arXiv subjects

Nirian Martin

Publications and source records attributed to Nirian Martin.

At least 19 recordsLinked to original sources

arXiv2023

Robust and efficient Breusch-Pagan test-statistic: an application of the beta-score Lagrange multipliers test for non-identically distributed individuals

In Econometrics, the Breusch-Pagan test-statistic has become an iconic application of the Lagrange multipliers (LM) test. We shall introduce beta-score LM tests for heteroscedasticity in linear regression models, which trades-off the degree of robustness and efficiency is through a tuning parameter beta>=0, being beta =0 the classical Breusch-Pagan test-statistic, the most efficient one under absence of outliers. A very elegant expression is obtained, with an appealing least squares interpretation. The construction of the test-statistic is performed extending the methodology of Basu et al. (2022) from identically distributed to non-identically distributed individuals, for composite null hypotheses. Detailed theoretical justifications about robustness and efficiency properties are given, all of them under normality. A modified version is derived, the Koenker's beta-score test-statistic.

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arXiv2020

Robust Wald-type test in GLM with random design based on minimum density power divergence estimators

We consider the problem of robust inference under the generalized linear model (GLM) with stochastic covariates. We derive the properties of the minimum density power divergence estimator of the parameters in GLM with random design and use this estimator to propose robust Wald-type tests for testing any general composite null hypothesis about the GLM. The asymptotic and robustness properties of the proposed tests are also examined for the GLM with random design. Application of the proposed robust inference procedures to the popular Poisson regression model for analyzing count data is discussed in detail both theoretically and numerically through simulation studies and real data examples.

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arXiv2019

A Robust Generalization of the Rao Test

This paper presents new families of Rao-type test statistics based on the minimum density power divergence estimators which provide robust generalizations for testing simple and composite null hypotheses. The asymptotic null distributions of the proposed tests are obtained and their robustness properties are also theoretically studied. Numerical illustrations are provided to substantiate the theory developed. On the whole, the proposed tests are seen to be excellent alternatives to the classical Rao test.

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arXiv2019

Robust semiparametric inference for polytomous logistic regression with complex survey design

Analyzing polytomous response from a complex survey scheme, like stratified or cluster sampling is very crucial in several socio-economics applications. We present a class of minimum quasi weighted density power divergence estimators for the polytomous logistic regression model with such a complex survey. This family of semiparametric estimators is a robust generalization of the maximum quasi weighted likelihood estimator exploiting the advantages of the popular density power divergence measure. Accordingly robust estimators for the design effects are also derived. Robust testing of general linear hypotheses on the regression coefficients are proposed using the new estimators. Their asymptotic distributions and robustness properties are theoretically studied and also empirically validated through a numerical example and an extensive Monte Carlo study.

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arXiv2018

A Robust Wald-type Test for Testing the Equality of Two Means from Log-Normal Samples

The log-normal distribution is one of the most common distributions used for modeling skewed and positive data. It frequently arises in many disciplines of science, specially in the biological and medical sciences. The statistical analysis for comparing the means of two independent log-normal distributions is an issue of significant interest. In this paper we present a robust test for this problem. The unknown parameters of the model are estimated by minimum density power divergence estimators (Basu et al 1998, Biometrika, 85(3), 549-559). The robustness as well as the asymptotic properties of the proposed test statistics are rigorously established. The performance of the test is explored through simulations and real data analysis. The test is compared with some existing methods, and it is demonstrated that the proposed test outperforms the others in the presence of outliers.

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arXiv2017

Robust Wald-type tests for non-homogeneous observations based on minimum density power divergence estimator

This paper considers the problem of robust hypothesis testing under non-identically distributed data. We propose Wald-type tests for both simple and composite hypothesis for independent but non-homogeneous observations based on the robust minimum density power divergence estimator of the common underlying parameter. Asymptotic and theoretical robustness properties of the proposed tests have been discussed. Application to the problem of testing the general linear hypothesis in a generalized linear model with fixed-design has been considered in detail with specific illustrations for its special cases under normal and Poisson distributions.

