Related papers: Estimating a Function and Its Derivatives Under a …

The work provides an upper estimate of the best accuracy for the problem of reconstructing derivatives based on function values at a given number of points for the functions of Besov classes meeting the mixed Hoelder conditions. In some…

To tackle difficulties for theoretical studies in situations involving nonsmooth functions, we propose a sequence of infinitely differentiable functions to approximate the nonsmooth function under consideration. A rate of approximation is…

We provide an upper bound as a random variable for the functions of estimators in high dimensions. This upper bound may help establish the rate of convergence of functions in high dimensions. The upper bound random variable may converge…

Combining information both within and across trajectories, we propose a simple estimator for the local regularity of the trajectories of a stochastic process. Independent trajectories are measured with errors at randomly sampled time…

Random samples are lossy summaries which allow queries posed over the data to be approximated by applying an appropriate estimator to the sample. The effectiveness of sampling, however, hinges on estimator selection. The choice of…

Given a data set (t_i, y_i), i=1,..., n with the t_i in [0,1] non-parametric regression is concerned with the problem of specifying a suitable function f_n:[0,1] -> R such that the data can be reasonably approximated by the points (t_i,…

We study a well-known estimator of the fractal index of a stochastic process. Our framework is very general and encompasses many models of interest; we show how to extend the theory of the estimator to a large class of non-Gaussian…

This paper presents uniform estimation and inference theory for a large class of nonparametric partitioning-based M-estimators. The main theoretical results include: (i) uniform consistency for convex and non-convex objective functions;…

Estimating linear regression using least squares and reporting robust standard errors is very common in financial economics, and indeed, much of the social sciences and elsewhere. For thick tailed predictors under heteroskedasticity this…

Fractional derivatives are a well-studied generalization of integer order derivatives. Naturally, for optimization, it is of interest to understand the convergence properties of gradient descent using fractional derivatives. Convergence…

The use of principal component methods to analyze functional data is appropriate in a wide range of different settings. In studies of ``functional data analysis,'' it has often been assumed that a sample of random functions is observed…

We investigate a semiparametric regression model where one gets noisy non linear non invertible functions of the observations. We focus on the application to bearings-only tracking. We first investigate the least squares estimator and prove…

We consider the problem of estimating the slope parameter in functional linear regression, where scalar responses Y1,...,Yn are modeled in dependence of second order stationary random functions X1,...,Xn. An orthogonal series estimator of…

We consider the problem of estimating the structural function in nonparametric instrumental regression, where in the presence of an instrument W a response Y is modeled in dependence of an endogenous explanatory variable Z. The proposed…

We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…

We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function $f$, consistent estimators of the mean embedding of a random variable…

We consider an additive regression model consisting of two components $f^0$ and $g^0$, where the first component $f^0$ is in some sense "smoother" than the second $g^0$. Smoothness is here described in terms of a semi-norm on the class of…

Theoretical guarantees are established for a standard estimator in a semi-parametric finite mixture model, where each component density is modeled as a product of univariate densities under a conditional independence assumption. The focus…

We discuss a number of estimates of the hazard under the assumption that the hazard is monotone on an interval [0,a]. The usual isotonic least squares estimators of the hazard are inconsistent at the boundary points 0 and a. We use…

A mathematical smooth function means that the function has continuous derivatives to a certain degree C(k). We call it a k-smooth function or a smooth function if k can grow infinitively. Based on quantum physics, there is no such smooth…