On the asymptotic behavior of general projection-pursuit estimators under the common principal components model

The common principal components model for several groups of multivariate observations assumes equal principal axes among the groups. Robust estimators can be defined replacing the sample variance by a robust dispersion measure. This paper studies the asymptotic distribution of robust projection-pursuit estimators under a common principal components model.     

Celtine,celtisine and breoganine,new phenolic cularine alkaloids from fumariaceae

Three new phenolic cularines have been isolated from Sarcocapnos and Corydalis species. Their structures have been elucidated on the basis of spectroscopic studies and chemical transformations.     

Robust estimation in single-index models when the errors have a unimodal density with unknown nuisance parameter

This paper develops a robust profile estimation method for the parametric and nonparametric components of a single-index model when the errors have a strongly unimodal density with unknown nuisance parameter. We derive consistency results for the link function estimators as well as consistency and asymptotic distribution results for the single-index parameter estimators. Under a log-Gamma model, the sensitivity to anomalous observations is studied using the empirical influence curve. We also discuss a robust K-fold cross-validation procedure to select the smoothing parameters. A numerical study carried on with errors following a log-Gamma model and for contaminated schemes shows the good robustness properties of the proposed estimators and the advantages of considering a robust approach instead of the classical one. A real data set illustrates the use of our proposal.

     

General projection-pursuit estimators for the common principal components model: influence functions and Monte Carlo study

The common principal components (CPC) model for several groups of multivariate observations assumes equal principal axes but possibly different variances along these axes among the groups. Under a CPCs model, generalized projection-pursuit estimators are defined by using score functions on the dispersion measure considered. Their partial influence functions are obtained and asymptotic variances are derived from them. When the score function is taken equal to the logarithm, it is shown that, under a proportionality model, the eigenvector estimators are optimal in the sense of minimizing the asymptotic variance of the eigenvectors, for a given scale measure.     

Ergodicity,geometric ergodicity and mixing conditions for nonparametric ARMA processes

In this paper, we introduce nonparametric ARMA models which provide an alternative to nonparametric autoregressive models, when there is a large dependence to the past observations. Conditions for ergodicity and geometric ergodicity are given when both the nonparametric autoregressive part and themoving average structure depend only one step behind. Also, a Fisher-consistent procedure is provided and its performance is studied through a simulated example. Received: 9 April 2002     

Robust nonparametric regression estimation

In this paper we define a robust conditional location functional without requiring any moment condition. We apply the nonparametric proposals considered by C. Stone (Ann. Statist. 5 (1977), 595–645) to this functional equation in order to obtain strongly consistent, robust nonparametric estimates of the regression function. We give some examples by using nearest neighbor weights or weights based on kernel methods under no assumptions whatsoever on the probability measure of the vector (X,Y). We also derive strong convergence rates and the asymptotic distribution of the proposed estimates.     

Secocularines: a new group of isoquinoline related alkaloids present in the fumariaceae

The isolation and structure of secocularine and secocularidine, the first two members of a new group of isoquinoline related alkaloids, the secocularines, is reported.     

Testing equality between several populations covariance operators

In many situations, when dealing with several populations, equality of the covariance operators is assumed. An important issue is to study whether this assumption holds before making other inferences. In this paper, we develop a test for comparing covariance operators of several functional data samples. The proposed test is based on the Hilbert–Schmidt norm of the difference between estimated covariance operators. In particular, when dealing with two populations, the test statistic is just the squared norm of the difference between the two covariance operators estimators. The asymptotic behaviour of the test statistic under both the null hypothesis and local alternatives is obtained. The computation of the quantiles of the null asymptotic distribution is not feasible in practice. To overcome this problem, a bootstrap procedure is considered. The performance of the test statistic for small sample sizes is illustrated through a Monte Carlo study and on a real data set.     

Robust estimation for nonparametric generalized regression

This paper focuses on nonparametric regression estimation for the parameters of a discrete or continuous distribution, such as the Poisson or Gamma distributions, when anomalous data are present. The proposal is a natural extension of robust methods developed in the setting of parametric generalized linear models. Robust estimators bounding either large values of the deviance or of the Pearson residuals are introduced and their asymptotic behaviour is derived. Through a Monte Carlo study, for the Poisson and Gamma distributions, the finite properties of the proposed procedures are investigated and their performance is compared with that of the classical ones. A resistant cross-validation method to choose the smoothing parameter is also considered.