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arXiv2017

A new class of robust two-sample Wald-type tests

Parametric hypothesis testing associated with two independent samples arises frequently in several applications in biology, medical sciences, epidemiology, reliability and many more. In this paper, we propose robust Wald-type tests for testing such two sample problems using the minimum density power divergence estimators of the underlying parameters. In particular, we consider the simple two-sample hypothesis concerning the full parametric homogeneity of the samples as well as the general two-sample (composite) hypotheses involving nuisance parameters also. The asymptotic and theoretical robustness properties of the proposed Wald-type tests have been developed for both the simple and general composite hypotheses. Some particular cases of testing against one-sided alternatives are discussed with specific attention to testing the effectiveness of a treatment in clinical trials. Performances of the proposed tests have also been illustrated numerically through appropriate real data examples.

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arXiv2016

A logistic regression analysis approach for sample survey data based on phi-divergence measures

A new family of minimum distance estimators for binary logistic regression models based on $ϕ$-divergence measures is introduced. The so called "pseudo minimum phi-divergence estimator"(PM$ϕ$E) family is presented as an extension of "minimum phi-divergence estimator" (M$ϕ$E) for general sample survey designs and contains, as a particular case, the pseudo maximum likelihood estimator (PMLE) considered in Roberts et al. \cite{r}. Through a simulation study it is shown that some PM$ϕ$Es have a better behaviour, in terms of efficiency, than the PMLE.

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arXiv2016

Best prediction under a nested error model with log transformation

In regression models involving economic variables such as income, log transformation is typically taken to achieve approximate normality and stabilize the variance. However, often the interest is predicting individual values or means of the variable in the original scale. Back transformation of predicted values introduces a non-negligible bias. Moreover, assessing the uncertainty of the actual predictor is not straightforward. In this paper, a nested error model for the log transformation of the target variable is considered. Nested error models are widely used for estimation of means in subpopulations with small sample sizes (small areas), by linking all the areas through common parameters. These common parameters are estimated using the overall set of sample data, which leads to much more efficient small area estimators. Analytical expressions for the best predictors of individual values of the original variable and of small area means are obtained under the nested error model with log transformation of the target variable. Empirical best predictors are defined by estimating the unknown model parameters in the best predictors. Exact mean squared errors of the best predictors and second order approximations to the mean squared errors of the empirical best predictors are derived. Mean squared error estimators that are second order correct are also obtained. An example with Mexican data on living conditions illustrates the procedures.

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arXiv2016

Semiparametric clustered overdispersed multinomial goodness-of-fit of log-linear models

Traditionally, the Dirichlet-multinomial distribution has been recognized as a key model for contingency tables generated by cluster sampling schemes. There are, however, other possible distributions appropriate for these contingency tables. This paper introduces new test-statistics capable to test log-linear modeling hypotheses with no distributional specification, when the individuals of the clusters are possibly homogeneously correlated. The estimator for the intracluster correlation coefficient proposed in Alonso-Revenga et al. (2016), valid for different cluster sizes, plays a crucial role in the construction of the goodness-of-fit test-statistic.

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arXiv2016

A Wald-type test statistic for testing linear hypothesis in logistic regression models based on minimum density power divergence estimator

In this paper a robust version of the classical Wald test statistics for linear hypothesis in the logistic regression model is introduced and its properties are explored. We study the problem under the assumption of random covariates although some ideas with non random covariates are also considered. The family of tests considered is based on the minimum density power divergence estimator instead of the maximum likelihood estimator and it is referred to as the Wald-type test statistic in the paper. We obtain the asymptotic distribution and also study the robustness properties of the Wald type test statistic. The robustness of the tests is investigated theoretically through the influence function analysis as well as suitable practical examples. It is theoretically established that the level as well as the power of the Wald-type tests are stable against contamination, while the classical Wald type test breaks down in this scenario. Some classical examples are presented which numerically substantiate the theory developed. Finally a simulation study is included to provide further confirmation of the validity of the theoretical results established in the paper.

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arXiv2016

Pseudo minimum phi-divergence estimator for multinomial logistic regression with complex sample design

This article develops the theoretical framework needed to study the multinomial logistic regression model for complex sample design with pseudo minimum phi-divergence estimators. Through a numerical example and simulation study new estimators are proposed for the parameter of the logistic regression model with overdispersed multinomial distributions for the response variables, the pseudo minimum Cressie-Read divergence estimators, as well as new estimators for the intra-cluster correlation coefficient. The results show that the Binder's method for the intra-cluster correlation coefficient exhibits an excellent performance when the pseudo minimum Cressie-Read divergence estimator, with lambda = 2/3 , is plugged.

