# Alexandre PatriotaUniversity of São Paulo | USP · Department of Statistics (IME) (São Paulo)

Alexandre Patriota

Ph.D. in Statistics

Associate Professor of Statistics

## About

41

Publications

6,562

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349

Citations

Introduction

Additional affiliations

January 2012 - present

**Independent Researcher**

Position

- Professor

January 2012 - present

January 2012 - July 2017

Education

September 2006 - June 2010

**Independent Researcher**

Field of study

- Statistics

## Publications

Publications (41)

We present for the first time a justification on the basis of central limit theorems for the family of life distributions generated from scale-mixture of normals. This family was proposed by Balakrishnan et al. (2009) and can be used to accommodate unexpected observations for the usual Birnbaum–Saunders distribution generated from the normal one. T...

In this paper we introduce a q-Exponential regression model for fitting data with discrepant observations. Maximum likelihood estimators for the model parameters and the (observed and expected) Fisher information matrix are derived. Moreover, we also present sufficient conditions to have consistent and asymptotically normally distributed estimators...

In science, the most widespread statistical quantities are perhaps
$p$-values. A typical advice is to reject the null hypothesis $H_0$ if the
corresponding p-value is sufficiently small (usually smaller than 0.05). Many
criticisms regarding p-values have arisen in the scientific literature. The
main issue is that in general optimal p-values (based...

The present paper considers an evidence measure built under the likelihood
ratio approach. The resulting likelihood-ratio measure can be used for testing
general hypotheses in a simple manner. Moreover, it satisfies the entailment
condition (the logical consequence), which is required to maintain a special
type of coherence over the space of hypoth...

This paper studies the s-value, a monotone frequentist measure of evidence, in a linear mixed model with a general parameter space that includes null variance components for the random effects. Under this nonregular parameter space, an asymptotic version of the s-value based on likelihood ratio statistics is defined and discussed under null varianc...

Frequentist methods, without the coherence guarantees of fully Bayesian methods, are known to yield self-contradictory inferences in certain settings. The framework introduced in this paper provides a simple adjustment to p values and confidence sets to ensure the mutual consistency of all inferences without sacrificing frequentist validity. Based...

Feng et al. (2013) revealed that the usual mean value theorem should not be applied directly to a vector-valued function (e.g., the score function or a general estimating function under a multiparametric model). This note shows that the application of the Cramer-Wold’s device to a corrected version of the mean value theorem is sufficient to obtain...

Clustering is an important tool in biological data investigation. For example, in neuroscience, one major hypothesis is that the presence or not of a disorder can be explained by the differences in how brain’s regions of interest cluster. In molecular biology, genes may cluster in a different manner in controls and patients or also among different...

Bayesian and classical statistical approaches are based on different types of logical principles. In order to avoid mistaken inferences and misguided interpretations, the practitioner must respect the inference rules embedded into each statistical method. Ignoring these principles leads to the paradoxical conclusions that the hypothesis [Formula] c...

Confidence sets are generally interpreted in terms of replications of an experiment. However, this interpretation is only valid before observing the sample. After observing the sample, any confidence sets have probability zero or one to contain the parameter value. In this paper, we provide a confidence set analysis for an observed sample based on...

This paper investigates improved testing inferences under a general
multivariate elliptical regression model. The model is very flexible in terms
of the specification of the mean vector and the dispersion matrix, and of the
choice of the error distribution. The error terms are allowed to follow a
multivariate distribution in the class of the ellipt...

The problem of reducing the bias of maximum likelihood estimator in a general multivariate elliptical regression model is considered. The model is very flexible and allows the mean vector and the dispersion matrix to have parameters in common. Many frequently used models are special cases of this general formulation, namely: errors-in-variables mod...

Statistical inference of functional magnetic resonance imaging (fMRI) data is an important tool in neuroscience investigation. One major hypothesis in neuroscience is that the presence or not of a psychiatric disorder can be explained by the differences in how neurons cluster in the brain. Therefore, it is of interest to verify whether the properti...

In the classical paradigm, the famous p-value is employed for testing scientific hypotheses. It is used as a discrepancy thermometer between the proposed hypothesis and the observed data: the smaller is the p-value, the larger is the discrepancy of the hypothesis of interest to explain the data behavior. In this paper, we discuss some known “incons...

An important and yet unsolved problem in unsupervised data clustering is how to determine the number of clusters. The proposed slope statistic is a non-parametric and data driven approach for estimating the number of clusters in a dataset. This technique uses the output of any clustering algorithm and identifies the maximum number of groups that br...

Statistical inference on functional magnetic resonance imaging (fMRI) data is
an important task in brain imaging. One major hypothesis is that the presence
or not of a psychiatric disorder can be explained by the differential
clustering of neurons in the brain. In view of this fact, it is clearly of
interest to address the question of whether the p...

Background
A common approach for time series gene expression data analysis includes the clustering of genes with similar expression patterns throughout time. Clustered gene expression profiles point to the joint contribution of groups of genes to a particular cellular process. However, since genes belong to intricate networks, other features, besid...

In this paper, we develop a modified version of the likelihood ratio test for
multivariate heteroskedastic errors-in-variables regression models. The error
terms are allowed to follow a multivariate distribution in the elliptical class
of distributions, which has the normal distribution as a special case. We
derive the Skovgaard adjusted likelihood...

