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Quick and easy one‐step parameter estimation in differential equations
Author(s) -
Hall Peter,
Ma Yanyuan
Publication year - 2014
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12040
Subject(s) - estimation theory , estimator , cascade , computer science , spline (mechanical) , polynomial , mathematical optimization , least squares function approximation , differential equation , mathematics , algorithm , statistics , engineering , mathematical analysis , structural engineering , chemical engineering
Summary Differential equations are customarily used to describe dynamic systems. Existing methods for estimating unknown parameters in those systems include parameter cascade, which is a spline‐based technique, and pseudo‐least‐squares, which is a local‐polynomial‐based two‐step method. Parameter cascade is often referred to as a ‘one‐step method’, although it in fact involves at least two stages: one to choose the tuning parameter and another to select model parameters. We propose a class of fast, easy‐to‐use, genuinely one‐step procedures for estimating unknown parameters in dynamic system models. This approach does not need extraneous estimation of the tuning parameter; it selects that quantity, as well as all the model parameters, in a single explicit step, and it produces root‐ n ‐consistent estimators of all the model parameters. Although it is of course not as accurate as more complex methods, its speed and ease of use make it particularly attractive for exploratory data analysis.