Related papers: Best estimation of functional linear models
Streamflow, as a natural phenomenon, is continuous in time and so are the meteorological variables which influence its variability. In practice, it can be of interest to forecast the whole flow curve instead of points (daily or hourly). To…
Various indicators and measures of the real life procedures rise up as functionals of the quantile process of a parent random variable Z. However, Z can be observed only through a response in a linear model whose covariates are not under…
We consider the problem of inferring a latent function in a probabilistic model of data. When dependencies of the latent function are specified by a Gaussian process and the data likelihood is complex, efficient computation often involve…
Continuous-time Markov processes over finite state-spaces are widely used to model dynamical processes in many fields of natural and social science. Here, we introduce an maximum likelihood estimator for constructing such models from data…
Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these…
Measurement error is an important problem that has not been very well studied in the context of Functional Data Analysis. To the best of our knowledge, there are no existing methods that address the presence of functional measurement errors…
Nonparametric estimators for the mean and the covariance functions of functional data are proposed. The setup covers a wide range of practical situations. The random trajectories are, not necessarily differentiable, have unknown regularity,…
We consider regression models with parametric (linear or nonlinear) regression function and allow responses to be ``missing at random.'' We assume that the errors have mean zero and are independent of the covariates. In order to estimate…
We consider building predictors when the data have missing values. We study the seemingly-simple case where the target to predict is a linear function of the fully-observed data and we show that, in the presence of missing values, the…
The problem of estimating the parameters of a linear regression model $Z(s,t)=m_1g_1(s,t)+ \cdots + m_pg_p(s,t)+U(s,t)$ based on observations of $Z$ on a spatial domain $G$ of special shape is considered, where the driving process $U$ is a…
The recent thought-provoking paper by Hansen [2022, Econometrica] proved that the Gauss-Markov theorem continues to hold without the requirement that competing estimators are linear in the vector of outcomes. Despite the elegant proof, it…
In some real world applications, such as spectrometry, functional models achieve better predictive performances if they work on the derivatives of order m of their inputs rather than on the original functions. As a consequence, the use of…
Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…
Functional data are typically modeled as sample paths of smooth stochastic processes in order to mitigate the fact that they are often observed discretely and noisily, occasionally irregularly and sparsely. The smoothness assumption is…
Many processes in biology, chemistry, physics, medicine, and engineering are modeled by a system of differential equations. Such a system is usually characterized via unknown parameters and estimating their 'true' value is thus required. In…
Functional linear regression analysis aims to model regression relations which include a functional predictor. The analog of the regression parameter vector or matrix in conventional multivariate or multiple-response linear regression…
In this paper several related estimation problems are addressed from a Bayesian point of view and optimal estimators are obtained for each of them when some natural loss functions are considered. Namely, we are interested in estimating a…
As with classic statistics, functional regression models are invaluable in the analysis of functional data. While there are now extensive tools with accompanying theory available for linear models, there is still a great deal of work to be…
This paper investigates the nonparametric estimation of a circular regression function in an errors-in-variables framework. Two settings are studied, depending on whether the covariates are circular or linear. Adaptive estimators are…
Suppose we observe an invertible linear process with independent mean-zero innovations and with coefficients depending on a finite-dimensional parameter, and we want to estimate the expectation of some function under the stationary…