# Universal Local Linear Kernel Estimators in Nonparametric Regression

@article{Linke2022UniversalLL, title={Universal Local Linear Kernel Estimators in Nonparametric Regression}, author={Yu. Yu. Linke and Igor' Semenovich Borisov and Pavel S. Ruzankin and Vladimir Kutsenko and Elena Yarovaya and S. A. Shalnova}, journal={Mathematics}, year={2022} }

New local linear estimators are proposed for a wide class of nonparametric regression models. The estimators are uniformly consistent regardless of satisfying traditional conditions of dependence of design elements. The estimators are the solutions of a specially weighted least-squares method. The design can be fixed or random and does not need to meet classical regularity or independence conditions. As an application, several estimators are constructed for the mean of dense functional data…

## References

SHOWING 1-10 OF 67 REFERENCES

### Universal weighted kernel-type estimators for some class of regression models

- Mathematics
- 2020

For a wide class of nonparametric regression models with random design, we suggest consistent weighted least square estimators, asymptotic properties of which do not depend on correlation of the…

### On internally corrected and symmetrized kernel estimators for nonparametric regression

- Mathematics
- 2010

We investigate the properties of a kernel-type multivariate regression estimator first proposed by Mack and Müller (Sankhya 51:59–72, 1989) in the context of univariate derivative estimation. Our…

### Asymptotic distributions of nonparametric regression estimators for longitudinal or functional data

- Mathematics
- 2007

### Efficient Estimation of the Nonparametric Mean and Covariance Functions for Longitudinal and Sparse Functional Data

- MathematicsJournal of the American Statistical Association
- 2018

ABSTRACT We consider the estimation of mean and covariance functions for longitudinal and sparse functional data by using the full quasi-likelihood coupling a modification of the local kernel…

### Uniform convergence rates for nonparametric regression and principal component analysis in functional/longitudinal data

- Mathematics
- 2010

We consider nonparametric estimation of the mean and covariance functions for functional/longitudinal data. Strong uniform convergence rates are developed for estimators that are local-linear…

### Consistency of the recursive nonparametric regression estimation for dependent functional data

- Mathematics
- 2013

We consider the recursive estimation of a regression functional where the explanatory variables take values in some functional space. We prove the almost sure convergence of such estimates for…

### Trapezoidal rule and sampling designs for the nonparametric estimation of the regression function in models with correlated errors

- Mathematics
- 2018

ABSTRACT The problem of estimating the regression function in a fixed design models with correlated observations is considered. Such observations are obtained from several experimental units, each of…