A New Approach to Statistical Efficiency of Weighted Least Squares Fitting Algorithms for Reparameterization of Nonlinear Regression Models

Shimin Zheng; A. K. Gupta

doi:10.1016/j.jspi.2011.11.011

A New Approach to Statistical Efficiency of Weighted Least Squares Fitting Algorithms for Reparameterization of Nonlinear Regression Models

Shimin Zheng, A. K. Gupta

Department of Biostatistics and Epidemiology

Bowling Green State University

Research output: Contribution to journal › Article › peer-review

Abstract

We study nonlinear least-squares problem that can be transformed to linear problem by change of variables. We derive a general formula for the statistically optimal weights and prove that the resulting linear regression gives an optimal estimate (which satisfies an analogue of the Rao–Cramer lower bound) in the limit of small noise.

Original language	American English
Journal	Journal of Statistical Planning and Inference
Volume	142
DOIs	https://doi.org/10.1016/j.jspi.2011.11.011
State	Published - Apr 1 2012

Keywords

Rao–Cramer bound
efficiency
nonlinear regression
reparameterization
small sigma asymptotic
weighted least squares

Disciplines

Biostatistics
Mathematics

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10.1016/j.jspi.2011.11.011License: Unspecified

https://doi.org/10.1016/j.jspi.2011.11.011

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title = "A New Approach to Statistical Efficiency of Weighted Least Squares Fitting Algorithms for Reparameterization of Nonlinear Regression Models",

abstract = " We study nonlinear least-squares problem that can be transformed to linear problem by change of variables. We derive a general formula for the statistically optimal weights and prove that the resulting linear regression gives an optimal estimate (which satisfies an analogue of the Rao–Cramer lower bound) in the limit of small noise.",

keywords = "Rao–Cramer bound, efficiency, nonlinear regression, reparameterization, small sigma asymptotic, weighted least squares",

author = "Shimin Zheng and Gupta, \{A. K.\}",

year = "2012",

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AU - Zheng, Shimin

AU - Gupta, A. K.

PY - 2012/4/1

Y1 - 2012/4/1

N2 - We study nonlinear least-squares problem that can be transformed to linear problem by change of variables. We derive a general formula for the statistically optimal weights and prove that the resulting linear regression gives an optimal estimate (which satisfies an analogue of the Rao–Cramer lower bound) in the limit of small noise.

AB - We study nonlinear least-squares problem that can be transformed to linear problem by change of variables. We derive a general formula for the statistically optimal weights and prove that the resulting linear regression gives an optimal estimate (which satisfies an analogue of the Rao–Cramer lower bound) in the limit of small noise.

KW - Rao–Cramer bound

KW - efficiency

KW - nonlinear regression

KW - reparameterization

KW - small sigma asymptotic

KW - weighted least squares

UR - https://dc.etsu.edu/etsu-works/36

UR - https://doi.org/10.1016/j.jspi.2011.11.011

U2 - 10.1016/j.jspi.2011.11.011

DO - 10.1016/j.jspi.2011.11.011

M3 - Article

VL - 142

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

ER -

A New Approach to Statistical Efficiency of Weighted Least Squares Fitting Algorithms for Reparameterization of Nonlinear Regression Models

Abstract

Keywords

Disciplines

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