Analytical Methods in Statistics

Matús Maciak is an Assistant Professor at the Department of Probability and Mathematical Statistics, Charles University, Prague, Czech Republic. His research interests include innovative statistical approaches concerning nonparametric and semiparametric regression models, sparse fitting via convex optimization (atomic pursuit / LASSO), estimation under various shape constraints, robustness and quantiles, and changepoint detection and estimation within various data structures. He also has practical experience in applied statistics, especially in empirical econometrics and finance, insurance, ecology, and the medical sciences.

Michal Pesta is an Associate Professor at the Department of Probability and Mathematical Statistics, Charles University, Prague, Czech Republic. His research interests include asymptotic methods for changepoint, weak dependence, copulae, resampling methods, panel data, nonparametric regression, and errors-in-variables modeling. He is also interested in developing complex statistical methodology frameworks for various real-life settings, including empirical econometrics, finance, and non-life insurance.

Martin Schindler is an Assistant Professor of Applied Mathematics at the Technical University of Liberec, Czech Republic. His research interests include robust and nonparametric statistics, statistical computing and simulations. He has also worked on various inference procedures based on regression rank scores used in both linear and nonlinear models. During his postdoctoral studies at the University of Tampere he worked on nonparametric procedures for microarray data.

This book collects peer-reviewed contributions on modern statistical methods and topics, stemming from the third workshop on Analytical Methods in Statistics, AMISTAT 2019, held in Liberec, Czech Republic, on September 16-19, 2019. Real-life problems demand statistical solutions, which in turn require new and profound mathematical methods. As such, the book is not only a collection of solved problems but also a source of new methods and their practical extensions. The authoritative contributions focus on analytical methods in statistics, asymptotics, estimation and Fisher information, robustness, stochastic models and inequalities, and other related fields; further, they address e.g. average autoregression quantiles, neural networks, weighted empirical minimum distance estimators, implied volatility surface estimation, the Grenander estimator, non-Gaussian component analysis, meta learning, and high-dimensional errors-in-variables models.

Preface.- Y. Güney, J. Jurecková and O. Arslan, Averaged Autoregression Quantiles in Autoregressive Model.- J. Kalina and P. Vidnerová, Regression Neural Networks with a Highly Robust Loss Function.- H. L. Koul and P. Geng, Weighted Empirical Minimum Distance Estimators in Berkson Measurement Error Regression Models.- M. Maciak, M. Pesta and S. Vitali, Implied Volatility Surface Estimation via Quantile Regularization.- I. Mizera, A remark on the Grenander estimator.- U. Radojicic and K. Nordhausen, Non-Gaussian Component Analysis: Testing the Dimension of the Signal Subspace.- P. Vidnerová, J. Kalina and Y. Güney, A Comparison of Robust Model Choice Criteria within a Metalearning Study.- S. Zwanzig and R. Ahmad, On Parameter Estimation for High Dimensional Errors-in-Variables Models.