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May, 1974 Regression Designs in Autoregressive Stochastic Processes
Jaroslav Hajek, George Kimeldorf
Ann. Statist. 2(3): 520-527 (May, 1974). DOI: 10.1214/aos/1176342711

Abstract

This paper extends some recent results on asymptotically optimal sequences of experimental designs for regression problems in stochastic processes. In the regression model $Y(t) = \beta f(t) + X(t), 0 \leqq t \leqq 1$, the constant $\beta$ is to be estimated based on observations of $Y(t)$ and its first $m - 1$ derivatives at each of a set $T_n$ of $n$ distinct points. The function $f$ is assumed known as is the covariance kernel of $X(t)$, a zero-mean $m$th order autoregressive process. Under certain conditions, we derive a sequence $\{T_n\}$ of experimental designs which are asymptotically optimal for estimating $\beta$.

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Jaroslav Hajek. George Kimeldorf. "Regression Designs in Autoregressive Stochastic Processes." Ann. Statist. 2 (3) 520 - 527, May, 1974. https://doi.org/10.1214/aos/1176342711

Information

Published: May, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0282.62067
MathSciNet: MR356412
Digital Object Identifier: 10.1214/aos/1176342711

Subjects:
Primary: 62K05
Secondary: 62M10

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 3 • May, 1974
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