Mixed-rates asymptotics

A general method is presented for deriving the limiting behavior of estimators that are defined as the values of parameters optimizing an empirical criterion function. The asymptotic behavior of such estimators is typically deduced from uniform limit theorems for rescaled and reparametrized criterion functions. The new method can handle cases where the standard approach does not yield the complete limiting behavior of the estimator. The asymptotic analysis depends on a decomposition of criterion functions into sums of components with different rescalings. The method is explained by examples from Lasso-type estimation, $k$-means clustering, Shorth estimation and partial linear models.Comment: Published in at http://dx.doi.org/10.1214/009053607000000668 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Stratonovich-type integral with respect to a general stochastic measure

Let $\mu$ be a general stochastic measure, where we assume for $\mu$ only $\sigma$-additivity in probability and continuity of paths. We prove that the symmetric integral $\int_{[0,T]}f(\mu_t, t)\circ\,{\rm d}\mu_t$ is well defined. For stochastic equations with this integral, we obtain the existence and uniqueness of a solution.Comment: Stochastics: An International Journal of Probability and Stochastic Processes, 201

Oil price volatility and the asymmetric response of gasoline prices to oil price increases and decreases

This paper analyzes the effect of volatility in oil prices on the degree of asymmetry in the response of gasoline prices to oil price increases and decreases. Several time series measures of the asymmetry between the responses of gasoline prices to oil price increases and decreases and several measures of the oil price volatility are constructed. In all models, the degree of asymmetry in gasoline prices declines with an increase in oil price volatility. The results support the oligopolistic coordination theory as a likely explanation of the observed asymmetry and are not consistent with the standard search theory and the search theory with Bayesian updating.gasoline price response, asymmetric response, search theory

Microservices Validation: Methodology and Implementation

Due to the wide spread of cloud computing, arises actual question about architecture, design and implementation of cloud applications. The microservice model describes the design and development of loosely coupled cloud applications when computing resources are provided on the basis of automated IaaS and PaaS cloud platforms. Such applications consist of hundreds and thousands of service instances, so automated validation and testing of cloud applications developed on the basis of microservice model is a pressing issue. There are constantly developing new methods of testing both individual microservices and cloud applications at a whole. This article presents our vision of a framework for the validation of the microservice cloud applications, providing an integrated approach for the implementation of various testing methods of such applications, from basic unit tests to continuous stability testing

North Korea’s nuclear test

North Korea’s nuclear test serves several purposes. Its first purpose is to bolster the flagging legitimacy of the regime and, by drumming up war hysteria, achieve domestic mobilization in the face of mounting internal difficulties. Throughout North Korea’s turbulent history, the regime has periodically resorted to war hysteria, at times on even grander scale than what we have recently seen. North Korea’s Songun (army-first) policy requires periodic crises to maintain the myth of enemy encirclement and the army prestige. If history is any judge, the North Koreans will step away from the brink when their domestic aims have been achieved

The Discrete Dantzig Selector: Estimating Sparse Linear Models via Mixed Integer Linear Optimization

We propose a novel high-dimensional linear regression estimator: the Discrete Dantzig Selector, which minimizes the number of nonzero regression coefficients subject to a budget on the maximal absolute correlation between the features and residuals. Motivated by the significant advances in integer optimization over the past 10-15 years, we present a Mixed Integer Linear Optimization (MILO) approach to obtain certifiably optimal global solutions to this nonconvex optimization problem. The current state of algorithmics in integer optimization makes our proposal substantially more computationally attractive than the least squares subset selection framework based on integer quadratic optimization, recently proposed in [8] and the continuous nonconvex quadratic optimization framework of [33]. We propose new discrete first-order methods, which when paired with state-of-the-art MILO solvers, lead to good solutions for the Discrete Dantzig Selector problem for a given computational budget. We illustrate that our integrated approach provides globally optimal solutions in significantly shorter computation times, when compared to off-the-shelf MILO solvers. We demonstrate both theoretically and empirically that in a wide range of regimes the statistical properties of the Discrete Dantzig Selector are superior to those of popular $\ell_{1}$-based approaches. We illustrate that our approach can handle problem instances with p = 10,000 features with certifiable optimality making it a highly scalable combinatorial variable selection approach in sparse linear modeling