may occur with interval sampling and other sampling designs. In such a case the ordinary empirical distribution function is a consistent and fully efficient estimator that generally brings remarkable variance improvements compared to the nonparametric maximum likelihood estimator. Thus, identification of such situations is critical for the simple and efficient estimation of the target distribution. In this paper we introduce for the first time formal testing procedures for the null hypothesis of ignorable sampling bias with doubly truncated data. The asymptotic properties of the proposed test statistic are investigated. A bootstrap algorithm to approximate the null distribution of the test in practice is introduced. The finite sample performance of the method is studied in simulated scenarios. Finally, applications to data on onset for childhood cancer and Parkinson's disease are given. Variance improvements in estimation are discussed and illustrated.

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arXiv2021

Smoothing methods to estimate the hazard rate under double truncation

In Survival Analysis, the observed lifetimes often correspond to individuals for which the event occurs within a specific calendar time interval. With such interval sampling, the lifetimes are doubly truncated at values determined by the birth dates and the sampling interval. This double truncation may induce a systematic bias in estimation, so specific corrections are needed. A relevant target in Survival Analysis is the hazard rate function, which represents the instantaneous probability for the event of interest. In this work we introduce a flexible estimation approach for the hazard rate under double truncation. Specifically, a kernel smoother is considered, in both a fully nonparametric setting and a semiparametric setting in which the incidence process fits a given parametric model. Properties of the kernel smoothers are investigated both theoretically and through simulations. In particular, an asymptotic expression of the mean integrated squared error is derived, leading to a data-driven bandwidth for the estimators. The relevance of the semiparametric approach is emphasized, in that it is generally more accurate and, importantly, it avoids the potential issues of nonexistence or nonuniqueness of the fully nonparametric estimator. Applications to the age of diagnosis of Acute Coronary Syndrome (ACS) and AIDS incubation times are included.

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arXiv2021

Nonparametric Estimation of a distribution function from doubly truncated data under dependence

The NPMLE of a distribution function from doubly truncated data was introduced in the seminal paper of Efron and Petrosian. The consistency of the Efron-Petrosian estimator depends however on the assumption of independent truncation. In this work we introduce an extension of the Efron-Petrosian NPMLE when the variable of interest and the truncation variables may be dependent. The proposed estimator is constructed on the basis of a copula function which represents the dependence structure between the variable of interest and the truncation variables. Two different iterative algorithms to compute the estimator in practice are introduced, and their performance is explored through an intensive Monte Carlo simulation study. We illustrate the use of the estimators on two real data examples.

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arXiv2020

Improved $q$-values for discrete uniform and homogeneous tests: a comparative study

Large scale discrete uniform and homogeneous $P$-values often arise in applications with multiple testing. For example, this occurs in genome wide association studies whenever a nonparametric one-sample (or two-sample) test is applied throughout the gene loci. In this paper we consider $q$-values for such scenarios based on several existing estimators for the proportion of true null hypothesis, $π_0$, which take the discreteness of the $P$-values into account. The theoretical guarantees of the several approaches with respect to the estimation of $π_0$ and the false discovery rate control are reviewed. The performance of the discrete $q$-values is investigated through intensive Monte Carlo simulations, including location, scale and omnibus nonparametric tests, and possibly dependent $P$-values. The methods are applied to genetic and financial data for illustration purposes too. Since the particular estimator of $π_0$ used to compute the $q$-values may influence the power, relative advantages and disadvantages of the reviewed procedures are discussed. Practical recommendations are given.

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arXiv2020

R packages for the statistical analysis of doubly truncated data: a review

Random double truncation refers a situation in which the variable of interest is observed only when it falls within two random limits. Such phenomenon occurs in many applications of Survival Analysis and Epidemiology, among many other fields. There exist several R packages to analyze doubly truncated data which implement, for instance, estimators for the cumulative distribution, the cumulative incidences of competing risks, or the regression coefficients in the Cox model. In this paper the main features of these packages are reviewed. The relative merits of the libraries are illustrated through the analysis of simulated and real data. This includes the study of the statistical accuracy of the implemented techniques as well as of their computational speed. Practical recommendations are given.

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