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About tests of the “simplifying” assumption for conditional copulas

100%
Derumigny A., Fermanian J.-D.
Dependence Modeling
|
2017
|
tom 5
|
nr 1
154-197
EN
We discuss the so-called “simplifying assumption” of conditional copulas in a general framework. We introduce several tests of the latter assumption for non- and semiparametric copula models. Some related test procedures based on conditioning subsets instead of point-wise events are proposed. The limiting distributions of such test statistics under the null are approximated by several bootstrap schemes, most of them being new. We prove the validity of a particular semiparametric bootstrap scheme. Some simulations illustrate the relevance of our results.
2
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Bias-variance decomposition in Genetic Programming

84%
Kowaliw T., Doursat R.
Open Mathematics
|
2016
|
tom 14
|
nr 1
62-80
EN
We study properties of Linear Genetic Programming (LGP) through several regression and classification benchmarks. In each problem, we decompose the results into bias and variance components, and explore the effect of varying certain key parameters on the overall error and its decomposed contributions. These parameters are the maximum program size, the initial population, and the function set used. We confirm and quantify several insights into the practical usage of GP, most notably that (a) the variance between runs is primarily due to initialization rather than the selection of training samples, (b) parameters can be reasonably optimized to obtain gains in efficacy, and (c) functions detrimental to evolvability are easily eliminated, while functions well-suited to the problem can greatly improve performance-therefore, larger and more diverse function sets are always preferable.
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