Random coefficient regressions: parametric goodness of fit tests

Random coefficient regression models have been applied in different fields during recent years and they are a unifying frame for many statistical models. Recently, Beran and Hall (1992) opened the question of the nonparametric study of the distribution of the coefficients. Nonparametric goodness of fit tests were considered in Delicado and Romo (1994.). In this paper we propose statistics for parametric goodness of fit tests and we obtain their asymptotic distributions. Moreover, we construct bootstrap approximations to these distributions, proving their validity. Finally, a simulation study illustrates our results

Goodness of fit tests in random coefficient regression models

Random coefficient regressions have been applied in a wide range of fields, from biology to economics, and constitute a common frame for several important statistical models. A nonparametric approach to inference in random coefficient models was initiated by Beran and Hall. In this paper we introduce and study goodness of fit tests for the coefficient distributions; their asymptotic behaviour under the null hypothesis is obtained. We also propose bootstrap resampling strategies to approach these distributions and prove their asymptotic validity using results by Gine and Zinn on bootstrap empirical processes. A simulation study illustrates the properties of these tests

Another look at principal curves and surfaces

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/Principal curves have been defined as smooth curves passing through the “middle” of a multidimensional data set. They are nonlinear generalizations of the first principal component, a characterization of which is the basis of the definition of principal curves. We establish a new characterization of the first principal component and base our new definition of a principal curve on this property. We introduce the notion of principal oriented points and we prove the existence of principal curves passing through these points. We extend the definition of principal curves to multivariate data sets and propose an algorithm to find them. The new notions lead us to generalize the definition of total variance. Successive principal curves are recursively defined from this generalization. The new methods are illustrated on simulated and real data sets.Peer ReviewedPostprint (author's final draft

Bootstraping the general linear hypothesis test

We discuss the use of bootstrap methodology in hypothesis testing, focusing on the classical F-test for linear hypotheses in the linear model. A modification of the F-statistics which allows for resampling under the null hypothesis is proposed. This approach is specifically considered in the one-way analysis of variance model. A simulation study illustrating the behaviour of our proposal is presented

NOPARAM: estimacion funcional no-parametrica, un acercamiento del software CURVDAT al usuario

En los últimos tiempos las técnicas de estimación no-paramétrica de funciones han experimentado un gran desarrollo teórico. Sin embargo, el software asociado a ellas es escaso. La colección CURVDAT de subrutinas FORTRAN es una de las herramientas que penniten hacer estimaciones no-paramétricas unidimensionales. En este documento se presenta NOPARAM, consistente en varios programas FORTRAN que permiten el uso de las subrutinas CURVDAT sin necesidad de programar y ofrecen directamente gráficos de las funciones estimadas

Predicción con datos faltantes: aplicación a un caso real

En este artículo se realiza un estudio comparativo de modelos lineales y modelos mixtos, mezcla de un componente lineal y un componente no lineal en la parte estacional, para predecir la altura significativa de ola. Los datos proceden de una boya situada en el mar Cantábrico que registra la altura de ola cada tres horas. El interés central es obtener predicciones a corto plazo, dos días, que permitan advertir del estado de mar a los puertos. El principal problema que presenta esta serie para su modelización es el alto porcentaje de datos faltantes. Se completa la serie con un interpolador lineal óptimo, en el sentido de minimizar el error cuadrático medio

Using boostrap to derive a prior distribution

Constructing a prior distribution when there is no available information is usually an interesting challenge. In this paper, a new method based on bootstrap and non parametric density estimation ideas is proposed. Its ability to detect and partially correct misspecifications is illustrated with a simulation study

Analysing musical performance through functional data analysis: rhythmic structure in Schumann's Träumerei

Functional data analysis (FDA) is a relatively new branch of statistics devoted to describing and modelling data that are complete functions. Many relevant aspects of musical performance and perception can be understood and quantified as dynamic processes evolving as functions of time. In this paper, we show that FDA is a statistical methodology well suited for research into the field of quantitative musical performance analysis. To demonstrate this suitability, we consider tempo data for 28 performances of Schumann's Träumerei and analyse them by means of functional principal component analysis (one of the most powerful descriptive tools included in FDA). Specifically, we investigate the commonalities and differences between different performances regarding (expressive) timing, and we cluster similar performances together. We conclude that musical data considered as functional data reveal performance structures that might otherwise go unnoticed.Peer ReviewedPostprint (author's final draft

Measuring non-linear dependence for two random variables distributed along a curve

The final publication is available at link.springer.comWe propose new dependence measures for two real random variables not necessarily linearly related. Covariance and linear correlation are expressed in terms of principal components and are generalized for variables distributed along a curve. Properties of these measures are discussed. The new measures are estimated using principal curves and are computed for simulated and real data sets. Finally, we present several statistical applications for the new dependence measures.Peer ReviewedPostprint (author's final draft

Statistics in archaeology: New directions

Connections between Statistics and Archaeology have always appeared very fruitful. The objective of this paper is to offer an outlook of some statistical techniques that are being developed in the most recent years and that can be of interest for archaeologists in the short run.Artificial neural networks, bayesian statistics, bootstrap, multivariate analysis, nonparametric statistics, statistical software