Estimation of Analog Parametric Test Metrics Using Copulas

© 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.International audienceA new technique for the estimation of analog parametric test metrics at the design stage is presented in this paper. This technique employs the copulas theory to estimate the distribution between random variables that represent the performances and the test measurements of the circuit under test (CUT). A copulas-based model separates the dependencies between these random variables from their marginal distributions, providing a complete and scale-free description of dependence that is more suitable to be modeled using well-known multivariate parametric laws. The model can be readily used for the generation of an arbitrarily large sample of CUT instances. This sample is thereafter used for estimating parametric test metrics such as defect level (or test escapes) and yield loss. We demonstrate the usefulness of the proposed technique to evaluate a built-in-test technique for a radio frequency low noise amplifier and to set test limits that result in a desired tradeoff between test metrics. In addition, we compare the proposed technique with previous ones that rely on direct density estimation

Analog Performance Prediction Based on Archimedean Copulas Generation Algorithm

International audienceTesting analog circuits is a complex and very time consuming task. In contrary to digital circuits, testing analog circuits needs different configurations, each of them targets a certain set of output parameters which are the performances and the test measures. One of the solutions to simplify the test task and optimize test time is the reduction of the number of to-be-tested performances by eliminating redundant ones. However, the main problem with such a solution is the identification of redundant performances. Traditional methods based on calculation of the correlation between different performances or on the defect level are shown to be not sufficient. This paper presents a new method based on the Archimedean copula generation algorithm. It predicts the performance value from each output parameter value based on the dependence (copula) between the two values. Therefore, different performances can be represented by a single output parameter; as a result, less test configurations are required. To validate the proposed approach, a CMOS imager with two performances and one test measure is used. The simulation results show that the two performances can be replaced by a single test measure. Industrial results are also reported to prove the superiority of the proposed approach

Stock market confidence and copula-based Markov models

This paper presents a descriptive model of stock market confidence conditional on stock market uncertainty in a first-order copula-based Markov approach. By using monthly closing prices of the VIX as a stock market uncertainty proxy for the United States and the copula of Fang et al. (2000) a stable nonlinear relation between confidence and uncertainty is derived. Based on the existence of a specific dependence structure uncertainty-reducing policies by US institutions which are intended to recover stock market confidence are evaluated with respect to its efficiency. The model implication for high uncertainty regimes is an aggressive uncertainty-reducing policy in order to avoid sticking in an uncertainty trap. Furthermore, uncertainty driving profit expectations force an uncertainty level which does not correspond to high confidence and calls for regulatory actions. Additionally, the methodological approach is appropriate for conditional quantile forecasts and a potential tool in risk management

The Kalai-Smorodinski solution for many-objective Bayesian optimization

An ongoing aim of research in multiobjective Bayesian optimization is to extend its applicability to a large number of objectives. While coping with a limited budget of evaluations, recovering the set of optimal compromise solutions generally requires numerous observations and is less interpretable since this set tends to grow larger with the number of objectives. We thus propose to focus on a specific solution originating from game theory, the Kalai-Smorodinsky solution, which possesses attractive properties. In particular, it ensures equal marginal gains over all objectives. We further make it insensitive to a monotonic transformation of the objectives by considering the objectives in the copula space. A novel tailored algorithm is proposed to search for the solution, in the form of a Bayesian optimization algorithm: sequential sampling decisions are made based on acquisition functions that derive from an instrumental Gaussian process prior. Our approach is tested on four problems with respectively four, six, eight, and nine objectives. The method is available in the Rpackage GPGame available on CRAN at https://cran.r-project.org/package=GPGame

Weak convergence of the empirical copula process with respect to weighted metrics

The empirical copula process plays a central role in the asymptotic analysis of many statistical procedures which are based on copulas or ranks. Among other applications, results regarding its weak convergence can be used to develop asymptotic theory for estimators of dependence measures or copula densities, they allow to derive tests for stochastic independence or specific copula structures, or they may serve as a fundamental tool for the analysis of multivariate rank statistics. In the present paper, we establish weak convergence of the empirical copula process (for observations that are allowed to be serially dependent) with respect to weighted supremum distances. The usefulness of our results is illustrated by applications to general bivariate rank statistics and to estimation procedures for the Pickands dependence function arising in multivariate extreme-value theory.Comment: 39 pages + 7 pages of supplementary material, 1 figur

Estimation of copulas via Maximum Mean Discrepancy

This paper deals with robust inference for parametric copula models. Estimation using Canonical Maximum Likelihood might be unstable, especially in the presence of outliers. We propose to use a procedure based on the Maximum Mean Discrepancy (MMD) principle. We derive non-asymptotic oracle inequalities, consistency and asymptotic normality of this new estimator. In particular, the oracle inequality holds without any assumption on the copula family, and can be applied in the presence of outliers or under misspecification. Moreover, in our MMD framework, the statistical inference of copula models for which there exists no density with respect to the Lebesgue measure on $[0,1]^d$, as the Marshall-Olkin copula, becomes feasible. A simulation study shows the robustness of our new procedures, especially compared to pseudo-maximum likelihood estimation. An R package implementing the MMD estimator for copula models is available