Table Of ContentSpringer Proceedings in Mathematics & Statistics
Matúš Maciak
Michal Pešta
Martin Schindler Editors
Analytical
Methods in
Statistics
AMISTAT, Liberec, Czech Republic,
September 2019
Springer Proceedings in Mathematics &
Statistics
Volume 329
Springer Proceedings in Mathematics & Statistics
This book series features volumes composed of selected contributions from
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community with well-edited, authoritative reports on developments in the most
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More information about this series at http://www.springer.com/series/10533
úš š
Mat Maciak Michal Pe ta Martin Schindler
(cid:129) (cid:129)
Editors
Analytical Methods
in Statistics
AMISTAT, Liberec, Czech Republic,
September 2019
123
Editors
Matúš Maciak Michal Pešta
Department ofProbability Department ofProbability
andMathematical Statistics andMathematical Statistics
CharlesUniversity CharlesUniversity
Prague,Czech Republic Prague,Czech Republic
Martin Schindler
Department ofApplied Mathematics
Technical University of Liberec
Liberec,Czech Republic
ISSN 2194-1009 ISSN 2194-1017 (electronic)
SpringerProceedings in Mathematics& Statistics
ISBN978-3-030-48813-0 ISBN978-3-030-48814-7 (eBook)
https://doi.org/10.1007/978-3-030-48814-7
MathematicsSubjectClassification: 62B05,62C12,62F03,62F12,62F35,62F40,62G08,62G20
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Preface
This proceeding volume follows the third workshop on Analytical Methods in
Statistics (AMISTAT 2019) which took place in Liberec (Czech Republic) in
September 16–19, 2019. The workshop was organized after two successful work-
shops AMISTAT 2015 and AMISTAT 2011 by the Department of Applied
Mathematics attheFacultyofScience, HumanitiesandEducationattheTechnical
University of Liberec and the Department of Probability and Mathematical
Statistics at the Faculty of Mathematics and Physics at the Charles University.
The workshop brought together several scientists, researchers, and young
scholarsfromaroundtheWorld(Austria,Belgium,Canada,Finland,France,India,
Russia,Serbia,Slovakia,Sweden,Turkey,UK,USA,andtheCzechRepublic)and
itofferedagreatopportunityforaseriesofinterestingandhighlyappreciatedtalks,
manyformalandinformal discussions,andalsosomevaluabletimespent together
among colleagues and friends. Many interesting topics and ideas arising from
everydayproblemswerecoveredinvariouscontributionsfocusingespeciallyatthe
analytical methods in statistics, asymptotics, estimation and Fisher information,
robustness,stochasticmodelsandinequalities,andmanyothers.Asmallpartofthe
contributions,bythoseauthorswhoconsideredtheirworkbeingpartiallycomplete,
is contained in the present book.
The joint motto of this proceeding, the workshop itself, and the talks is the
“analyticalstatistics”withthemainemphasizesonthefactthatthestatisticsalways
providesmathematicianswithnew,challenging,andalsoexcitingproblemsasthey
are usually all based in some real life situations. For such problems one can rarely
determineanyaxiomsordeterministicapproaches,butratheranalyticalmethodsare
needed to asses the problems properly. The statisticians, in general, utilize a
knowledgefromallareasofmathematicsincludingabstractcalculations,numerical
and algorithmic computation, or formal interpretation of the results. Statisticians
are, therefore, expected to find a solution to real problems and the answer that the
solution does not exist is not plausible. At least a solution optimal under some
acceptableconstraintsisusedasacounterpart.TheAMISTAT2019workshopwas
again full of such fresh ideas, proposals, and approaches. We are grateful for this
opportunity and also for the contributions included in this proceeding book.
v
vi Preface
Last, but not least, we would like to express our great thanks to Dr. Veronika
Rosteck, Springer Editor of Statistics, for her effort, encouragement, and help
needed when preparing this book. We thank all the authors of the chapters and all
referees for their work, consideration, and appreciation.
Prague, Czech Republic Matúš Maciak
April 2020 Michal Pešta
Martin Schindler
Contents
Averaged Autoregression Quantiles in Autoregressive Model. . . . . . . . . 1
Yeşim Güney, Jana Jurečková, and Olcay Arslan
Regression Neural Networks with a Highly Robust Loss
Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Jan Kalina and Petra Vidnerová
Weighted Empirical Minimum Distance Estimators in Berkson
Measurement Error Regression Models . . . . . . . . . . . . . . . . . . . . . . . . . 31
Hira L. Koul and Pei Geng
Implied Volatility Surface Estimation via Quantile
Regularization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Matúš Maciak, Michal Pešta, and Sebastiano Vitali
A Remark on the Grenander Estimator. . . . . . . . . . . . . . . . . . . . . . . . . 89
Ivan Mizera
Non-Gaussian Component Analysis: Testing the Dimension
of the Signal Subspace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Una Radojičić and Klaus Nordhausen
A Comparison of Robust Model Choice Criteria
Within a Metalearning Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Petra Vidnerová, Jan Kalina, and Yeşim Güney
On Parameter Estimation for High Dimensional
Errors-in-Variables Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Silvelyn Zwanzig and Rauf Ahmad
vii
Contributors
Rauf Ahmad Department of Statistics, Uppsala University, Uppsala, Sweden
Olcay Arslan Faculty of Science, Department of Statistics, Ankara University,
Tandogan, Ankara, Turkey
PeiGeng DepartmentofMathematics,CollegeofArtsandSciences,IllinoisState
University, Normal, IL, USA
Yeşim Güney Faculty of Science, Department of Statistics, Ankara University,
Tandogan, Ankara, Turkey
Jana Jurečková Faculty of Mathematics and Physics, Department of Statistics,
Charles University in Prague, Prague, Czech Republic
Jan Kalina The Czech Academy of Sciences, Institute of Computer Science,
Praha 8, Czech Republic
HiraL.Koul DepartmentofStatisticsandProbability,MichiganStateUniversity,
East Lansing, MI, USA
Matúš Maciak Faculty of Mathematics and Physics, Department of Probability
and Mathematical Statistics, Charles University, Prague, Czech Republic
Ivan Mizera University of Alberta, Mathematical and Statistical Sciences,
Edmonton, Alberta, Canada
KlausNordhausen InstituteofStatistics&MathematicalMethodsinEconomics,
Vienna University of Technology, Vienna, Austria
MichalPešta FacultyofMathematicsandPhysics,DepartmentofProbabilityand
Mathematical Statistics, Charles University, Prague, Czech Republic
Una Radojičić Institute of Statistics & Mathematical Methods in Economics,
Vienna University of Technology, Vienna, Austria
ix
x Contributors
PetraVidnerová TheCzechAcademyofSciences,InstituteofComputerScience,
Praha 8, Czech Republic
SebastianoVitali FacultyofMathematicsandPhysics,DepartmentofProbability
and Mathematical Statistics, Charles University, Prague, Czech Republic;
University of Bergamo, Department of Management, Economics and Quantitative
Methods, Bergamo, Italy
Silvelyn Zwanzig Department of Mathematics, Uppsala University, Uppsala,
Sweden
