Daniela Rodriguez

Kernel Density Estimation on Riemannian Manifolds: Asymptotic Results

The paper concerns the strong uniform consistency and the asymptotic distribution of the kernel density estimator of random objects on a Riemannian manifolds, proposed by Pelletier (Stat. Probab. Lett., 73(3):297–304, 2005). The estimator is illustrated via one example based on a real data.

Testing the Equality of Covariance Operators

In many situations, when dealing with several populations, equality of the covariance operators is assumed. In this work, we will study a hypothesis test to validate this assumption.

Robust inference in generalized partially linear models

In many situations, data follow a generalized partly linear model in which the mean of the responses is modeled, through a link function, linearly on some covariates and nonparametrically on the remaining ones. A new class of robust estimates for the smooth function @h, associated to the nonparametric component, and for the parameter @b, related to the linear one, is defined. The robust estimators are based on a three-step procedure, where large values of the deviance or Pearson residuals are bounded through a score function. These estimators allow us to make easier inferences on the regression parameter @b and also improve computationally those based on a robust profile likelihood approach. The resulting estimates of @b turn out to be root-n consistent and asymptotically normally distributed. Besides, the empirical influence function allows us to study the sensitivity of the estimators to anomalous observations. A robust Wald test for the regression parameter is also provided. Through a Monte Carlo study, the performance of the robust estimators and the robust Wald test is compared with that of the classical ones.

Robust bandwidth selection in semiparametric partly linear regression models: Monte Carlo study and influential analysis

In this paper, under a semiparametric partly linear regression model with fixed design, we introduce a family of robust procedures to select the bandwidth parameter. The robust plug-in proposal is based on nonparametric robust estimates of the @nth derivatives and under mild conditions, it converges to the optimal bandwidth. A robust cross-validation bandwidth is also considered and the performance of the different proposals is compared through a Monte Carlo study. We define an empirical influence measure for data-driven bandwidth selectors and, through it, we study the sensitivity of the data-driven bandwidth selectors. It appears that the robust selector compares favorably to its classical competitor, despite the need to select a pilot bandwidth when considering plug-in bandwidths. Moreover, the plug-in procedure seems to be less sensitive than the cross-validation in particular, when introducing several outliers. When combined with the three-step procedure proposed by Bianco and Boente [2004. Robust estimators in semiparametric partly linear regression models. J. Statist. Plann. Inference 122, 229-252] the robust selectors lead to robust data-driven estimates of both the regression function and the regression parameter.

Inference under functional proportional and common principal component models

In many situations, when dealing with several populations with different covariance operators, equality of the operators is assumed. Usually, if this assumption does not hold, one estimates the covariance operator of each group separately, which leads to a large number of parameters. As in the multivariate setting, this is not satisfactory since the covariance operators may exhibit some common structure. In this paper, we discuss the extension to the functional setting of the common principal component model that has been widely studied when dealing with multivariate observations. Moreover, we also consider a proportional model in which the covariance operators are assumed to be equal up to a multiplicative constant. For both models, we present estimators of the unknown parameters and we obtain their asymptotic distribution. A test for equality against proportionality is also considered.

Robust nonparametric regression on Riemannian manifolds

In this study, we introduce two families of robust kernel-based regression estimators when the regressors are random objects taking values in a Riemannian manifold. The first proposal is a local M-estimator based on kernel methods, adapted to the geometry of the manifold. For the second proposal, the weights are based on k-nearest neighbour kernel methods. Strong uniform consistent results as well as the asymptotical normality of both families are established. Finally, a Monte Carlo study is carried out to compare the performance of the robust proposed estimators with that of the classical ones, in normal and contaminated samples and a cross-validation method is discussed.

Asymmetries in kinesin‐2 and cytoplasmic dynein contributions to melanosome transport

The mechanisms involved in bidirectional transport along microtubules remain largely unknown. We explored the collective action of kinesin‐2 and dynein motors during transport of melanosomes inXenopus laevis melanophores. These motors are attached to organelles through accessory proteins establishing a complex molecular linker. We determined both the stiffness of this linker and the organelles speed and observed that these parameters depended on the organelle size and cargo direction. Our results suggest that melanosome transport is driven by two dissimilar teams: whereas dynein motors compete with kinesin‐2 affecting the properties of plus‐end directed organelles, kinesin‐2 does not seem to play a similar role during minus‐end transport.

Threshold selection for extremes under a semiparametric model

In this work we propose a semiparametric likelihood procedure for the threshold selection for extreme values. This is achieved under a semiparametric model, which assumes there is a threshold above which the excess distribution belongs to the generalized Pareto family. The motivation of our proposal lays on a particular characterization of the threshold under the aforementioned model. A simulation study is performed to show empirically the properties of the proposal and we also compare it with other estimators.

Partly linear models on Riemannian manifolds

In partly linear models, the dependence of the response y on (x T, t) is modeled through the relationship y=x T β+g(t)+ϵ, where ϵ is independent of (x T, t). We are interested in developing an estimation procedure that allows us to combine the flexibility of the partly linear models, studied by several authors, but including some variables that belong to a non-Euclidean space. The motivating application of this paper deals with the explanation of the atmospheric SO2 pollution incidents using these models when some of the predictive variables belong in a cylinder. In this paper, the estimators of β and g are constructed when the explanatory variables t take values on a Riemannian manifold and the asymptotic properties of the proposed estimators are obtained under suitable conditions. We illustrate the use of this estimation approach using an environmental data set and we explore the performance of the estimators through a simulation study.

Robust estimators in partly linear regression models on Riemannian manifolds

Under a partly linear model we study a family of robust estimates for the regression parameter and the regression function when some of the predictors take values on a Riemannian manifold. We obtain the consistency and the asymptotic normality of the proposed estimators. Simulations and an application to a real dataset show the good performance of our proposal under small samples and contamination.