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Conditional logspline density estimation
Author(s) -
Mâacsse Benoît R.,
Truong Young K.
Publication year - 1999
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 - 10.2307/3316133
Subject(s) - mathematics , spline (mechanical) , conditional probability distribution , logarithm , differentiable function , conditional expectation , polynomial , quantile regression , density estimation , quantile , probability density function , quantile function , conditional variance , statistics , econometrics , cumulative distribution function , pure mathematics , mathematical analysis , estimator , volatility (finance) , structural engineering , engineering , autoregressive conditional heteroskedasticity
In conditional logspline modelling , the logarithm of the conditional density function, log f ( y |x), is modelled by using polynomial splines and their tensor products. The parameters of the model (coefficients of the spline functions) are estimated by maximizing the conditional log‐likelihood function. The resulting estimate is a density function (positive and integrating to one) and is twice continuously differentiable. The estimate is used further to obtain estimates of regression and quantile functions in a natural way. An automatic procedure for selecting the number of knots and knot locations based on minimizing a variant of the AIC is developed. An example with real data is given. Finally, extensions and further applications of conditional logspline models are discussed.