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Estimation and prediction for low degree polynomial models under measurement errors with an application to forest harvesters
Author(s) -
Nummi Tapio,
Möttönen Jyrki
Publication year - 2004
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.1111/j.1467-9876.2004.05138.x
Subject(s) - degree (music) , tree (set theory) , sequence (biology) , statistics , mathematics , polynomial , least squares function approximation , algorithm , observational error , computer science , mathematical analysis , physics , estimator , biology , acoustics , genetics
Summary. In a modern computer‐based forest harvester, tree stems are run in sequence through the measuring equipment root end first, and simultaneously the length and diameter are stored in a computer. These measurements may be utilized for example in the determination of the optimal cutting points of the stems. However, a problem that is often passed over is that these variables are usually measured with error. We consider estimation and prediction of stem curves when the length and diameter measurements are subject to errors. It is shown that only in the simplest case of a first‐order model can the estimation be carried out unbiasedly by using standard least squares procedures. However, both the first‐ and the second‐degree models are unbiased in prediction. Also a study on real stem is used to illustrate the models that are discussed.