Open Access
January, 1977 Optimal Allocation of Observations in Inverse Linear Regression
S. K. Perng, Y. L. Tong
Ann. Statist. 5(1): 191-196 (January, 1977). DOI: 10.1214/aos/1176343753


Consider the problem of estimating $x$ under the inverse linear regression model $Y_i = \alpha + \beta x_i + \varepsilon_i,\quad Z_j = \alpha + \beta x + \varepsilon_j'$ for $i = 1,\cdots, n,\cdots, j = 1,\cdots, m,\cdots,$ where $\{\varepsilon_i\}, \{\varepsilon_j'\}$ are two sequences of i.i.d. rv's with 0 means and finite variances, $\{x_i\}$ is a sequence of known constants and $\alpha, \beta, x$ are unknown parameters. For fixed $T = m + n$, this paper considers a sequential procedure for the optimal allocation of $m$ and $n$. It is shown that, as $T \rightarrow \infty$, the procedure is asymptotically optimal.


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S. K. Perng. Y. L. Tong. "Optimal Allocation of Observations in Inverse Linear Regression." Ann. Statist. 5 (1) 191 - 196, January, 1977.


Published: January, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0379.62060
MathSciNet: MR494726
Digital Object Identifier: 10.1214/aos/1176343753

Primary: 62J05
Secondary: 62L12

Keywords: allocation of observations , Inverse linear regression , sequential methods

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 1 • January, 1977
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