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Differential equation models for statistical functions
Author(s) -
Ramsay James O.
Publication year - 2000
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315975
Subject(s) - smoothing , mathematics , differential equation , stochastic differential equation , scope (computer science) , function (biology) , residual , monotone polygon , computer science , mathematical optimization , algorithm , mathematical analysis , statistics , geometry , evolutionary biology , biology , programming language
Differential equations have been used in statistics to define functions such as probability densities. But the idea of using differential equation formulations of stochastic models has a much wider scope. The author gives several examples, including simultaneous estimation of a regression model and residual density, monotone smoothing, specification of a link function, differential equation models of data, and smoothing over complicated multidimensional domains. This paper aims to stimulate interest in this approach to functional estimation problems, rather than provide carefully worked out methods.