Professor Zdzisław Hellwig (1925–2013) a Giant in the Renaissance Style

On 8th November 2013, with great sadness we said goodbye to our dear Master and Teacher, Professor Zdzisław Hellwig. He walked away from us forever. Professor Zdzisław Hellwig (1925 – 2013) was a great man with impressive biography. Primarily professor Zdzisław Hellwig was prominent, widely recognized, eminent scholar of international standing in the field of statistics. His most important works are Elements of probability and mathematical statistics, Linear Regression and its applications in economics and Stochastic approximation. On 8th November 2013, with great sadness we said goodbye to our dear Master and Teacher, Professor Zdzisław Hellwig. He walked away from us forever. Professor Zdzisław Hellwig (1925 – 2013) was a great man with impressive biography. Primarily professor Zdzisław Hellwig was prominent, widely recognized, eminent scholar of international standing in the field of statistics. His most important works are Elements of probability and mathematical statistics, Linear Regression and its applications in economics and Stochastic approximation. His second field of achievements was econometrics. The rich scientific achievements in the field of econometrics of Professor Zdzisław Hellwig cover numerous studies dealing with the theory and application, including modeling of the socio – economic development, economic forecasting, and multidimensional comparative analysis and taxsonometrics. Professor Zdzisław Hellwig has a standing as economist. Professor Zdzisław Hellwig is a precursor of research in the field referred to as sustainable development, and early warning system for the national economy. He is considered pioneer of computer science in Poland. His international activities gave him the global scholar rank. Professor Zdzisław Hellwig was exceptionally gifted teacher and educator with long list of prominent followers. He has notable achievements as an organizer. Achievements of Professor Zdzisław Hellwig were widely acknowledged, both in the home university, countywide and abroad.

Faster Randomized Interior Point Methods for Tall/Wide Linear Programs

Linear programming (LP) is an extremely useful tool which has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such as combinatorics. It is also used in many machine learning applications, such as $\ell_1$-regularized SVMs, basis pursuit, nonnegative matrix factorization, etc. Interior Point Methods (IPMs) are one of the most popular methods to solve LPs both in theory and in practice. Their underlying complexity is dominated by the cost of solving a system of linear equations at each iteration. In this paper, we consider both feasible and infeasible IPMs for the special case where the number of variables is much larger than the number of constraints. Using tools from Randomized Linear Algebra, we present a preconditioning technique that, when combined with the iterative solvers such as Conjugate Gradient or Chebyshev Iteration, provably guarantees that IPM algorithms (suitably modified to account for the error incurred by the approximate solver), converge to a feasible, approximately optimal solution, without increasing their iteration complexity. Our empirical evaluations verify our theoretical results on both real-world and synthetic data.Comment: Extended version of the NeurIPS 2020 submission. arXiv admin note: substantial text overlap with arXiv:2003.0807

Econometrics: A bird's eye view

As a unified discipline, econometrics is still relatively young and has been transforming and expanding very rapidly over the past few decades. Major advances have taken place in the analysis of cross sectional data by means of semi-parametric and non-parametric techniques. Heterogeneity of economic relations across individuals, firms and industries is increasingly acknowledge and attempts have been made to take them into account either by integrating out their effects or by modeling the sources of heterogeneity when suitable panel data exists. The counterfactual considerations that underlie policy analysis and treatment evaluation have been given a more satisfactory foundation. New time series econometric techniques have been developed and employed extensively in the areas of macroeconometrics and finance. Non-linear econometric techniques are used increasingly in the analysis of cross section and time series observations. Applications of Bayesian techniques to econometric problems have been given new impetus largely thanks to advances in computer power and computational techniques. The use of Bayesian techniques have in turn provided the investigators with a unifying framework where the tasks and forecasting, decision making, model evaluation and learning can be considered as parts of the same interactive and iterative process; thus paving the way for establishing the foundation of the "real time econometrics". This paper attempts to provide an overview of some of these developments

Measurement of inequality with a finite number of pay states : the majorization set and its applications

I am grateful to Vassily Gorbanov, Tarik Yalcin and Fabrizio Germano for extended discussions and suggestions, and to an associate editor and a reviewer for constructive comments. I also wish to thank Francesco Andreoli, Geoffrey Burton, Joe Swierzbinski, Alain Trannoy, Claudio Zoli and seminar participants at the Aix-Marseille School of Economics for discussions. I am responsible for any errors.Peer reviewedPostprin

Models and metaphors: complexity theory and through-life management in the built environment

Complexity thinking may have both modelling and metaphorical applications in the through-life management of the built environment. These two distinct approaches are examined and compared. In the first instance, some of the sources of complexity in the design, construction and maintenance of the built environment are identified. The metaphorical use of complexity in management thinking and its application in the built environment are briefly examined. This is followed by an exploration of modelling techniques relevant to built environment concerns. Non-linear and complex mathematical techniques such as fuzzy logic, cellular automata and attractors, may be applicable to their analysis. Existing software tools are identified and examples of successful built environment applications of complexity modelling are given. Some issues that arise include the definition of phenomena in a mathematically usable way, the functionality of available software and the possibility of going beyond representational modelling. Further questions arising from the application of complexity thinking are discussed, including the possibilities for confusion that arise from the use of metaphor. The metaphor of a 'commentary machine' is suggested as a possible way forward and it is suggested that an appropriate linguistic analysis can in certain situations reduce perceived complexity

An Introduction to Mechanized Reasoning

Mechanized reasoning uses computers to verify proofs and to help discover new theorems. Computer scientists have applied mechanized reasoning to economic problems but -- to date -- this work has not yet been properly presented in economics journals. We introduce mechanized reasoning to economists in three ways. First, we introduce mechanized reasoning in general, describing both the techniques and their successful applications. Second, we explain how mechanized reasoning has been applied to economic problems, concentrating on the two domains that have attracted the most attention: social choice theory and auction theory. Finally, we present a detailed example of mechanized reasoning in practice by means of a proof of Vickrey's familiar theorem on second-price auctions