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November, 1976 Consistency in Concave Regression
D. L. Hanson, Gordon Pledger
Ann. Statist. 4(6): 1038-1050 (November, 1976). DOI: 10.1214/aos/1176343640


For each $t$ in some subinterval $T$ of the real line let $F_t$ be a distribution function with mean $m(t)$. Suppose $m(t)$ is concave. Let $t_1, t_2, \cdots$ be a sequence of points in $T$ and let $Y_1, Y_2, \cdots$ be an independent sequence of random variables such that the distribution function of $Y_k$ is $F_{t_k}$. We consider estimators $m_n(t) = m_n(t; Y_1, \cdots, Y_n)$ which are concave in $t$ and which minimize $\sum^n_{i=1} \lbrack m_n(t_i; Y_1, \cdots, Y_n) - Y_i\rbrack^2$ over the class of concave functions. We investigate their consistency and the convergence of $\{m_n'(t)\}$ to $m'(t)$.


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D. L. Hanson. Gordon Pledger. "Consistency in Concave Regression." Ann. Statist. 4 (6) 1038 - 1050, November, 1976.


Published: November, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0341.62034
MathSciNet: MR426273
Digital Object Identifier: 10.1214/aos/1176343640

Primary: 62G05
Secondary: 90C20

Keywords: Concave , concave regression , consistency , convex , convex regression , Nonparametric regression , regression

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 6 • November, 1976
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