Premium
The asymptotic behavior of monotone percentile regression estimates
Author(s) -
Wright F. T.
Publication year - 1984
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3314752
Subject(s) - mathematics , percentile , estimator , statistics , monotone polygon , rate of convergence , least absolute deviations , nonparametric regression , regression , regression analysis , asymptotic distribution , regression function , nonparametric statistics , function (biology) , statistical inference , computer science , computer network , channel (broadcasting) , geometry , evolutionary biology , biology
The least‐absolute‐deviation estimate of a monotone regression function on an interval has been studied in the literature. If the observation points become dense in the interval, the almost sure rate of convergence has been shown to be O( n 1/4 ). Applying the techniques used by Brunk (1970, Nonparametric, Techniques in Statistical Inference . Cambridge Univ. Press), the asymptotic distribution of the l 1 estimator at a point is obtained. If the underlying regression function has positive slope at the point, the rate of convergence is seen to be O(n 1/3 ) . Monotone percentile regression estimates are also considered.