article · 2009
1.1 Difference Polynomial Kernel Estimation
Zhihua Su, Z. Su, P. Qiu
Cited by 0Abstract and details only
Abstract
In the one-dimensional case, we formulate a jump regression model as follows: f(x) = g(x) + p∑ djI(x> sj), for x ∈ [0, 1], i=1 where g is a continuous function, p is the number of jump points, {sj, j = 1, 2,..., p} are the jump positions, and {dj, j = 1, 2,..., p} are the corresponding jump magnitudes. But in reality, our observations will also contain noises. And here for simplicity, we assume the noises ɛi’s are independent and identically distributed random errors with E(ɛi) = 0 and V ar(ɛi) = σ 2 (Xi). But for simplicity, here we just assume that the noise level for all the design points are the same. So we have Yi | Xi = f(Xi) + ɛi, i = 1, 2, · · · , n, where Yi’s are data we can observe. And Xi’s, which are called the design points, are the locations we take observations. 1 One approach to detect jumps is to use a difference polynomial kernel estimation procedure. This procedure estimate the left limit of a design point and also the right limit of a design point by a local polynomial kernel estimator. For an example, if we use a local kernel estimator (polynomial order equals to 0), the estimator will be: MDKE(x) = 1 nhn n∑ i=1
Cite this paper
Su, Z., Su, Z., & Qiu, P. (2009). 1.1 Difference Polynomial Kernel Estimation.
Su, Zhihua, et al. “1.1 Difference Polynomial Kernel Estimation.” 2009.
Su, Zhihua, Z. Su, and P. Qiu. 2009. “1.1 Difference Polynomial Kernel Estimation.”
Su, Z., Su, Z. and Qiu, P. (2009) ‘1.1 Difference Polynomial Kernel Estimation’.
@article{su2009difference,
title = {{1.1 Difference Polynomial Kernel Estimation}},
author = {Su, Zhihua and Su, Z. and Qiu, P.},
year = {2009}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.