TY - JOUR A1 - Gaigall, Daniel T1 - On a new approach to the multi-sample goodness-of-fit problem JF - Communications in Statistics - Simulation and Computation N2 - Suppose we have k samples X₁,₁,…,X₁,ₙ₁,…,Xₖ,₁,…,Xₖ,ₙₖ with different sample sizes ₙ₁,…,ₙₖ and unknown underlying distribution functions F₁,…,Fₖ as observations plus k families of distribution functions {G₁(⋅,ϑ);ϑ∈Θ},…,{Gₖ(⋅,ϑ);ϑ∈Θ}, each indexed by elements ϑ from the same parameter set Θ, we consider the new goodness-of-fit problem whether or not (F₁,…,Fₖ) belongs to the parametric family {(G₁(⋅,ϑ),…,Gₖ(⋅,ϑ));ϑ∈Θ}. New test statistics are presented and a parametric bootstrap procedure for the approximation of the unknown null distributions is discussed. Under regularity assumptions, it is proved that the approximation works asymptotically, and the limiting distributions of the test statistics in the null hypothesis case are determined. Simulation studies investigate the quality of the new approach for small and moderate sample sizes. Applications to real-data sets illustrate how the idea can be used for verifying model assumptions. KW - Goodness-of-fit test KW - Multi-sample problem KW - Parametric bootstrap Y1 - 2019 U6 - https://doi.org/10.1080/03610918.2019.1618472 SN - 1532-4141 VL - 53 IS - 10 SP - 2971 EP - 2989 PB - Taylor & Francis CY - London ER - TY - JOUR A1 - Ditzhaus, Marc A1 - Gaigall, Daniel T1 - A consistent goodness-of-fit test for huge dimensional and functional data JF - Journal of Nonparametric Statistics N2 - A nonparametric goodness-of-fit test for random variables with values in a separable Hilbert space is investigated. To verify the null hypothesis that the data come from a specific distribution, an integral type test based on a Cramér-von-Mises statistic is suggested. The convergence in distribution of the test statistic under the null hypothesis is proved and the test's consistency is concluded. Moreover, properties under local alternatives are discussed. Applications are given for data of huge but finite dimension and for functional data in infinite dimensional spaces. A general approach enables the treatment of incomplete data. In simulation studies the test competes with alternative proposals. KW - Cramér-von-Mises statistic KW - separable Hilbert space KW - huge dimensional data KW - functional data Y1 - 2018 U6 - https://doi.org/10.1080/10485252.2018.1486402 SN - 1029-0311 VL - 30 IS - 4 SP - 834 EP - 859 PB - Taylor & Francis CY - Abingdon ER - TY - JOUR A1 - Kleefeld, Andreas A1 - Pieronek, J. T1 - Elastic transmission eigenvalues and their computation via the method of fundamental solutions JF - Applicable Analysis N2 - A stabilized version of the fundamental solution method to catch ill-conditioning effects is investigated with focus on the computation of complex-valued elastic interior transmission eigenvalues in two dimensions for homogeneous and isotropic media. Its algorithm can be implemented very shortly and adopts to many similar partial differential equation-based eigenproblems as long as the underlying fundamental solution function can be easily generated. We develop a corroborative approximation analysis which also implicates new basic results for transmission eigenfunctions and present some numerical examples which together prove successful feasibility of our eigenvalue recovery approach. KW - elastic scattering KW - method of fundamental solutions KW - Interior transmission eigenvalues Y1 - 2020 U6 - https://doi.org/10.1080/00036811.2020.1721473 SN - 1563-504X VL - 100 IS - 16 SP - 3445 EP - 3462 PB - Taylore & Francis CY - London ER - TY - JOUR A1 - Baringhaus, Ludwig A1 - Gaigall, Daniel T1 - On Hotelling’s T² test in a special paired sample case JF - Communications in Statistics - Theory and Methods N2 - In a special paired sample case, Hotelling’s T² test based on the differences of the paired random vectors is the likelihood ratio test for testing the hypothesis that the paired random vectors have the same mean; with respect to a special group of affine linear transformations it is the uniformly most powerful invariant test for the general alternative of a difference in mean. We present an elementary straightforward proof of this result. The likelihood ratio test for testing the hypothesis that the covariance structure is of the assumed special form is derived and discussed. Applications to real data are given. KW - complete block symmetry KW - Hotelling’s T² test KW - likelihood ratio test KW - uniformly most powerful invariant test Y1 - 2017 U6 - https://doi.org/10.1080/03610926.2017.1408828 SN - 1532-415X VL - 48 IS - 2 SP - 257 EP - 267 PB - Taylor & Francis CY - London ER - TY - JOUR A1 - Gaigall, Daniel T1 - Hoeffding-Blum-Kiefer-Rosenblatt independence test statistic on partly not identically distributed data JF - Communications in Statistics - Theory and Methods N2 - The established Hoeffding-Blum-Kiefer-Rosenblatt independence test statistic is investigated for partly not identically distributed data. Surprisingly, it turns out that the statistic has the well-known distribution-free limiting null distribution of the classical criterion under standard regularity conditions. An application is testing goodness-of-fit for the regression function in a non parametric random effects meta-regression model, where the consistency is obtained as well. Simulations investigate size and power of the approach for small and moderate sample sizes. A real data example based on clinical trials illustrates how the test can be used in applications. KW - Brownian Pillow KW - Hoeffding-Blum-Kiefer-Rosenblatt independence test KW - not identically distributed KW - random effects meta-regression model Y1 - 2020 U6 - https://doi.org/10.1080/03610926.2020.1805767 SN - 1532-415X VL - 51 IS - 12 SP - 4006 EP - 4028 PB - Taylor & Francis CY - London ER - TY - JOUR A1 - Baringhaus, Ludwig A1 - Gaigall, Daniel T1 - On an asymptotic relative efficiency concept based on expected volumes of confidence regions JF - Statistics - A Journal of Theoretical and Applied Statistic N2 - The paper deals with an asymptotic relative efficiency concept for confidence regions of multidimensional parameters that is based on the expected volumes of the confidence regions. Under standard conditions the asymptotic relative efficiencies of confidence regions are seen to be certain powers of the ratio of the limits of the expected volumes. These limits are explicitly derived for confidence regions associated with certain plugin estimators, likelihood ratio tests and Wald tests. Under regularity conditions, the asymptotic relative efficiency of each of these procedures with respect to each one of its competitors is equal to 1. The results are applied to multivariate normal distributions and multinomial distributions in a fairly general setting. KW - Volume of confidence regions KW - asymptotic relative efficiency KW - likelihood ratio test KW - multivariate normal distribution KW - multinomial distribution Y1 - 2019 U6 - https://doi.org/10.1080/02331888.2019.1683560 SN - 1029-4910 VL - 53 IS - 6 SP - 1396 EP - 1436 PB - Taylor & Francis CY - London ER -