@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{DitzhausGaigall2022,
  author    = {Ditzhaus, Marc and Gaigall, Daniel},
  title     = {Testing marginal homogeneity in Hilbert spaces with applications to stock market returns},
  series = {Test},
  volume    = {2022},
  journal   = {Test},
  number    = {31},
  publisher = {Springer},
  issn      = {1863-8260},
  doi       = {10.1007/s11749-022-00802-5},
  pages     = {749 -- 770},
  year      = {2022},
  abstract  = {This paper considers a paired data framework and discusses the question of marginal homogeneity of bivariate high-dimensional or functional data. The related testing problem can be endowed into a more general setting for paired random variables taking values in a general Hilbert space. To address this problem, a Cram{\´e}r-von-Mises type test statistic is applied and a bootstrap procedure is suggested to obtain critical values and finally a consistent test. The desired properties of a bootstrap test can be derived that are asymptotic exactness under the null hypothesis and consistency under alternatives. Simulations show the quality of the test in the finite sample case. A possible application is the comparison of two possibly dependent stock market returns based on functional data. The approach is demonstrated based on historical data for different stock market indices.},
  language  = {en}
}
@article{DiktaSubramanian2009,
  author    = {Dikta, Gerhard and Subramanian, Sundarraman},
  title     = {Inverse censoring weighted median regression / Sundarraman Subramanian and Gerhard Dikta},
  series = {Statistical Methodology. 6 (2009), H. 6},
  journal   = {Statistical Methodology. 6 (2009), H. 6},
  publisher = {Elsevier},
  address   = {Amsterdam},
  isbn      = {1572-3127},
  pages     = {594 -- 603},
  year      = {2009},
  language  = {en}
}
@article{DiktaReisselHarlass2016,
  author    = {Dikta, Gerhard and Reißel, Martin and Harlaß, Carsten},
  title     = {Semi-parametric survival function estimators deduced from an identifying Volterra type integral equation},
  series = {Journal of multivariate analysis},
  journal   = {Journal of multivariate analysis},
  number    = {147},
  publisher = {Elsevier},
  address   = {Amsterdam},
  doi       = {10.1016/j.jmva.2016.02.008},
  pages     = {273 -- 284},
  year      = {2016},
  abstract  = {Based on an identifying Volterra type integral equation for randomly right censored observations from a lifetime distribution function F, we solve the corresponding estimating equation by an explicit and implicit Euler scheme. While the first approach results in some known estimators, the second one produces new semi-parametric and pre-smoothed Kaplan-Meier estimators which are real distribution functions rather than sub-distribution functions as the former ones are. This property of the new estimators is particular useful if one wants to estimate the expected lifetime restricted to the support of the observation time. Specifically, we focus on estimation under the semi-parametric random censorship model (SRCM), that is, a random censorship model where the conditional expectation of the censoring indicator given the observation belongs to a parametric family. We show that some estimated linear functionals which are based on the new semi-parametric estimator are strong consistent, asymptotically normal, and efficient under SRCM. In a small simulation study, the performance of the new estimator is illustrated under moderate sample sizes. Finally, we apply the new estimator to a well-known real dataset.},
  language  = {en}
}
@article{DiktaKuehlheimMendoncaetal.2015,
  author    = {Dikta, Gerhard and K{\"u}hlheim, Ren{\´e} and Mendonca, Jorge and Una-Alcarez, Jacobo de},
  title     = {Asymptotic representation of presmoothed Kaplan-Meier integrals with covariates in a semiparametric censorship model},
  series = {Journal of Statistical Planning and Inference},
  volume    = {Vol. 171},
  journal   = {Journal of Statistical Planning and Inference},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0378-3758},
  doi       = {10.1016/j.jspi.2015.12.001},
  pages     = {10 -- 37},
  year      = {2015},
  language  = {en}
}
@article{DiktaKvesicSchmidt2006,
  author    = {Dikta, Gerhard and Kvesic, Marsel and Schmidt, Christian},
  title     = {Bootstrap Approximations in Model Checks for Binary Data},
  series = {Journal of the American Statistical Association. 101 (2006), H. 474},
  journal   = {Journal of the American Statistical Association. 101 (2006), H. 474},
  isbn      = {0162-1459},
  pages     = {521 -- 530},
  year      = {2006},
  language  = {en}
}
@article{DiktaKurtzStute1989,
  author    = {Dikta, Gerhard and Kurtz, B. and Stute, W.},
  title     = {Sequential Fixed-Width Confidence Bands for Distribution Functions Under Random Censoring},
  series = {Metrika. 36 (1989)},
  journal   = {Metrika. 36 (1989)},
  isbn      = {0026-1335},
  pages     = {167 -- 176},
  year      = {1989},
  language  = {en}
}
@article{DiktaHausmannSchmidt2002,
  author    = {Dikta, Gerhard and Hausmann, Rolf and Schmidt, Christian},
  title     = {Some Simulation Results under Random Censorship Models},
  pages     = {1 -- 12},
  year      = {2002},
  language  = {en}
}
@article{DiktaGhoraiSchmidt2005,
  author    = {Dikta, Gerhard and Ghorai, Jugal and Schmidt, Christian},
  title     = {The Central Limit Theorem under Semiparametric Random Censorship Models},
  series = {Journal of Statistical Planning and Inference. 127 (2005), H. 1},
  journal   = {Journal of Statistical Planning and Inference. 127 (2005), H. 1},
  isbn      = {0378-3758},
  pages     = {23 -- 51},
  year      = {2005},
  language  = {en}
}
@article{DiktaGhorai1990,
  author    = {Dikta, Gerhard and Ghorai, J. K.},
  title     = {Bootstrap Approximation with Censored Data under the Proportional Hazard Model},
  series = {Communications in Statistics: Theory and Methods. 19 (1990), H. 2},
  journal   = {Communications in Statistics: Theory and Methods. 19 (1990), H. 2},
  isbn      = {0361-0926},
  pages     = {573 -- 581},
  year      = {1990},
  language  = {en}
}