Andriy Olenko

Uniform Convergence of Wavelet Expansions of Gaussian Random Processes

New results on uniform convergence in probability for the most general classes of wavelet expansions of stationary Gaussian random processes are given.

Sojourn measures of Student and Fisher–Snedecor random fields

Limit theorems for the volumes of excursion sets of weakly and strongly dependent heavy-tailed random fields are proved. Some generalizations to sojourn measures above moving levels and for cross-correlated scenarios are presented. Special attention is paid to Student and Fisher–Snedecor random fields. Some simulation results are also presented.

Average Sampling Restoration of Harmonizable Processes

The harmonizable Piranashvili–type stochastic processes are approximated by finite time shifted average sampling sums. Explicit truncation error upper bounds are established. Various corollaries and special cases are discussed.

A precise upper bound for the error of interpolation of stochastic processes

We obtain a precise upper bound for the truncation error of interpolation of functions of the Paley–Wiener class with the help of finite Whittaker–Kotelnikov– Shannon sums. We construct an example of an extremal function for which the upper bound is achieved. We study the error of interpolation and the rate of the mean square convergence for stochastic processes of the weak Cramér class. The paper contains an extensive list of references concerning the upper bounds for errors of interpolation for both deterministic and stochastic cases. The final part of the paper contains a discussion of new directions in this field.

Bedroom air quality and vacuuming frequency are associated with repeat child asthma hospital admissions.

Abstract Objective: Indoor environment factors have been associated with risk of asthma exacerbations in children but little is known about their role on asthma hospital readmissions. As children in Western societies continually spend more time indoors, understanding the influence of these factors on asthma exacerbation is important. We examined the role of indoor environmental and lifestyle characteristics on child asthma readmissions. Methods: A hospital-based case–control study recruited 22 children readmitted for asthma and 22 controls not readmitted for asthma. Logistic regression models were used to examine the association between aeroallergens and fungi in the bedroom and indoor lifestyle characteristics factors for asthma readmissions. To determine the best possible set of predictors among a large set of risk factors, we used random forests (RF) techniques. Results: Higher levels of airborne Cladosporium and yeast in the child’s bedroom increased risk of readmission (OR = 1.68, 95% CI 1.04–2.72 and OR = 1.52, 95% CI 0.99–2.34, respectively). Carpeted floors in the bedroom and synthetic doonas were also associated with increase in asthma readmissions (OR = 4.07, 95% CI 1.03–16.06 and OR = 14.6, 95% CI 1.26–169.4, respectively). In the home, frequent vacuuming using bagged cleaners increased risk of asthma readmission OR = 15.7 (95% CI 2.82–87.2). Conclusions: Factors in the child’s bedroom play an important role in increasing the risk of asthma hospital readmissions. These findings have major clinical implications as the identified potential risk factors may be modifiable. Further epidemiological studies with larger samples are necessary to evaluate these associations further.

Uniform Convergence of Compactly Supported Wavelet Expansions of Gaussian Random Processes

New results on uniform convergence in probability for expansions of Gaussian random processes using compactly supported wavelets are given. The main result is valid for general classes of non stationary processes. An application of the obtained results to stationary processes is also presented. It is shown that the convergence rate of the expansions is exponential.

Limit Theorems for Weighted Functionals of Cyclical Long-Range Dependent Random Fields

The article investigates isotropic random fields for which the spectral density is unbounded at some frequencies. Limit theorems for weighted functionals of these random fields are established. It is shown that for a wide class of functionals, which includes the Donsker scheme, the limit is not affected by singularities at non-zero frequencies. For general schemes, in contrast to the Donsker line, we demonstrate that the singularities at non-zero frequencies play a role even for linear functionals.

Double Entropy Inter-Rater Agreement Indices

The proper application of the most frequently used inter-rater agreement indices can be problematic for the case of a single target, for example, a psychotherapy patient, a student’s thesis, a grant proposal, and the lifestyle in a country. The majority of indices that can handle this case assess either the deviation of ranks from some central/average value or the pattern of ranks’ distribution. Contrary to other approaches, this article defines disagreement rating results using the unpredictability/complexity of scores. The article discusses alternative entropy methods for measuring inter-rater agreement or consensus in survey responses for the case of a single target. A new inter-rater agreement index is proposed. Comparisons between this index and the known inter-rater agreement measures show some limitations of the most frequently used indices. Various important methodological issues such as disagreement assumptions, average sensitivity, adjustments to deal with outliers, and missing or incorrectly recorded data are discussed. Examples of applications to actual data are presented.

Convergence Rate of Wavelet Expansions of Gaussian Random Processes

This article characterizes uniform convergence rate for general classes of wavelet expansions of stationary Gaussian random processes. The convergence in probability is considered.

On the rate of convergence to Rosenblatt-type distribution

The main result of the article is the rate of convergence to the Rosenblatt-type distributions in non-central limit theorems. Specifications of the main theorem are discussed for several scenarios. In particular, special attention is paid to the Cauchy, generalized Linnik’s, and local-global distinguisher random processes and fields. Direct analytical methods are used to investigate the rate of convergence in the uniform metric.