This book presents recent non-asymptotic results for approximations in multivariate statistical analysis. The book is unique in its focus on results with the correct error structure for all the parameters involved. Firstly, it discusses the computable error bounds on correlation coefficients, MANOVA tests and discriminant functions studied in recent papers. It then introduces new areas of research in high-dimensional approximations for bootstrap procedures, Cornish–Fisher expansions, power-divergence statistics and approximations of statistics based on observations with random sample size. Lastly, it proposes a general approach for the construction of non-asymptotic bounds, providing relevant examples for several complicated statistics. It is a valuable resource for researchers with a basic understanding of multivariate statistics.
We get the computable error bounds for generalized Cornish–Fisher expansions for quantiles of statistics provided that the computable error bounds for Edgeworth–Chebyshev type expansions for distributions of these statistics are known. The results are illustrated by examples.
The paper investigates macrofinancial linkages in the sample of 16 European economies over January 1997–December 2019 from a new twofold perspective. First, we put a particular emphasis on the role of news‐based sentiment measures in these relationships, that is, economic policy uncertainty and global geopolitical risk. Second, we pursue a hybrid econometric approach to capture a presumably nonlinear nature of these linkages by building on different quantiles of the data series and estimating impulse responses from smooth local projections (Barnichon and Brownlees, Review of Economics and Statistics, 101(3), 522–530, 2019). Our results legitimize such approach as the number of statistically significant impulse responses based on this approach is skewed towards upper (75th and 90th) quantiles. We find that global economic policy uncertainty index dampens the growth rates of industrial production in Austria, France, Italy, Luxembourg and Slovakia, which calls for specific measures to mitigate this adverse effect at the national level, for example, by curtailing yellow journalism, populist ideas and disbeliefs. However, there is only minor evidence for the relationship running between economic policy uncertainty and financial stress. Global geopolitical risk appears irrelevant in the country‐ and panel‐level analyses. Meanwhile, the VIX index performs a pervasive role in undermining industrial production and increasing economic policy uncertainty in Europe.