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Selección de la ventana en suavización tipo núcleo de la parte no paramétrica de un modelo parcialmente lineal con errores autorregresivos.

Germán Aneiros Pérez (2000)

Qüestiió

Supongamos que yi = ζiT β + m(ti) + εi, i = 1, ..., n, donde el vector (p x 1) β y la función m(·) son desconocidos, y los errores εi provienen de un proceso autorregresivo de orden uno (AR(1)) estacionario. Discutimos aquí el problema de la selección del parámetro ventana de un estimador tipo núcleo de la función m(·) basado en un estimador Generalizado de Mínimos Cuadrados de β. Obtenemos la expresión asintótica de una ventana óptima y proponemos un método para estimarla, de modo que dé lugar...

Semiparametric estimation of the parameters of multivariate copulas

Eckhard Liebscher (2009)

Kybernetika

In the paper we investigate properties of maximum pseudo-likelihood estimators for the copula density and minimum distance estimators for the copula. We derive statements on the consistency and the asymptotic normality of the estimators for the parameters.

Sign and Wilcoxon tests for quadratic versus cubic regression.

A. P. Gore, K. S. Madhava Rao (1984)

Trabajos de Estadística e Investigación Operativa

In this paper sign and Wilcoxon tests for testing the null hypothesis of quadratic regression versus the alternative, cubic regression are proposed. It is shown that in the case of a simple design consisting of multiple Y observations at each of the four levels of x, the proposed tests perform reasonably well as compared to their parametric competitors, while in the case of a general design consisting of a large number of levels of x, the loss in Pitman efficiency is considerable. However their...

Smoothing and preservation of irregularities using local linear fitting

Irène Gijbels (2008)

Applications of Mathematics

For nonparametric estimation of a smooth regression function, local linear fitting is a widely-used method. The goal of this paper is to briefly review how to use this method when the unknown curve possibly has some irregularities, such as jumps or peaks, at unknown locations. It is then explained how the same basic method can be used when estimating unsmooth probability densities and conditional variance functions.

Smoothing dichotomy in randomized fixed-design regression with strongly dependent errors based on a moving average

Artur Bryk (2014)

Applicationes Mathematicae

We consider a fixed-design regression model with errors which form a Borel measurable function of a long-range dependent moving average process. We introduce an artificial randomization of grid points at which observations are taken in order to diminish the impact of strong dependence. We show that the Priestley-Chao kernel estimator of the regression fuction exhibits a dichotomous asymptotic behaviour depending on the amount of smoothing employed. Moreover, the resulting estimator is shown to exhibit...

Some adaptive estimators for slope parameter

Tran Quoc Viet (1993)

Commentationes Mathematicae Universitatis Carolinae

An adaptive estimator (of a slope parameter) based on rank statistics is constructed and its asymptotic optimality is studied. A complete orthonormal system is incorporated in the adaptive determination of the score generating function. The proposed sequential procedure is based on a suitable stopping rule. Various properties of the sequential adaptive procedure and the stopping rule are studied. Asymptotic linearity results of linear rank statistics are also studied and some rates of the convergence...

Some consistent exponentiality tests based on Puri-Rubin and Desu characterizations

Marija Cuparić, Bojana Milošević, Yakov Yu. Nikitin, Marko Obradović (2020)

Applications of Mathematics

We present new goodness-of-fit tests for the exponential distribution based on equidistribution type characterizations. For the construction of the test statistics, we employ an L 2 -distance between the corresponding V-empirical distribution functions. The resulting test statistics are V-statistics, free of the scale parameter. The quality of the tests is assessed through local Bahadur efficiencies as well as the empirical power for small and moderate sample sizes. According to both criteria, for...

Statistical estimation of higher-order spectral densities by means of general tapering

M'hammed Baba Harra (1997)

Applicationes Mathematicae

Given a realization on a finite interval of a continuous-time stationary process, we construct estimators for higher order spectral densities. Tapering and shift-in-time methods are used to build estimators which are asymptotically unbiased and consistent for all admissible values of the argument. Asymptotic results for the fourth-order densities are given. Detailed attention is paid to the nth order case.

Statistical tools for discovering pseudo-periodicities in biological sequences

Bernard Prum, Élisabeth de Turckheim, Martin Vingron (2010)

ESAIM: Probability and Statistics


Many protein sequences present non trivial periodicities, such as cysteine signatures and leucine heptads. These known periodicities probably represent a small percentage of the total number of sequences periodic structures, and it is useful to have general tools to detect such sequences and their period in large databases of sequences. We compare three statistics adapted from those used in time series analysis: a generalisation of the simple autocovariance based on a similarity score and two statistics...

Statistical tools for discovering pseudo-periodicities in biological sequences

Bernard Prum, Élisabeth de Turckheim, Martin Vingron (2001)

ESAIM: Probability and Statistics

Many protein sequences present non trivial periodicities, such as cysteine signatures and leucine heptads. These known periodicities probably represent a small percentage of the total number of sequences periodic structures, and it is useful to have general tools to detect such sequences and their period in large databases of sequences. We compare three statistics adapted from those used in time series analysis: a generalisation of the simple autocovariance based on a similarity score and two statistics...

Strong uniform consistency rates of some characteristics of the conditional distribution estimator in the functional single-index model

Amina Angelika Bouchentouf, Tayeb Djebbouri, Abbes Rabhi, Khadidja Sabri (2014)

Applicationes Mathematicae

The aim of this paper is to establish a nonparametric estimate of some characteristics of the conditional distribution. Kernel type estimators for the conditional cumulative distribution function and for the successive derivatives of the conditional density of a scalar response variable Y given a Hilbertian random variable X are introduced when the observations are linked with a single-index structure. We establish the pointwise almost complete convergence and the uniform almost complete convergence...

Sumas acumuladas conjuntas. Tablas.

Carlos Polo Miranda, Montserrat Pepió Viñals (1990)

Qüestiió

Las Tablas de la Longitud de Ráfaga Media (LRM) para los Gráficos de Control por Sumas Acumuladas (SUMAC) sólo se habían deducido para el control de la media de un proceso distribuido normalmente, si bien también puede salir fuera de control por la variabilidad. Este trabajo describe cómo seleccionar los parámetros de un esquema SUMAC, para la media y desviación tipo muestrales, según la situación bajo control especificada conjuntamente por la media m0 y la desviación tipo σ0, y el estado fuera...

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