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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…
Estimating causal effects from observational data informs us about which factors are important in an autonomous system, and enables us to take better decisions. This is important because it has applications in selecting a treatment in…
The paper considers linear regression problems where the number of predictor variables is possibly larger than the sample size. The basic motivation of the study is to combine the points of view of model selection and functional regression…
Respondent-driven sampling is a widely-used network sampling technique, designed to sample from hard-to-reach populations. Estimation from the resulting samples is an area of active research, with software available to compute at least four…
In this paper, we construct an estimator of an errors-in-variables linear regression model. The regression model leads to a constrained total least squares problems with row and column constraints. Although this problem can be numerically…
We consider a problem in parametric estimation: given $n$ samples from an unknown distribution, we want to estimate which distribution, from a given one-parameter family, produced the data. Following Schulman and Vazirani, we evaluate an…
Gradient-based methods for optimisation of objectives in stochastic settings with unknown or intractable dynamics require estimators of derivatives. We derive an objective that, under automatic differentiation, produces low-variance…
A popular technique for selecting and tuning machine learning estimators is cross-validation. Cross-validation evaluates overall model fit, usually in terms of predictive accuracy. In causal inference, the optimal choice of estimator…
This paper deals with a projection least squares estimator of the drift function of a jump diffusion process $X$ computed from multiple independent copies of $X$ observed on $[0,T]$. Risk bounds are established on this estimator and on an…
We introduce a very general method for high-dimensional classification, based on careful combination of the results of applying an arbitrary base classifier to random projections of the feature vectors into a lower-dimensional space. In one…
We develop tests of the hypothesis of no effect for selected predictors in regression, without assuming a model for the conditional distribution of the response given the predictors. Predictor effects need not be limited to the mean…
To perform multiple regression, the least squares estimator is commonly used. However, this estimator is not robust to outliers. Therefore, robust methods such as S-estimation have been proposed. These estimators flag any observation with a…
We consider the estimation of a structural function which models a non-parametric relationship between a response and an endogenous regressor given an instrument in presence of dependence in the data generating process. Assuming an…
In functional linear regression, the parameters estimation involves solving a non necessarily well-posed problem and it has points of contact with a range of methodologies, including statistical smoothing, deconvolution and projection on…
We consider estimation of a sparse parameter vector that determines the covariance matrix of a Gaussian random vector via a sparse expansion into known "basis matrices". Using the theory of reproducing kernel Hilbert spaces, we derive lower…
This paper is concerned with inference on the regression function of a high-dimensional linear model when outcomes are missing at random. We propose an estimator which combines a Lasso pilot estimate of the regression function with a bias…
This paper discusses minimum distance estimation method in the linear regression model with dependent errors which are strongly mixing. The regression parameters are estimated through the minimum distance estimation method, and asymptotic…
A rank estimator in robust regression is a minimizer of a function which depends (in addition to other factors) on the ordering of residuals but not on their values. Here we focus on the optimization aspects of rank estimators. We…
We consider the problem of estimating covariance and precision matrices, and their associated discriminant coefficients, from normal data when the rank of the covariance matrix is strictly smaller than its dimension and the available sample…
We study policy evaluation of offline contextual bandits subject to unobserved confounders. Sensitivity analysis methods are commonly used to estimate the policy value under the worst-case confounding over a given uncertainty set. However,…