Objective: To assess the physical activity level of a group of women
residing in a region of low socioeconomic status, and to relate this variable
to time of scholarization, self perception of health, age and daily working
hours. Methods: Sixty adult and elderly women (mean age 51.3 ± 11.0 years
old) assisted by primary health units of the district...

We introduce a general elliptical multivariate regression model in which the mean vector and the scale matrix have parameters (or/and covariates) in common. This approach unifies several important elliptical models, such as nonlinear regression, mixed-effects models with nonlinear fixed effects, errors-in-variables models, etc. We discuss maximum l...

We consider the issue of assessing influence of observations in the class of Birnbaum-Saunders nonlinear regression models, which is useful in lifetime data analysis. Our results generalize those in Galea et al. [8] which are confined to Birnbaum-Saunders linear regression models. Some influence methods, such as the local influence, total local inf...

In this note, we show that the Carath\'eodory's extension theorem is still
valid for a class of subsets of $\Omega$ less restricted than a semi-ring,
which we call quasi-semi-ring.

This paper deals with asymptotic results on a multivariate ultrastructural errors-in-variables regression model with equation errors. Sufficient conditions for attaining consistent estimators for model parameters are presented. Asymptotic distributions for the line regression estimators are derived. Applications to the elliptical class of distribut...

Objetivo: Analisar o nível de atividade física de um grupo de mulheres
residentes numa região de baixo nível socioeconômico e relacionar esta
variável com escolaridade, auto-percepção de saúde, idade e horas diárias
de trabalho. Métodos: Sessenta mulheres adultas e idosas (média de idade
51,3 ± 11,0 anos) atendidas pelas Unidades Básicas de Saúde d...

This paper develops a bias correction scheme for a multivariate heteroskedastic errors-in-variables model. The applicability of this model is justified in areas such as astrophysics, epidemiology and analytical chemistry, where the variables are subject to measurement errors and the variances vary with the observations. We conduct Monte Carlo simul...

A.G. Patriota and A.J. Lemonte [Stat. Probab. Lett. 79, No. 15, 1655–1662 (2009; Zbl 1166.62308)] introduced a quite general multivariate normal regression model. This model considers that the mean vector and the covariance matrix share the same vector of parameters. We present some influence assessment for this model, such as the local influence,...

We propose a likelihood ratio test (LRT) with Bartlett correction in order to identify Granger causality between sets of
time series gene expression data. The performance of the proposed test is compared to a previously published bootstrap-based
approach. LRT is shown to be significantly faster and statistically powerful even within non-Normal dist...

This paper develops a method for estimating the parameters of a vector autoregression (VAR) observed in white noise. The estimation method assumes that the noise variance matrix is known and does not require any iterative process. This study provides consistent estimators and the asymptotic distribution of the parameters required for conducting tes...

In general, the normal distribution is assumed for the surrogate of the true covariates in the classical measurement error model. This paper considers a class of distributions, which includes the normal one, for the variables subject to error. An estimation approach yielding consistent estimators is developed and simulation studies reported.

We give a general matrix formula for computing the second-order skewness of maximum likelihood estimators. The formula was firstly presented in a tensorial version by K. O. Bowman and L. R. Shenton [Commun. Stat., Theory Methods 27, No. 11, 2743–2760 (1998; Zbl 0920.62030)]. Our matrix formulation has numerical advantages, since it requires only si...

There are several studies in the literature depicting measurement error in gene expression data and also, several others about regulatory network models. However, only a little fraction describes a combination of measurement error in mathematical regulatory networks and shows how to identify these networks under different rates of noise.
This artic...

This paper develops a bias correction scheme for a multivariate normal model under a general parameterization. In the model, the mean vector and the covariance matrix share the same parameters. It includes many important regression models available in the literature as special cases, such as (non)linear regression, errors-in-variables models, and s...

It is not uncommon with astrophysical and epidemiological data sets that the variances of the observations are accessible from an analytical treatment of the data collection process. Moreover, in a regression model, heteroscedastic measurement errors and equation errors are common situations when modelling such data. This article deals with the lim...

In many statistical inference problems, there is interest in estimation of only some elements of the parameter vector that defines the adopted model. In general, such elements are associated to measures of location and the additional terms, known as nuisance parameters, to control the dispersion and asymmetry of the underlying distributions. To est...

This paper provides general matrix formulas for computing the score function, the (expected and observed) Fisher information and the $\Delta$ matrices (required for the assessment of local influence) for a quite general model which includes the one proposed by Russo et al. (2009). Additionally, we also present an expression for the generalized leve...

En muchos problemas de inferencia estadística existe interés en estimar solamente algunos elementos del vector de parámetros que definen el modelo adoptado. Generalmente, esos elementos están asociados a las medidas de localización, y los parámetros adicionales -que en la mayoría de las veces están en el modelo solo para controlar la dispersión o l...

This paper develops a bias correction scheme for a multivariate heteroskedastic errors-in-variables model. The applicability of this model is justified in areas such as astrophysics, epidemiology and analytical chemistry, where the variables are subject to measurement errors and the variances vary with the observations. We conduct Monte Carlo simul...

With epidemiological and astronomical data, it is common to observe variances that vary with the observations. Further, values for those variances typically are available from follow-up studies or replications. This paper deals with consistent estimation and hypothesis testing in a heteroscedastic polynomial model with measurement error in both axe...

## Projects

Projects (5)

Research on statistical applications of possibility theory. Older research:
https://davidbickel.com/category/methods/possibility-theory/