@article{Gaigall2020, author = {Gaigall, Daniel}, title = {Rothman-Woodroofe symmetry test statistic revisited}, series = {Computational Statistics \& Data Analysis}, volume = {2020}, journal = {Computational Statistics \& Data Analysis}, number = {142}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0167-9473}, doi = {10.1016/j.csda.2019.106837}, pages = {Artikel 106837}, year = {2020}, abstract = {The Rothman-Woodroofe symmetry test statistic is revisited on the basis of independent but not necessarily identically distributed random variables. The distribution-freeness if the underlying distributions are all symmetric and continuous is obtained. The results are applied for testing symmetry in a meta-analysis random effects model. The consistency of the procedure is discussed in this situation as well. A comparison with an alternative proposal from the literature is conducted via simulations. Real data are analyzed to demonstrate how the new approach works in practice.}, language = {en} } @article{BaringhausGaigall2019, author = {Baringhaus, Ludwig and Gaigall, Daniel}, title = {On an asymptotic relative efficiency concept based on expected volumes of confidence regions}, series = {Statistics - A Journal of Theoretical and Applied Statistic}, volume = {53}, journal = {Statistics - A Journal of Theoretical and Applied Statistic}, number = {6}, publisher = {Taylor \& Francis}, address = {London}, issn = {1029-4910}, doi = {10.1080/02331888.2019.1683560}, pages = {1396 -- 1436}, year = {2019}, abstract = {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.}, language = {en} } @article{Gaigall2019, author = {Gaigall, Daniel}, title = {On a new approach to the multi-sample goodness-of-fit problem}, series = {Communications in Statistics - Simulation and Computation}, volume = {53}, journal = {Communications in Statistics - Simulation and Computation}, number = {10}, publisher = {Taylor \& Francis}, address = {London}, issn = {1532-4141}, doi = {10.1080/03610918.2019.1618472}, pages = {2971 -- 2989}, year = {2019}, abstract = {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.}, language = {en} } @article{DitzhausGaigall2018, author = {Ditzhaus, Marc and Gaigall, Daniel}, title = {A consistent goodness-of-fit test for huge dimensional and functional data}, series = {Journal of Nonparametric Statistics}, volume = {30}, journal = {Journal of Nonparametric Statistics}, number = {4}, publisher = {Taylor \& Francis}, address = {Abingdon}, issn = {1029-0311}, doi = {10.1080/10485252.2018.1486402}, pages = {834 -- 859}, year = {2018}, abstract = {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 Cram{\´e}r-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.}, language = {en} } @article{BaringhausGaigallThiele2018, author = {Baringhaus, Ludwig and Gaigall, Daniel and Thiele, Jan Philipp}, title = {Statistical inference for L²-distances to uniformity}, series = {Computational Statistics}, volume = {2018}, journal = {Computational Statistics}, number = {33}, publisher = {Springer}, address = {Berlin}, issn = {1613-9658}, doi = {10.1007/s00180-018-0820-0}, pages = {1863 -- 1896}, year = {2018}, abstract = {The paper deals with the asymptotic behaviour of estimators, statistical tests and confidence intervals for L²-distances to uniformity based on the empirical distribution function, the integrated empirical distribution function and the integrated empirical survival function. Approximations of power functions, confidence intervals for the L²-distances and statistical neighbourhood-of-uniformity validation tests are obtained as main applications. The finite sample behaviour of the procedures is illustrated by a simulation study.}, language = {en} } @article{BaringhausGaigall2017, author = {Baringhaus, Ludwig and Gaigall, Daniel}, title = {On Hotelling's T² test in a special paired sample case}, series = {Communications in Statistics - Theory and Methods}, volume = {48}, journal = {Communications in Statistics - Theory and Methods}, number = {2}, publisher = {Taylor \& Francis}, address = {London}, issn = {1532-415X}, doi = {10.1080/03610926.2017.1408828}, pages = {257 -- 267}, year = {2017}, abstract = {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.}, language = {en} } @article{BaringhausGaigall2017, author = {Baringhaus, Ludwig and Gaigall, Daniel}, title = {Hotelling's T² tests in paired and independent survey samples: An efficiency comparison}, series = {Journal of Multivariate Analysis}, volume = {2017}, journal = {Journal of Multivariate Analysis}, number = {154}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0047-259X}, doi = {10.1016/j.jmva.2016.11.004}, pages = {177 -- 198}, year = {2017}, abstract = {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.}, language = {en} } @article{Gaigall2023, author = {Gaigall, Daniel}, title = {Allocating and forecasting changes in risk}, series = {Journal of risk}, volume = {25}, journal = {Journal of risk}, number = {3}, editor = {AitSahlia, Farid}, publisher = {Infopro Digital Risk}, address = {London}, issn = {1755-2842}, doi = {10.21314/JOR.2022.048}, pages = {1 -- 24}, year = {2023}, abstract = {We consider time-dependent portfolios and discuss the allocation of changes in the risk of a portfolio to changes in the portfolio's components. For this purpose we adopt established allocation principles. We also use our approach to obtain forecasts for changes in the risk of the portfolio's components. To put the approach into practice we present an implementation based on the output of a simulation. Allocation is illustrated with an example portfolio in the context of Solvency II. The quality of the forecasts is investigated with an empirical study.}, language = {en} } @article{Gaigall2023, author = {Gaigall, Daniel}, title = {On the applicability of several tests to models with not identically distributed random effects}, series = {Statistics : A Journal of Theoretical and Applied Statistics}, volume = {57}, journal = {Statistics : A Journal of Theoretical and Applied Statistics}, publisher = {Taylor \& Francis}, address = {London}, isbn = {0323-3944}, issn = {1029-4910}, doi = {10.1080/02331888.2023.2193748}, pages = {14 Seiten}, year = {2023}, abstract = {We consider Kolmogorov-Smirnov and Cram{\´e}r-von-Mises type tests for testing central symmetry, exchangeability, and independence. In the standard case, the tests are intended for the application to independent and identically distributed data with unknown distribution. The tests are available for multivariate data and bootstrap procedures are suitable to obtain critical values. We discuss the applicability of the tests to random effects models, where the random effects are independent but not necessarily identically distributed and with possibly unknown distributions. Theoretical results show the adequacy of the tests in this situation. The quality of the tests in models with random effects is investigated by simulations. Empirical results obtained confirm the theoretical findings. A real data example illustrates the application.}, language = {en} } @article{GaigallGerstenberg2023, author = {Gaigall, Daniel and Gerstenberg, Julian}, title = {Cram{\´e}r-von-Mises tests for the distribution of the excess over a confidence level}, series = {Journal of Nonparametric Statistics}, journal = {Journal of Nonparametric Statistics}, publisher = {Taylor \& Francis}, issn = {1048-5252 (Print)}, doi = {10.1080/10485252.2023.2173958}, year = {2023}, abstract = {The Cram{\´e}r-von-Mises distance is applied to the distribution of the excess over a confidence level. Asymptotics of related statistics are investigated, and it is seen that the obtained limit distributions differ from the classical ones. For that reason, quantiles of the new limit distributions are given and new bootstrap techniques for approximation purposes are introduced and justified. The results motivate new one-sample goodness-of-fit tests for the distribution of the excess over a confidence level and a new confidence interval for the related fitting error. Simulation studies investigate size and power of the tests as well as coverage probabilities of the confidence interval in the finite sample case. A practice-oriented application of the Cram{\´e}r-von-Mises tests is the determination of an appropriate confidence level for the fitting approach. The adoption of the idea to the well-known problem of threshold detection in the context of peaks over threshold modelling is sketched and illustrated by data examples.}, language = {en} }