Related papers: Methodology and convergence rates for functional l…
Situations of a functional predictor paired with a scalar response are increasingly encountered in data analysis. Predictors are often appropriately modeled as square integrable smooth random functions. Imposing minimal assumptions on the…
Measurement uncertainty is a non trivial aspect of the laboratory component of most undergraduate physics courses. Confusion about the application of statistical tools calls for the elaboration of guidelines and the elimination of…
Functional linear regression has recently attracted considerable interest. Many works focus on asymptotic inference. In this paper we consider in a non asymptotic framework a simple estimation procedure based on functional Principal…
In this paper, a practical estimation method for a regression model is proposed using semiparametric efficient score functions applicable to data with various shapes of errors. First, I derive semiparametric efficient score vectors for a…
Nonparametric regression with random design is considered. The $L_2$ error with integration with respect to the design measure is used as the error criterion. An over-parametrized deep neural network regression estimate with logistic…
Convex regression is the problem of fitting a convex function to a data set consisting of input-output pairs. We present a new approach to this problem called spectrahedral regression, in which we fit a spectrahedral function to the data,…
We study principal component analysis (PCA) for mean zero i.i.d. Gaussian observations $X_1,\dots, X_n$ in a separable Hilbert space $\mathbb{H}$ with unknown covariance operator $\Sigma.$ The complexity of the problem is characterized by…
Incorporating covariates into functional principal component analysis (PCA) can substantially improve the representation efficiency of the principal components and predictive performance. However, many existing functional PCA methods do not…
We consider the problem of predicting a real random variable from a functional explanatory variable. The problem is attacked by mean of nonparametric kernel approach which has been recently adapted to this functional context. We derive…
The aim of this article is to overview the problem of mean square optimal estimation of linear functionals which depend on unknown values of periodically correlated stochastic process. Estimates are based on observations of this process and…
Neural networks are very successful tools in for example advanced classification. From a statistical point of view, fitting a neural network may be seen as a kind of regression, where we seek a function from the input space to a space of…
We consider the estimation of a regression function with random design and heteroscedastic noise in a nonparametric setting. More precisely, we address the problem of characterizing the optimal penalty when the regression function is…
Penalties that induce smoothness are common in nonparametric regression. In many settings, the amount of smoothness in the data generating function will not be known. Simon and Shojaie (2021) derived convergence rates for nonparametric…
We propose localized functional principal component analysis (LFPCA), looking for orthogonal basis functions with localized support regions that explain most of the variability of a random process. The LFPCA is formulated as a convex…
We consider the problem of estimating the slope function in a functional regression with a scalar response and a functional covariate. This central problem of functional data analysis is well known to be ill-posed, thus requiring a…
The problem of estimating a linear functional based on observational data is canonical in both the causal inference and bandit literatures. We analyze a broad class of two-stage procedures that first estimate the treatment effect function,…
We develop methodology to detect structural breaks in the slope function of a concurrent functional linear regression model for functional time series in $C[0,1]$. Our test is based on a CUSUM process of regressor-weighted OLS residual…
We consider the problem of estimating the value l({\phi}) of a linear functional, where the structural function {\phi} models a nonparametric relationship in presence of instrumental variables. We propose a plug-in estimator which is based…
A goodness-of-fit test for the Functional Linear Model with Scalar Response (FLMSR) with responses Missing at Random (MAR) is proposed in this paper. The test statistic relies on a marked empirical process indexed by the projected…
In sparse linear regression, the SLOPE estimator generalizes LASSO by penalizing different coordinates of the estimate according to their magnitudes. In this paper, we present a precise performance characterization of SLOPE in the…