Some theoretical results on approximation methods¹

¹Paper, presented at the 5th Intern. Summer School on Problems of Model Choice and Parameter Estimation in Regression Analysis, Sellin, 26.3-3. ,4. 1981

Abstract

In this paper we give an approximation procedure to surfaces which are defined on a _p-dimensional region and are observable (disturbed with some noice) according to an experimental design. In this procedure we combine clustering methods, discriminant analysis and smoothing techniques.

In the second part of the paper is considered some investigations on statistical properties of linear smoothing procedures. We assume linear models and for a broad class of models we prove the consistence of the estimation of the expectation of observations after smoothing.

In the last section we give some results on efficiency.

Keywords:

• non-parametric rstimation
• approximation
• spline approximation
• smoothing
• consistency
• efficiency

¹Paper, presented at the 5th Intern. Summer School on Problems of Model Choice and Parameter Estimation in Regression Analysis, Sellin, 26.3-3. ,4. 1981

¹Paper, presented at the 5th Intern. Summer School on Problems of Model Choice and Parameter Estimation in Regression Analysis, Sellin, 26.3-3. ,4. 1981

Notes

¹Paper, presented at the 5th Intern. Summer School on Problems of Model Choice and Parameter Estimation in Regression Analysis, Sellin, 26.3-3. ,4. 1981