Access
You are not currently logged in.
Access JSTOR through your library or other institution:
Estimating a Response Surface with an Uncertain Number of Parameters, Assuming Normal Errors
Corwin L. Atwood
Journal of the American Statistical Association
Vol. 70, No. 351 (Sep., 1975), pp. 613617
Published by: Taylor & Francis, Ltd. on behalf of the American Statistical Association
DOI: 10.2307/2285942
Stable URL: http://www.jstor.org/stable/2285942
Page Count: 5
 Item Type
 Article
 Thumbnails
 References
Abstract
Let Y(x) be independent normal random variables with mean f'(x)θ and variance σ^{2}, and partition the vectors f' and θ' into (f_{1}', f_{2}') and (θ_{1}',θ_{2}'). Estimate f'θ by $\lbrack 1  r(\mathbf{\hat\theta}_2' D^{1}\mathbf{\hat\theta}_2)\rbrack\mathbf{f}_1'\mathbf{\hat\theta}_1 + r(\mathbf{\hat\theta}_2' D^{1}\mathbf{\hat\theta}_2)\mathbf{f}'\mathbf{\hat\theta}$ , where $\mathbf{\hat \theta}$ and $\mathbf{\hat\theta}_2$ are the BLUEs of θ and $\mathbf{\theta}_2, \mathbf{\hat\theta}_1$ is the BLUE of θ_{1} assuming θ_{2} = 0, σ^{2D} is the covariance matrix of $\mathbf{\hat\theta}_2$ , and r is any bounded nonnegative nondecreasing function. Among such estimators with given fixed MSE when θ_{2} = 0, MSE is minimized for θ_{2} near 0 by making r constant. Numerical comparisons are given for the quadratic regression example.
Page Thumbnails

613

614

615

616

617
Journal of the American Statistical Association © 1975 American Statistical Association