J. L. Moreno-Rebollo

Outliers : a formal approach

Summary We propose an outline which enables us to analyse in a generic way the errors which can affect the experimental observations. From this we state a definition for the term outlier, and typify the problems of Identification Techniques of Outliers. This allows us to construct a general framework in which to carry out a qualitative analysis of data which when applied to the Analysis of Outliers presents certain advantages with respect to the classical approach.

Minimum ϕ-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.

Influence diagnostics in regression with complex designs through conditional bias

One of the areas of Statistics in which the influence analysis has been widely studied is the multiple linear regression model. Nevertheless, the influence diagnostics proposed in this context cannot be applied to regression in complex survey, under randomized inference, since the i.i.d. case does not incorporate any probability weighting or population structure, such as clustering, stratification or measures of size into the analysis.In this paper we introduce some influence diagnostics in regression in complex survey. They are built on the conditional bias concept (Moreno-Rebollo et al., 1999). We emphasize the similarities and differences of the proposed measures with respect to the existing ones for the i.i.d. case.

An Overview of Asymptotic Properties of Estimators in Truncated Distributions

In this article, a method is proposed to get the limiting distributions and asymptotic properties of estimators based on the minimum and/or maximum of a given srs of a truncated distribution. Following a common outline, a review is carried out by considering different kinds of truncated distributions, some new results are also developed.

Estimating the unknown sample size

Abstract Let us consider a random experiment repeated n times with outcomes y =(y 1 ,…,y n ) , and that we are given the value of a statistic, T( y ) , but not the sample size n . Our aim is to estimate the unknown sample size n with the information provided by T( y ) . If T is a discrete random variable such that the corresponding family of p.m.fs, {P n } n⩾1 , is uniparametric, n being the unknown parameter, and if a certain recursive relation holds, we obtain unbiased estimators for functions of the sample size, h(n) , and also we characterize the maximum likelihood estimators (m.l.e.) of n in terms of the modes of the family of p.m.fs {P n } n⩾1 . As an application, we estimate the unknown sample size when we only know the number of r -records in a random sample from an absolutely continuous distribution. Also we present other applications related with the Poissonian binomial sampling.

Case-deletion type diagnostics for calibration estimators in survey sampling

Based on the use of calibration techniques as a way of handling nonresponse, case-deletion diagnostics for calibration estimators are proposed. A deleted case is dealt with as it were a nonresponse case. Two types of diagnostics are proposed: one compares the calibration weights and the other compares the estimates. These diagnostics are studied in depth for the general regression estimator, and can be calculated from quantities related to the full data set. They are related to the Cook distance and their similarities and differences are highlighted. Both an artificial and a real example are included as illustrations of the diagnostics proposed.

Influence Analysis in Principal Component Analysis Through Power-Series Expansions

ABSTRACT In influence analysis several problems arise in the field of Principal Components when applying different sample versions. Among these are the difficulty of determining a certain correspondence between the eigenvalues before and after the deletion of observations, the choice of the sign of the eigenvectors and the computational problem derived from the resolution of a great number of eigenproblems. In this article, such problems are discussed from the joint influence point of view and a solution is proposed by using approximations. Furthermore, the influence on a new parameter of interest is introduced: the proportion of variance explained by a set of principal components.

Influence analysis on discriminant coordinates

Discriminant analysis (DA), particularly Discriminant Coordinates (DC), is broadly applied in the scientific literature and included in many statistical software packages. DC is used to analyze biomedical data, especially for differential diagnosis on the basis of laboratory profiles. Articles handling influence analysis in DA can be found in the literature; however, this topic has been scarcely touched upon in DC. In this article, the case-deletion approach is followed to introduce a perturbation in the data and influence measures are proposed to assess the effect on three statistics of interest: the transformation matrix, canonical directions, and configuration, of the sample centroids.

Lower bounds for the variance in certain nonregular distributions

Using expansions based on orthogonal polynomials, we study the properties (such as attainability) of a system of lower bounds for the variance of any unbiased estimator in certain distributions whose range depends on an unknown parameter. We also study the bound of the first order, and compare it with the Chapman-Robbins-Kiefer bound.

Estimation in uniform distributions using orthogonal polynomials

The purpose of this paper is to study some problems of parametric estimation in the U(0,θ) distribution. Using expansions in terms of orthogonal polynomials, we compare the asymptotic behaviour of the uniformly minimum variance unbiased estimator (UMVUE) and the maximum likelihood estimator (MLE) for a given one-parameter estimable function. We also give conditions under which the results obtained can be extended to certain distributions whose range depends on an unknown parameter.