## The Annals of Statistics

### Regression Designs in Autoregressive Stochastic Processes

#### 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 $\beta$.

#### Article information

Source
Ann. Statist., Volume 2, Number 3 (1974), 520-527.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176342711

Digital Object Identifier
doi:10.1214/aos/1176342711

Mathematical Reviews number (MathSciNet)
MR356412

Zentralblatt MATH identifier
0282.62067

JSTOR