Every Latin square of prime or prime power order s corresponds to a polynomial in 2 variables over the finite field on s elements, called the local permutation polynomial. What characterizes this polynomial is that its restrictions to one variable are permutations. We discuss the general form of local permutation polynomials and prove that their total degree is at most 2s−4, and that this bound...

Nonparametric regression estimates a conditional expectation of a response given a predictor variable without requiring parametric assumptions about this conditional expectation. There are many methods of nonparametric regression including kernel estimation, smoothing splines, regression splines, and orthogonal series. Local regression ts parametric models locally by using kernel weights. Local...

This paper presents a novel disparity estimation algorithm based on local polynomial expansion of the images in a stereo pair. Being a spin-off from work on two-frame motion estimation, it is primarily intended as a proof of concept for some of the underlying ideas. It may, however, be useful on its own as well, since it is very simple and fast. The accuracy still remains to be determined.

The adaptive local polynomial Fourier transform is employed for improvement of the ISAR images in complex reflector geometry cases, as well as in cases of fast maneuvering targets. It has been shown that this simple technique can produce significantly improved results with a relatively modest calculation burden. Two forms of the adaptive LPFT are proposed. Adaptive parameter in the first form i...

B. Seifert Th. Gasser University of Zurich Department of Biostatistics Sumatrastrasse 30 CH{8006 Z urich, Switzerland Abstract When estimating a regression function r or its th derivative, local polynomials are an attractive choice due to their exibility and asymptotic performance. Seifert & Gasser (1996) proposed local polynomial ridging to overcome problems of local polynomials with variance...

Many practical problems require nonparametric estimates of regression functions, and local polynomial regression has emerged as a leading approach. In applied settings practitioners often adopt either the local constant or local linear variants, or choose the order of the local polynomial to be slightly greater than the order of the maximum derivative estimate required. But such ad hoc determin...

We propose a new approach to conditional quantile function estimation that combines both parametric and nonparametric techniques. At each design point, a global, possibly incorrect, pilot parametric model is locally adjusted through a kernel smoothing fit. The resulting quantile regression estimator behaves like a parametric estimator when the latter is correct and converges to the nonparametri...