Person:
Morales González, Domingo

First Name

Domingo

Last Name

Morales González

URI

https://hdl.handle.net/20.500.14352/83591

Affiliation

Universidad Complutense de Madrid

Faculty / Institute

Ciencias Matemáticas

Area

Estadística e Investigación Operativa

Identifiers

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Now showing 1 - 10 of 10

Extension of the Wald statistic to models with dependent observations
(Metrika, 2000) Morales González, Domingo; Pardo Llorente, Leandro; Pardo Llorente, María del Carmen; Vadja, Igor
A generalization of the Wald statistic for testing composite hypotheses is suggested for dependent data from exponential models which include Levy processes and diffusion fields. The generalized statistic is proved to be asymptotically chi-squared distributed under regular composite hypotheses. It is simpler and more easily available than the generalized likelihood ratio statistic. Simulations in an example where the latter statistic is available show that the generalized Wald test achieves higher average power than the generalized likelihood ratio test.
Informational distances and related statistics in mixed continuous and categorical variables
(Journal of Statistical Planning and Inference, 1998) Morales González, Domingo; Pardo Llorente, Leandro; Zografos, Konstantinos
A general class of dissimilarity measures among k greater than or equal to 2 distributions and their sample estimators are considered, for mixed continuous and categorical variables. The distributional properties are studied for the location model and the asymptotic distributions are investigated, in the general parametric case. The asymptotic distributions of the resulting statistics are used in various settings, to test statistical hypotheses.
Renyi statistics in directed families of exponential experiments
(Statistics, 2000) Morales González, Domingo; Pardo Llorente, Leandro; Vadja, Igor
Renyi statistics are considered in a directed family of general exponential models. These statistics are defined as Renyi distances between estimated and hypothetical model. An asymptotically quadratic approximation to the Renyi Statistics is established, leading to similar asymptotic distribution results as established in the literature For the likelihood ratio statistics. Some arguments in favour of the Renyi statistics are discussed, and a numerical comparison of the Renyi goodness-of-fit tests with the Likelihood ratio test is presented.
Some approximations to power functions of phi-divergence tests in parametric models
(Test, 2001) Morales González, Domingo; Pardo Llorente, Leandro
In Morales et al (1997) phi-divergence statistics were proposed for testing hypotheses in general populations. In this paper we present some approximations to the power function of these new tests statistics for the cases of the simple null hypotheses and the composite null hypotheses.
Approximations to powers of phi-disparity goodness-of-fit tests
(Communications in statistics. Theory and methods, 2001) Menéndez Calleja, María Luisa; Morales González, Domingo; Pardo Llorente, Leandro; Vadja, Igor
The paper studies a class of tests based on disparities between the real-valued data and theoretical models resulting either from fixed partitions of the observation space, or from the partitions by the sample quantiles of fixed orders. In both cases there are considered the goodness-of-fit tests of simple and composite hypotheses. All tests are shown to be consistent, and their power is evaluated at the nonlocal as well as local alternatives.
Asymptotic laws for disparity statistics in product multinomial models
(Journal of multivariate analysis, 2003) Morales González, Domingo; Pardo Llorente, Leandro; Vadja, Igor
The paper presents asymptotic distributions of phi-disparity goodness-of-fit statistics in product multinomial models, under hypotheses and alternatives assuming sparse and nonsparse cell frequencies. The phi-disparity statistics include the power divergences of Read and Cressie (Goodness-of-fit Statistics for Discrete Multivariate Data, Springer, New York, 1988), the phi-divergences of Ciszar (Studia Sci. Math. Flungar. 2 (1967) 299) and the robust goodness of fit statistics of Lindsay (Ann. Statist. 22 (1994) 1081).
Some new statistics for testing hypotheses in parametric models
(Journal of multivariate analysis, 1997) Morales González, Domingo; Pardo Llorente, Leandro; Vadja, Igor
The paper deals with simple and composite hypotheses in statistical models with i.i.d. observations and with arbitrary families dominated by a finite measures and parametrized by vector-valued variables. It introduces phi-divergence testing statistics as alternatives to the classical ones: the generalized likelihood ratio and the statistics of Wald and Rao. It is shown that, under the assumptions of standard type about hypotheses and model densities, the results about asymptotic distribution of the classical statistics established so far for the counting and Lebesgue dominating measures (discrete and continuous models) remain true also in the general case. Further, these results are extended to the phi-divergence statistics with smooth convex functions phi. The choice of phi-divergence statistics optimal from the point of view of power is discussed and illustrated by several examples.
Tests based on divergences for and against ordered alternatives in cubic contingency tables
(Applied Mathematics and Computation, 2003) Menéndez Calleja, María Luisa; Morales González, Domingo; Pardo Llorente, Leandro
Cubic contingency tables arise frequently in medical sciences when individuals are measured before, during and after the application of some treatment for a given illness, and data are recorded on an ordered categorical scale. By assigning increasing values to the levels of the illness, the efficiency of the medical treatment can be checked by testing for a given ordering of the cell probabilities p(ijk)'s. One possibility is to consider the hypothesis H-1 that p(ijk) less than or equal to p(i'j'f') if and only if (i', j', k') can be obtained from (i, j, k) through successive pairwise interchanges of adjacent components resulting each time in a decreasing order of the two interchanged components. In this paper we introduce two families of divergence statistics to test for and against H-1, and their asymptotic distributions are obtained. It is also shown that likelihood-ratio test statistics of Barmi and Zimmermann [Statist. Prob. Lett. 45 (1999) 1] are included in these families.
Minimum divergence estimators based on grouped data
(Annals of the Institute of Statistical Mathematics, 2001) Menéndez Calleja, María Luisa; Morales González, Domingo; Pardo Llorente, Leandro; Vadja, Igor
The paper considers statistical models with real-valued observations i.i.d. by F(x, theta (0)) from a family of distribution functions (F(x, theta); theta is an element of Theta), Theta subset of R-s, s greater than or equal to 1. For random quantizations defined by sample quantiles (F-n(-1)(lambda (1)),..., F-n(-1)(lambda (m-1))) of arbitrary fixed orders 0 < (1) < ... < lambda (m-1) < 1, there are studied estimators (phi ,n) of theta (0) which minimize phi -divergences of the theoretical and empirical probabilities. Under an appropriate regularity, all these estimators are shown to be as efficient (first order, in the sense of Rao) as the MLE in the model quantified nonrandomly by (F-1(lambda (1), theta (0)),..., F-1(lambda (m-1), theta (0))). Moreover, the Fisher information matrix I-m(theta (0), lambda) of the latter model with the equidistant orders lambda = (lambda (j) = j/m : 1 less than or equal to j less than or equal to m-1) arbitrarily closely approximates the Fisher information F(theta (0)) of the original model when m is appropriately large. Thus the random binning by a large number of quantiles of equidistant orders leads to appropriate estimates of the above considered type.
φ-divergences and nested models.
(Applied Mathematics Letters, 1997) Menéndez Calleja, María Luisa; Morales González, Domingo; Pardo Llorente, Leandro
We consider a wide class of statistics, namely phi-divergences. We obtain asymptotic distributions of these statistics in nested models. Our result generalizes previous results in this field.