# Strong convergence in nonparametric estimation of regression functions

K. F. Cheng

Research output: Contribution to journalArticle

1 Citation (Scopus)

### Abstract

The nonparametric regression problem has the objective of estimating conditional expectation. Consider the model {Mathematical expression}, where the random variable Z has mean zero and is independent of X. The regression function R(x) is the conditional expectation of Y given X = x. For an estimator of the form {Mathematical expression}, we obtain the rate of strong uniform convergence {Mathematical expression}. Here X is a d-dimensional variable and C is a suitable subset of Rd.

Original language English 177-187 11 Periodica Mathematica Hungarica 14 2 https://doi.org/10.1007/BF01855429 Published - Jun 1983 Yes

### Fingerprint

Nonparametric Estimation
Regression Function
Strong Convergence
Conditional Expectation
Nonparametric Regression
Uniform convergence
Random variable
Mathematical Model
Estimator
Subset
Zero

### Keywords

• AMS (MOS) subject classifications (1970): Primary 62G05, Secondary 60F15
• Nonparametric regression
• strong convergence

### ASJC Scopus subject areas

• Mathematics(all)

### Cite this

In: Periodica Mathematica Hungarica, Vol. 14, No. 2, 06.1983, p. 177-187.

Research output: Contribution to journalArticle

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