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arXiv2016

On divergences tests for composite hypotheses under composite likelihood

It is well-known that in some situations it is not easy to compute the likelihood function as the datasets might be large or the model is too complex. In that contexts composite likelihood, derived by multiplying the likelihoods of subjects of the variables, may be useful. The extension of the classical likelihood ratio test statistics to the framework of composite likelihoods is used as a procedure to solve the problem of testing in the context of composite likelihood. In this paper we introduce and study a new family of test statistics for composite likelihood: Composite ϕ-divergence test statistics for solving the problem of testing a simple null hypothesis or a composite null hypothesis. To do that we introduce and study the asymptotic distribution of the restricted maximum composite likelihood estimate.

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arXiv2016

Empirical phi-divergence test-statistics for the equalityof means of two populations

Empirical phi-divergence test-statistics have demostrated to be a useful technique for the simple null hypothesis to improve the finite sample behaviour of the classical likelihood ratio test-statistic, as well asfor model misspecification problems, in both cases for the one population problem. This paper introduces this methodology for two sample problems. A simulation study illustrates situations in which the new test-statistics become a competitive tool with respect to the classical z-test and the likelihood ratio test-statistic.

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arXiv2015

Testing Composite Hypothesis based on the Density Power Divergence

In any parametric inference problem, the robustness of the procedure is a real concern. A procedure which retains a high degree of efficiency under the model and simultaneously provides stable inference under data contamination is preferable in any practical situation over another procedure which achieves its efficiency at the cost of robustness or vice versa. The density power divergence family of Basu et al. (1998) provides a flexible class of divergences where the adjustment between efficiency and robustness is controlled by a single parameter $β$. In this paper we consider general tests of parametric hypotheses based on the density power divergence. We establish the asymptotic null distribution of the test statistic and explore its asymptotic power function. Numerical results illustrate the performance of the theory developed.

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arXiv2015

Influence Analysis of Robust Wald-type Tests

We consider a robust version of the classical Wald test statistics for testing simple and composite null hypotheses for general parametric models. These test statistics are based on the minimum density power divergence estimators instead of the maximum likelihood estimators. An extensive study of their robustness properties is given though the influence functions as well as the chi-square inflation factors. It is theoretically established that the level and power of these robust tests are stable against outliers, whereas the classical Wald test breaks down. Some numerical examples confirm the validity of the theoretical results.

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arXiv2015

Generalized Wald-type Tests based on Minimum Density Power Divergence Estimators

In testing of hypothesis the robustness of the tests is an important concern. Generally, the maximum likelihood based tests are most efficient under standard regularity conditions, but they are highly non-robust even under small deviations from the assumed conditions. In this paper we have proposed generalized Wald-type tests based on minimum density power divergence estimators for parametric hypotheses. This method avoids the use of nonparametric density estimation and the bandwidth selection. The trade-off between efficiency and robustness is controlled by a tuning parameter $β$. The asymptotic distributions of the test statistics are chi-square with appropriate degrees of freedom. The performance of the proposed tests are explored through simulations and real data analysis.

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arXiv2014

Robust Tests for the Equality of Two Normal Means based on the Density Power Divergence

Statistical techniques are used in all branches of science to determine the feasibility of quantitative hypotheses. One of the most basic applications of statistical techniques in comparative analysis is the test of equality of two population means, generally performed under the assumption of normality. In medical studies, for example, we often need to compare the effects of two different drugs, treatments or preconditions on the resulting outcome. The most commonly used test in this connection is the two sample $t$-test for the equality of means, performed under the assumption of equality of variances. It is a very useful tool, which is widely used by practitioners of all disciplines and has many optimality properties under the model. However, the test has one major drawback; it is highly sensitive to deviations from the ideal conditions, and may perform miserably under model misspecification and the presence of outliers. In this paper we present a robust test for the two sample hypothesis based on the density power divergence measure (Basu et al., 1998), and show that it can be a great alternative to the ordinary two sample $t$-test. The asymptotic properties of the proposed tests are rigorously established in the paper, and their performances are explored through simulations and real data analysis.

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