TY  - JOUR
A1  - Baringhaus, Ludwig
A1  - Gaigall, Daniel
T1  - A goodness-of-fit test for the compound Poisson exponential model
JF  - Journal of Multivariate Analysis
N2  - On the basis of bivariate data, assumed to be observations of independent copies of a random vector (S,N), we consider testing the hypothesis that the distribution of (S,N) belongs to the parametric class of distributions that arise with the compound Poisson exponential model. Typically, this model is used in stochastic hydrology, with N as the number of raindays, and S as total rainfall amount during a certain time period, or in actuarial science, with N as the number of losses, and S as total loss expenditure during a certain time period. The compound Poisson exponential model is characterized in the way that a specific transform associated with the distribution of (S,N) satisfies a certain differential equation. Mimicking the function part of this equation by substituting the empirical counterparts of the transform we obtain an expression the weighted integral of the square of which is used as test statistic. We deal with two variants of the latter, one of which being invariant under scale transformations of the S-part by fixed positive constants. Critical values are obtained by using a parametric bootstrap procedure. The asymptotic behavior of the tests is discussed. A simulation study demonstrates the performance of the tests in the finite sample case. The procedure is applied to rainfall data and to an actuarial dataset. A multivariate extension is also discussed.
KW  - Bootstrapping
KW  - Collective risk model
Y1  - 2022
U6  - http://dx.doi.org/10.1016/j.jmva.2022.105154
SN  - 0047-259X
SN  - 1095-7243
VL  - 195
IS  - Article 105154
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Baringhaus, Ludwig
A1  - Gaigall, Daniel
T1  - Hotelling’s T² tests in paired and independent survey samples: An efficiency comparison
JF  - Journal of Multivariate Analysis
N2  - Hotelling’s T² tests in paired and independent survey samples are compared using the traditional asymptotic efficiency concepts of Hodges–Lehmann, Bahadur and Pitman, as well as through criteria based on the volumes of corresponding confidence regions. Conditions characterizing the superiority of a procedure are given in terms of population canonical correlation type coefficients. Statistical tests for checking these conditions are developed. Test statistics based on the eigenvalues of a symmetrized sample cross-covariance matrix are suggested, as well as test statistics based on sample canonical correlation type coefficients.
Y1  - 2017
U6  - http://dx.doi.org/10.1016/j.jmva.2016.11.004
SN  - 0047-259X
VL  - 2017
IS  - 154
SP  - 177
EP  - 198
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Baringhaus, Ludwig
A1  - Gaigall, Daniel
T1  - On an independence test approach to the goodness-of-fit problem
JF  - Journal of Multivariate Analysis
N2  - Let X₁,…,Xₙ be independent and identically distributed random variables with distribution F. Assuming that there are measurable functions f:R²→R and g:R²→R characterizing a family F of distributions on the Borel sets of R in the way that the random variables f(X₁,X₂),g(X₁,X₂) are independent, if and only if F∈F, we propose to treat the testing problem H:F∈F,K:F∉F by applying a consistent nonparametric independence test to the bivariate sample variables (f(Xᵢ,Xⱼ),g(Xᵢ,Xⱼ)),1⩽i,j⩽n,i≠j. A parametric bootstrap procedure needed to get critical values is shown to work. The consistency of the test is discussed. The power performance of the procedure is compared with that of the classical tests of Kolmogorov–Smirnov and Cramér–von Mises in the special cases where F is the family of gamma distributions or the family of inverse Gaussian distributions.
KW  - Goodness-of-fit test
KW  - Independence test
KW  - Parametric bootstrap
KW  - Vapnik–Čhervonenkis class
KW  - Gamma distribution
Y1  - 2015
U6  - http://dx.doi.org/10.1016/j.jmva.2015.05.013
SN  - 0047-259X
VL  - 2015
IS  - 140
SP  - 193
EP  - 208
PB  - Elsevier
CY  - Amsterdam
ER  -