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Robust estimation and variable selection procedure are developed for the extended t-process regression model with functional data. Statistical properties such as consistency of estimators and predictions are obtained. Numerical studies show…
We introduce flexible robust functional regression models, using various heavy-tailed processes, including a Student $t$-process. We propose efficient algorithms in estimating parameters for the marginal mean inferences and in predicting…
Functional logistic regression is a popular model to capture a linear relationship between binary response and functional predictor variables. However, many methods used for parameter estimation in functional logistic regression are…
A function-on-function regression model with quadratic and interaction effects of the covariates provides a more flexible model. Despite several attempts to estimate the model's parameters, almost all existing estimation strategies are…
Gaussian process regression (GPR) model is well-known to be susceptible to outliers. Robust process regression models based on t-process or other heavy-tailed processes have been developed to address the problem. However, due to the nature…
Functional linear regression is a widely used approach to model functional responses with respect to functional inputs. However, classical functional linear regression models can be severely affected by outliers. We therefore introduce a…
Functional data analysis is a fast evolving branch of modern statistics and the functional linear model has become popular in recent years. However, most estimation methods for this model rely on generalized least squares procedures and…
Functional quadratic regression models postulate a polynomial relationship between a scalar response rather than a linear one. As in functional linear regression, vertical and specially high-leverage outliers may affect the classical…
Functional data analysis is a fast evolving branch of statistics. Estimation procedures for the popular functional linear model either suffer from lack of robustness or are computationally burdensome. To address these shortcomings, a…
Generalized Linear Models are routinely used in data analysis. The classical procedures for estimation are based on Maximum Likelihood and it is well known that the presence of outliers can have a large impact on this estimator. Robust…
This paper addresses the problem of providing robust estimators under a functional logistic regression model. Logistic regression is a popular tool in classification problems with two populations. As in functional linear regression,…
The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…
Machine learning and data analysis have been used in many robotics fields, especially for modelling. Data are usually the result of sensor measurements and, as such, they might be subjected to noise and outliers. The presence of outliers…
A robust estimator is proposed for the parameters that characterize the linear regression problem. It is based on the notion of shrinkages, often used in Finance and previously studied for outlier detection in multivariate data. A thorough…
Fully robust versions of the elastic net estimator are introduced for linear and logistic regression. The algorithms to compute the estimators are based on the idea of repeatedly applying the non-robust classical estimators to data subsets…
Nonparametric regression models offer a way to understand and quantify relationships between variables without having to identify an appropriate family of possible regression functions. Although many estimation methods for these models have…
Missing data is frequently encountered in many areas of statistics. Propensity score weighting is a popular method for handling missing data. The propensity score method employs a response propensity model, but correct specification of the…
Linear regression with normally distributed errors - including particular cases such as ANOVA, Student's t-test or location-scale inference - is a widely used statistical procedure. In this case the ordinary least squares estimator…
This paper deals with the problem of outliers in high frequency observation data from diffusion processes. Robust estimation methods are needed because the inclusion of outliers can lead to incorrect statistical inference even in the…
Tensor-on-tensor (TOT) regression is an important tool for the analysis of tensor data, aiming to predict a set of response tensors from a corresponding set of predictor tensors. However, standard TOT regression is sensitive to outliers,…