Non-asymptotic sequential confidence regions with fixed sizes for the multivariate nonlinear parameters of regression

In this paper we consider a sequential design for the estimation of nonlinear parameters of regression with guaranteed accuracy. Non-asymptotic confidence regions with fixed sizes for the least squares estimates are used. The obtained confidence region is valid for finite numbers of data points when the distributions of the observations are unknown.     

Experimental designs for binary data in switching measurements on superconducting Josephson junctions

Summary.  We study the optimal design of switching measurements of small Josephsonjunction circuits which operate in the macroscopic quantum tunnelling regime. In the experiment, sequences of current pulses are applied to the Josephson junction sample, while the voltage over the structure is monitored. The appearance of a voltage pulse to a single applied current pulse, being governed by the laws of quantum mechanics, is purely random. Starting from the D -optimality criterion we derive the optimal design for the estimation of the unknown parameters of the underlying Gumbel-type distribution. As a practical method for the measurements, we propose a sequential design that combines heuristic search for initial estimates and maximum likelihood estimation. The design presented has immediate applications in the area of superconducting electronics, implying faster data acquisition. The experimental results presented confirm the usefulness of the method.     

Efficient design of experiments in the Monod model

Summary. Estimation and experimental design in a non-linear regression model that is used in microbiology are studied. The Monod model is defined implicitly by a differential equation and has numerous applications in microbial growth kinetics, water research, pharmacokinetics and plant physiology. It is proved that least squares estimates are asymptotically unbiased and normally distributed. The asymptotic covariance matrix of the estimator is the basis for the construction of efficient designs of experiments. In particular locally D -, E - and c -optimal designs are determined and their properties are studied theoretically and by simulation. If certain intervals for the non-linear parameters can be specified, locally optimal designs can be constructed which are robust with respect to a misspecification of the initial parameters and which allow efficient parameter estimation. Parameter variances can be decreased by a factor of 2 by simply sampling at optimal times during the experiment.     

The guaranteed estimation of the Lipschitz classifier accuracy: Confidence set approach

This paper introduces an original method for the guaranteed estimation of the Lipschitz classifier accuracy in the case of a large number of classes. The solution was obtained as a finite closed set of alternative hypotheses, which contains an object of classification with probability of not less than the specified value. Thus, the classification is represented by a set of hypothetical classes. In this case, the smaller the cardinality of the discrete set of hypothetical classes is, the higher is the classification accuracy. This problem is relevant in practical biometrics, when the number of analyzed samples amounts to tens of thousands, and many of them are distinguished vaguely in the primary feature space.     

Russia 2020

The authors describe four idealized alternative scenarios for Russia in 2020—Kremlin Gambit, Fortress Russia, Russian Mosaic, and New Dream—and analyze the views of focus-group participants concerning their probability and desirability. They find that these views are influenced only marginally by electoral preferences.     

Testing monotonicity of pricing kernels

The behaviour of market agents has been extensively covered in the literature. Risk averse behaviour, described by Von Neumann and Morgenstern (Theory of games and economic behavior. Princeton University Press, Princeton, 1944) via a concave utility function, is considered to be a cornerstone of classical economics. Agents prefer a fixed profit over an uncertain choice with the same expected value, however, lately there has been a lot of discussion about the empirical evidence of such risk averse behaviour. Some authors have shown that there are regions where market utility functions are locally convex. In this paper we construct a test to verify uncertainty about the concavity of agents’ utility function by testing the monotonicity of empirical pricing kernels (EPKs). A monotonically decreasing EPK corresponds to a concave utility function while a not monotonically decreasing EPK means non-averse pattern on one or more intervals of the utility function. We investigate the EPKs for German DAX data for the years 2000, 2002 and 2004 and find evidence of non-concave utility functions: the null hypothesis of a monotonically decreasing pricing kernel is rejected for the data under consideration. The test is based on approximations of spacings through exponential random variables. In a simulation we investigate its performance and calculate the critical values (surface).