49,277 research outputs found
Boosting Functional Response Models for Location, Scale and Shape with an Application to Bacterial Competition
We extend Generalized Additive Models for Location, Scale, and Shape (GAMLSS)
to regression with functional response. This allows us to simultaneously model
point-wise mean curves, variances and other distributional parameters of the
response in dependence of various scalar and functional covariate effects. In
addition, the scope of distributions is extended beyond exponential families.
The model is fitted via gradient boosting, which offers inherent model
selection and is shown to be suitable for both complex model structures and
highly auto-correlated response curves. This enables us to analyze bacterial
growth in \textit{Escherichia coli} in a complex interaction scenario,
fruitfully extending usual growth models.Comment: bootstrap confidence interval type uncertainty bounds added; minor
changes in formulation
Quantifying dependencies for sensitivity analysis with multivariate input sample data
We present a novel method for quantifying dependencies in multivariate
datasets, based on estimating the R\'{e}nyi entropy by minimum spanning trees
(MSTs). The length of the MSTs can be used to order pairs of variables from
strongly to weakly dependent, making it a useful tool for sensitivity analysis
with dependent input variables. It is well-suited for cases where the input
distribution is unknown and only a sample of the inputs is available. We
introduce an estimator to quantify dependency based on the MST length, and
investigate its properties with several numerical examples. To reduce the
computational cost of constructing the exact MST for large datasets, we explore
methods to compute approximations to the exact MST, and find the multilevel
approach introduced recently by Zhong et al. (2015) to be the most accurate. We
apply our proposed method to an artificial testcase based on the Ishigami
function, as well as to a real-world testcase involving sediment transport in
the North Sea. The results are consistent with prior knowledge and heuristic
understanding, as well as with variance-based analysis using Sobol indices in
the case where these indices can be computed
Optimal estimation of the mean function based on discretely sampled functional data: Phase transition
The problem of estimating the mean of random functions based on discretely
sampled data arises naturally in functional data analysis. In this paper, we
study optimal estimation of the mean function under both common and independent
designs. Minimax rates of convergence are established and easily implementable
rate-optimal estimators are introduced. The analysis reveals interesting and
different phase transition phenomena in the two cases. Under the common design,
the sampling frequency solely determines the optimal rate of convergence when
it is relatively small and the sampling frequency has no effect on the optimal
rate when it is large. On the other hand, under the independent design, the
optimal rate of convergence is determined jointly by the sampling frequency and
the number of curves when the sampling frequency is relatively small. When it
is large, the sampling frequency has no effect on the optimal rate. Another
interesting contrast between the two settings is that smoothing is necessary
under the independent design, while, somewhat surprisingly, it is not essential
under the common design.Comment: Published in at http://dx.doi.org/10.1214/11-AOS898 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
- …