Computer algebra and algorithms for unbiased moment estimation of arbitrary order

Algorithms for computer algebra

Linearly Unbiased Estimation of Conditional Moment and Correlation Functions

We consider a random-design regression model with vector-valued observations and develop nonparametric estimation of smooth conditional moment functions in the predictor variable. This includes estimation of higher order mixed moments and also functionals of the moments, such as conditional covariance, correlation, variance, and skewness functions. Our asymptotic analysis targets the limit dist...

Mathematics and Algorithms for Computer Algebra

I now want to apply the basic notions of computational representations and abstract algebra that I have developed so far to concrete algorithms, and briefly to consider their complexity. As I explained earlier, underlying all of computer algebra are the integers, so I will begin by considering algorithms for performing arithmetic on integers of unlimited magnitude, which I will call long intege...

Mathematics and Algorithms for Computer Algebra

This course will be mainly mathematics, some computer science and a little computing. Little or no essential use will be made of actual computer languages, although I may occasionally use Pascal, C, Lisp or REDUCE for concrete examples. The aim of the course is to provide an entry into the current research literature, but not to present the most recent research results. The first half of the co...

Computer Algebra Algorithms*

INTRODUCTION ...................................................................................................................... 1 ARITHMETIC ........................................................................................................................... 2 Integer and Polynomial Addition, Multiplication, and Division with Remainder ............. 2 Integer and Polynomial Greatest C...