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Consider the problem of estimating the mean of a Gaussian random vector when the mean vector is assumed to be in a given convex set. The most natural solution is to take the Euclidean projection of the data vector on to this convex set; in…
A partial least squares regression is proposed for estimating the function-on-function regression model where a functional response and multiple functional predictors consist of random curves with quadratic and interaction effects. The…
We consider least squares estimation in a general nonparametric regression model. The rate of convergence of the least squares estimator (LSE) for the unknown regression function is well studied when the errors are sub-Gaussian. We find…
Nonparametric regression subject to convexity or concavity constraints is increasingly popular in economics, finance, operations research, machine learning, and statistics. However, the conventional convex regression based on the least…
Shape constraints in nonparametric regression provide a powerful framework for estimating regression functions under realistic assumptions without tuning parameters. However, most existing methods$\unicode{x2013}$except additive…
The problem of prediction in functional linear regression is conventionally addressed by reducing dimension via the standard principal component basis. In this paper we show that an alternative basis chosen through weighted least-squares,…
We consider the minimization of composite objective functions composed of the expectation of quadratic functions and an arbitrary convex function. We study the stochastic dual averaging algorithm with a constant step-size, showing that it…
There has been substantial recent work on methods for estimating the slope function in linear regression for functional data analysis. However, as in the case of more conventional finite-dimensional regression, much of the practical…
The function-on-function linear regression model in which the response and predictors consist of random curves has become a general framework to investigate the relationship between the functional response and functional predictors.…
Regression analysis is an important instrument to determine the effect of the explanatory variables on response variables. When outliers and bias errors are present, the standard weighted least squares estimator may perform poorly. For this…
Estimation of a quadratic functional over parameter spaces that are not quadratically convex is considered. It is shown, in contrast to the theory for quadratically convex parameter spaces, that optimal quadratic rules are often rate…
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…
We address the inference problem concerning regression coefficients in a classical linear regression model using least squares estimates. The analysis is conducted under circumstances where network dependency exists across units in the…
We study the least square estimator, in the framework of simple linear regression, when the deviance term $\varepsilon$ with respect to the linear model is modeled by a uniform distribution. In particular, we give the law of this estimator,…
In this paper, the estimation problem for sparse reduced rank regression (SRRR) model is considered. The SRRR model is widely used for dimension reduction and variable selection with applications in signal processing, econometrics, etc. The…
We find the local rate of convergence of the least squares estimator (LSE) of a one dimensional convex regression function when (a) a certain number of derivatives vanish at the point of interest, and (b) the true regression function is…
We consider the kernel partial least squares algorithm for non-parametric regression with stationary dependent data. Probabilistic convergence rates of the kernel partial least squares estimator to the true regression function are…
The linear regression models are widely used statistical techniques in numerous practical applications. The standard regression model requires several assumptions about the regres- sors and the error term. The regression parameters are…
The partial least squares algorithm for dependent data realisations is considered. Consequences of ignoring the dependence for the algorithm performance are studied both theoretically and in simulations. It is shown that ignoring certain…
In this paper, we focus on regression estimation in both the inductive and the transductive case. We assume that we are given a set of features (which can be a base of functions, but not necessarily). We begin by giving a deviation…