A quantile regression model for bounded responses based on the exponential-geometric distribution

The paper first introduces a new two-parameter continuous probability distribution with bounded support from the extended exponential-geometric distribution. Closed-form expressions are given for the moments, moments of the order statistics and quantile function of the new law; it is also shown that the members of this family of distributions can be ordered in terms of the likelihood ratio order. The parameter estimation is carried out by the method of maximum likelihood and a closed-form expression is given for the Fisher information matrix, which is helpful for asymptotic inferences. Then, a new regression model is introduced by considering the proposed distribution, which is adequate for situations where the response variable is restricted to a bounded interval, as an alternative to the well-known beta regression model, among others. It relates the median response to a linear predictor through a link function. Extensions for other quantiles can be similarly performed. The suitability of this regression model is exemplified by means of a real data application

Una generalización de la métrica de Hausdorff sobre C(Rn)

En este trabajo hacemos una extensión de la métrica de Hausdorff H sobre C(R n), el espacio de todos los conjuntos difusos cerrados en R n, obteniendo una familia de métricas Df . Estudiamos algunas propiedades topológicas del espacio métrico (C(R n ), Df )

Goodness-of-fit tests for parametric specifications of conditionally heteroscedastic models

We consider a goodness-of-fit test for certain parametrizations of conditionally heteroscedastic time series with unobserved components. Our test is quite general in that it can be employed to validate any given specification of arbitrary order and may even be invoked for testing not just GARCH models but also some related models such as autoregressive conditional duration models. The test statistic utilizes the characterization of Bierens (J Econom 20:105–134, 1982) and may be written down in a convenient closed-form expression. Consistency of the test is proved, and the asymptotic distribution of the test statistic under the null hypothesis is studied. Since this distribution depends on unknown quantities, two bootstrap resampling schemes are investigated and compared in order to approximate critical points and actually carry out the test. Finite-sample results are presented as well as applications of the proposed procedures to real data from the financial markets. © 2019, Sociedad de Estadística e Investigación Operativa

A class of goodness-of-fit tests for circular distributions based on trigonometric moments

We propose a class of goodness-of-fit test procedures for arbitrary parametric families of circular distributions with unknown parameters. The tests make use of the specific form of the characteristic function of the family being tested, and are shown to be consistent. We derive the asymptotic null distribution and suggest that the new method be implemented using a bootstrap resampling technique that approximates this distribution consistently. As an illustration, we then specialize this method to testing whether a given data set is from the von Mises distribution, a model that is commonly used and for which considerable theory has been developed. An extensive Monte Carlo study is carried out to compare the new tests with other existing omnibus tests for this model. An application involving five real data sets is provided in order to illustrate the new procedure. © 2019 Institut d'Estadistica de Catalunya. All rights reserved

Tests for conditional ellipticity in multivariate GARCH models

Tests are proposed for the assumption that the conditional distribution of a multivariate GARCH process is elliptic. These tests are of Kolmogorov–Smirnov and Cramér–von Mises-type and make use of the common geometry underlying the characteristic function of any spherically symmetric distribution. The asymptotic null distribution of the test statistics as well as the consistency of the tests is investigated under general conditions. It is shown that both the finite sample and the asymptotic null distribution depend on the unknown distribution of the Euclidean norm of the innovations. Therefore a conditional Monte Carlo procedure is used to actually carry out the tests. The validity of this resampling scheme is formally justified. Results on the behavior of the new tests in finite-samples are included along with comparisons with other tests. © 2016 Elsevier B.V

Bootstrap estimation of the distribution of Matusita distance in the mixed case

In this paper we show that the bootstrap approximates consistently the distribution of the sample Matusita distance between two conditional Gaussian distributions, under the null hypothesis of homogeneity. We also study by simulation the finite sample performance of the bootstrap distribution and compare it with the asymptotic approximation.Matusita distance Conditional Gaussian distribution Bootstrap Consistency

A test for the two-sample problem based on empirical characteristic functions

A class of tests for the two sample problem that is based on the empirical characteristic function is investigated. They can be applied to continuous as well as to discrete data of any arbitrary fixed dimension. The tests are consistent against any fixed alternatives for adequate choices of the weight function involved in the definition of the test statistic. Both the bootstrap and the permutation procedures can be employed to estimate consistently the null distribution. The goodness of these approximations and the power of some tests in this class for finite sample sizes are investigated by simulation.

Minimum [phi]-divergence estimation in misspecified multinomial models

The consequences of model misspecification for multinomial data when using minimum [phi]-divergence or minimum disparity estimators to estimate the model parameters are considered. These estimators are shown to converge to a well-defined limit. Two applications of the results obtained are considered. First, it is proved that the bootstrap consistently estimates the null distribution of certain class of test statistics for model misspecification detection. Second, an application to the model selection test problem is studied. Both applications are illustrated with numerical examples.Minimum phi-divergence estimator Consistency Asymptotic normality Goodness-of-fit Bootstrap distribution estimator Model selection

Goodness-of-fit tests based on empirical characteristic functions

A class of goodness-of-fit tests based on the empirical characteristic function is studied. They can be applied to continuous as well as to discrete or mixed data with any arbitrary fixed dimension. The tests are consistent against any fixed alternative for suitable choices of the weight function involved in the definition of the test statistic. The bootstrap can be employed to estimate consistently the null distribution of the test statistic. The goodness of the bootstrap approximation and the power of some tests in this class for finite sample sizes are investigated by simulation.