J. M. Muñoz-Pichardo

Identification of outlier bootstrap samples

We define a variation of Efrons method II based on the outlier bootstrap sample concept. A criterion for the identification of such samples is given, with which a variation in the bootstrap sample generation algorithm is introduced. The results of several simulations are analyzed in which, in comparison with Efrons method II, a higher degree of closeness to the estimated quantities can be observed.

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.

The Frechet's metric as a measure of influence in multivariate linear models with random errors elliptically distributed

In general, the influence diagnostics are based on two aspects: the perturbation of the model and the comparison of the results. The most used scheme of perturbation is the omission of the cases and, generally, as a pattern of comparison, a metric is used. A sample version of the Frechets metric is proposed to quantify the deviation between the sample distributions of the statistics. This is the way that a generic influence measure is obtained which can be applied to a great deal of statistical techniques. In particular, for linear multivariate models with random errors elliptically distributed, it is applied on the BLUE of the estimable linear functions.

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.

Cressie and Read power-divergences as influence measures for logistic regression models

A sample version of the power-divergence measures of Cressie and Read is proposed for the influence analysis in the logistic regression model. Influence measures are obtained by quantifying the deviation between the sample distribution of an estimate obtained with all the observations and the sample distribution of the same estimate obtained without any observation. In particular, this approach is applied to three estimates of the model: the MLE of regression coefficients vector, the probabilities vector and the linear predictor of a future case. Some examples are considered to clarify the usefulness of the introduced diagnostics.

Local influence on the ratio and Horvitz–Thompson estimators through the second order approach

Abstract Since Cook introduced the notion of local influence in 1986 a great number of papers have appeared in statistics handling this topic in a wide variety of areas. However, until we know, there is no paper focussed on local influence in survey sampling. This paper assesses the local influence through the curvature of the perturbation-formed surface of the ratio estimator in a simple random sampling without replacement and the Horvitz–Thompson estimator in an inclusion proportional to size sampling design. Both estimators use auxiliary information ( x ) and can be obtained through a model-assisted reasoning where the ratio model with variance proportional to x plays an important role. Two perturbation schemes are considered, a model perturbation and an auxiliary variable perturbation. We illustrate the effectiveness of the method in order to identify influential points with two real examples.

Consistency of maximum likelihood estimators in finite mixture models of the union of °W-type families

ABSTRACT In finite mixture models, maximum likelihood estimators have good properties, such as efficiency, consistency, and asymptotic normality under some uniform integrability assumptions on the mixture and its derivatives up to the third order. These conditions are frequently not easy to check because complex computations on bounding a lot of derivatives are involved. We give results implying these conditions for a new class of families of distributions, 𝒲-type families, which make it easier to check the conditions in many cases. Many useful and known families of distributions such as Weibull, Generalized Gamma, Log-gamma, inverse Log-gamma, inverse Gaussian, and all of the exponential families are 𝒲-type families. Hence, these results have broad applications.

Using conditional bias in principal component analysis for the evaluation of joint influence on the eigenvalues of the covariance matrix

Abstract Influence Analysis in Principal Component Analysis has usually been tackled using the influence function [1] or local influence [2] approaches. The main objective of this paper is that of proposing influence diagnostics for the eigenvalues of the covariance matrix, that is, for the variance explained by the principal components, from a different angle: that of the conditional bias [3] . An approximation of the conditional bias of the simple eigenvalues of the sample covariance matrix is calculated under normality and some influence diagnostics are proposed. The study is carried by considering joint influence.