Testing the equality of nonparametric regression curves

This paper proposes a test for the equality of nonparametric regression curves that does not depend on the choice of a smoothing number. The test statistic is a weighted empirical process easy to compute. It is powerful under alternatives that converge to the null at a rate n­½. The disturbance distributions are arbitrary and possibly unequal, and conditions on the regressors distribution are very mild. A simulation study demonstrates that the test enjoys good level and power properties in small samples. We also study extensions to multiple regression, and testing the equality of several regression curves

Testing serial independence using the sample distribution function

This paper presents and discusses a nonparametric test for detecting serial dependence. We consider a Cramèr-v.Mises statistic based on the difference between the joint sample distribution and the product of the marginals. Exact critical values can be approximated from the asymptotic null distribution or by resampling, randomly permuting the original series. The approximation based on resampling is more accurate and the corresponding test enjoys, like other bootstrap based procedures, excellent level accuracy, with level error of order T-3/2. A Monte Carlo experiment illustrates the test performance with small and moderate sample sizes. The paper also includes an application, testing the random walk hypothesis of exchange rate returns for several currencies

Specification testing

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Computing Nonparametric Functional Estimates in Semiparametric Problems

The purpose of this note is to provide a brief account of available FORTRAN Routines for computing nonparametric functional estimates, Frequently used in semiparametric problems, evaluated at each data point. Then semiparametric estimates can be computed employing the use-favored economic software.Publicad

The New SI and the Fundamental Constants of Nature

The launch in 2019 of the new international system of units is an opportunity to highlight the key role that the fundamental laws of physics and chemistry play in our lives and in all the processes of basic research, industry and commerce. The main objective of these notes is to present the new SI in an accessible way for a wide audience. After reviewing the fundamental constants of nature and its universal laws, the new definitions of SI units are presented using, as a unifying principle, the discrete nature of energy, matter and information in these universal laws. The new SI system is here to stay: although the experimental realizations may change due to technological improvements, the definitions will remain unaffected. Quantum metrology is expected to be one of the driving forces to achieve new quantum technologies of the second generation. ----- La puesta en marcha en 2019 del nuevo sistema internacional de unidades es una oportunidad para resaltar el papel fundamental que las leyes fundamentales de la F\'{\i}sica y la Qu\'{\i}mica juegan en nuestra vida y en todos los procesos de la investigaci\'on fundamental, la industria y el comercio. El principal objetivo de estas notas es presentar el nuevo SI de forma accesible para una audiencia amplia. Tras repasar las constantes fundamentales de la naturaleza y sus leyes universales, se presentan las nuevas definiciones de las unidades SI utilizando como principio unificador la naturaleza discreta de la energ\'{\i}a, la materia y la informaci\'on en esas leyes universales. El nuevo sistema SI tiene vocaci\'on de futuro: aunque las realizaciones experimentales cambien por mejoras tecnol\'gicas, las definiciones permanecer\'an inalteradas. La Metrolog\'{\i}a cu\'antica est\'a llamada a ser uno de las fuerzas motrices para conseguir nuevas tecnolog\'{\i}as cu\'anticas de segunda generaci\'on.Comment: Revtex file, color figures. English version y en espa\~no

A nonparametric test for serial independence of errors in linear regression

A test for serial independence of regression errors, consistent in the direction of first order alternatives, is proposed. The test statistic is a function of a Hoeffding-Blum-Kiefer-Rosenblatt type of empirical process, based on residuals. The resultant statistic converges, surprisingly, to the same limiting distribution as the corresponding statistic based on true errors

Nonparametric checks for count data models: an application to demand for health care in Spain

This paper presents model specification checking procedures for count data regression models which are consistent in the direction of nonparametric alternatives. The discussion is motivated in the context of a model of demand for health care in Spain. The parameters of the regression model are estimated by maximum likelihood based on Poisson and Negative Binomial specifications as well as by ordinary least squares and semiparametric generalized least squares. However, our interest is not only centered on the estimation ofthe regression parameters, but also the conditional probabilities of counts. Therefore, the specification of the conditional distribution function of counts is the main focus of attention. A useful preliminary diagnosis tool consists of comparing the conditional probabilities estimates by nonparametric regression and by maximum likelihood methods based on alternative models. We present formal specification procedures based on new developed testing methods for regression model checking. The test statistics are based on marked empirical processes which are not distribution free, but their critical values are well approximated by bootstrap. Such tests are valid for testing the functional form of the conditional mean and conditional probabilities resulting from alternative distributional specifications. In our health care demand model, the linear exponential regression model with a Negative Binomial seems to be appropiate for this data set

Nonparametric estimation of structural breakpoints

This paper proposes point and interval estimates of location and size of jumps in multiple regression curves or its derivatives. We are mainly concerned with time series models where structural breaks occur at a given period of time or they are explained by the value taken by some predictor (e.g. threshold models). No previous knowledge of the underlying regression function is required. Left and right limits of the function, with respect to the regressor explaining the break, are estimated at each data point using multivariate multiplicative kernels. The univariate kernel corresponding to the regressor explaining the break is one-sided, with all its mass at the right or left of zero. Since left and right limits are the same, except at the break point, the location of the jump is estimated as the observed regressor value maximizing the difference between left and right limit estimates. This difference, evaluated at the estimated location point, is the estimation of the jump size. A small Monte Carlo study and an empirical application to USA macroecomic data illustrates the performance of the procedure in small samples. The paper also discusses some extensions, in particular the identification of the coordinate explaining the break, the application of the procedure to the estimation of parametric models, and robustification of the method for the influence of outliers

Distribution-free specification tests of conditional models

This article proposes a class of asymptotically distribution-free specification tests for parametric conditional distributions. These tests are based on a martingale transform of a proper sequential empirical process of conditionally transformed data. Standard continuous functionals of this martingale provide omnibus tests while linear combinations of the orthogonal components in its spectral representation form a basis for directional tests. Finally, Neyman-type smooth tests, a compromise between directional and omnibus tests, are discussed. As a special example we study in detail the construction of directional tests for the null hypothesis of conditional normality versus heteroskedastic contiguous alternatives. A small Monte Carlo study shows that our tests attain the nominal level already for small sample sizes.Publicad