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Second order asymptotics in nonlinear regression
Authors:Wolfgang H Schmidt  S Zwanzig
Institution:Humboldt-Universität, Berlin, DDR-1086 German Democratic Republic;Institut für Mathematik, ADW der DDR, Berlin, DDR-1086 German Democratic Republic
Abstract:It is a well known part of statistical knowledge that first order asymptotically efficient procedures can be misleading for moderate sample sizes. Usually this is demonstrated for some popular special cases including numerical comparisons. Typically the situation is worse if nuisance parameters are present. In this paper we give second order asymptotically efficient tests, confidence regions, and estimators for the nonlinear regression model which are based on the least-squares estimator and the residual sum of squares.
Keywords:Nonlinear regression  Edgeworth expansion  second order asymptotics  hypothesis testing  median unbiased estimators  confidence regions
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