arXiv subjects

Daniela Rodriguez

Publications and source records attributed to Daniela Rodriguez.

9 recordsLinked to original sources

arXiv2023

Threshold detection under a semiparametric regression model

Linear regression models have been extensively considered in the literature. However, in some practical applications they may not be appropriate all over the range of the covariate. In this paper, a more flexible model is introduced by considering a regression model $Y=r(X)+\varepsilon$ where the regression function $r(\cdot)$ is assumed to be linear for large values in the domain of the predictor variable $X$. More precisely, we assume that $r(x)=\alpha_0+\beta_0 x$ for $x> u_0$, where the value $u_0$ is identified as the smallest value satisfying such a property. A penalized procedure is introduced to estimate the threshold $u_0$. The considered proposal focusses on a semiparametric approach since no parametric model is assumed for the regression function for values smaller than $u_0$. Consistency properties of both the threshold estimator and the estimators of $(\alpha_0,\beta_0)$ are derived, under mild assumptions. Through a numerical study, the small sample properties of the proposed procedure and the importance of introducing a penalization are investigated. The analysis of a real data set allows us to demonstrate the usefulness of the penalized estimators.

math.ST↗

arXiv2023

Asymptotic results for nonparametric regression estimators after sufficient dimension reduction estimation

Prediction, in regression and classification, is one of the main aims in modern data science. When the number of predictors is large, a common first step is to reduce the dimension of the data. Sufficient dimension reduction (SDR) is a well established paradigm of reduction that keeps all the relevant information in the covariates X that is necessary for the prediction of Y . In practice, SDR has been successfully used as an exploratory tool for modelling after estimation of the sufficient reduction. Nevertheless, even if the estimated reduction is a consistent estimator of the population, there is no theory that supports this step when non-parametric regression is used in the imputed estimator. In this paper, we show that the asymptotic distribution of the non-parametric regression estimator is the same regardless if the true SDR or its estimator is used. This result allows making inferences, for example, computing confidence intervals for the regression function avoiding the curse of dimensionality.

stat.ME↗

arXiv2018

The spatial sign covariance operator: Asymptotic results and applications

Due to the increasing recording capability, functional data analysis has become an important research topic. For functional data the study of outlier detection and/or the development of robust statistical procedures has started recently. One robust alternative to the sample covariance operator is the sample spatial sign covariance operator. In this paper, we study the asymptotic behaviour of the sample spatial sign covariance operator when location is unknown. Among other possible applications of the obtained results, we derive the asymptotic distribution of the principal directions obtained from the sample spatial sign covariance operator and we develop test to detect differences between the scatter operators of two populations. In particular, the test performance is illustrated through a Monte Carlo study for small sample sizes.

math.ST↗

arXiv2018

Robust estimators in a generalized partly linear regression model under monotony constraints

In this paper, we consider the situation in which the observations follow an isotonic generalized partly linear model. Under this model, the mean of the responses is modelled, through a link function, linearly on some covariates and nonparametrically on an univariate regressor in such a way that the nonparametric component is assumed to be a monotone function. A class of robust estimates for the monotone nonparametric component and for the regression parameter, related to the linear one, is defined. The robust estimators are based on a spline approach combined with a score function which bounds large values of the deviance. As an application, we consider the isotonic partly linear log--Gamma regression model. Through a Monte Carlo study, we investigate the performance of the proposed estimators under a partly linear log-Gamma regression model with increasing nonparametric component.

math.ST↗

arXiv2016

On the instability of two entropic dynamical models

In this paper we study two entropic dynamical models from the viewpoint of information geometry. We study the geometry structures of the associated statistical manifolds. In order to analyse the character of the instability of the systems, we obtain their geodesics and compute their Jacobi vector fields. The results of this work improve and extend a recent advance in this topics studied in [13]

math-ph↗

arXiv2014

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 if 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 tests statistic is just the squared norm of the difference between the two covariance operators estimators. The asymptotic behaviour of the test statistic under the null and under local alternatives is obtained. Since the statistic null asymptotic distribution does not allow to obtain easily its quantiles, a bootstrap procedure to compute the critical values is considered. The performance of the test statistics for small sample sizes is illustrated through a Monte Carlo study.

math.ST↗

arXiv2011

k-Nearest neighbor density estimation on Riemannian Manifolds

In this paper, we consider a k-nearest neighbor kernel type estimator when the random variables belong in a Riemannian manifolds. We study asymptotic properties such as the consistency and the asymptotic distribution. A simulation study is also consider to evaluate the performance of the proposal. Finally, to illustrate the potential applications of the proposed estimator, we analyzed two real example where two different manifolds are considered.

math.ST↗

arXiv2010

Robust Estimators in Partly Linear Regression Models on Riemannian Manifolds

Under a partially linear models we study a family of robust estimates for the regression parameter and the regression function when some of the predictor variables take values on a Riemannian manifold. We obtain the consistency and the asymptotic normality of the proposed estimators. Also, we consider a robust cross validation procedure to select the smoothing parameter. Simulations and application to real data show the performance of our proposal under small samples and contamination.

math.ST↗

arXiv2010

Partially linear models on Riemannian manifolds

In partially 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 εis independent of (x^T,t). In this paper, estimators of βand g are constructed when the explanatory variables t take values on a Riemannian manifold. Our proposal combine the flexibility of these models with the complex structure of a set of explanatory variables. We prove that the resulting estimator of βis asymptotically normal under the suitable conditions. Through a simulation study, we explored the performance of the estimators. Finally, we applied the studied model to an example based on real dataset.

math.ST↗