Some Issues in Multivariate Stochastic Root Finding
نویسندگان
چکیده
The stochastic root finding problem (SRFP) involves finding points in a region where a function attains a prespecified target value, using only a consistent estimator of the function. Due to the properties that the SRFP contexts entail, the development of good solutions to SRFPs has proven difficult, at least in the multi-dimensional setting. This paper discusses certain key issues, insights and complexities for SRFPs. Some of these are important in that they point to phenomena that contribute to the difficulties that arise in the development of efficient algorithms for SRFPs. Others are simply observations, sometimes obvious, but important for providing useful insight into algorithm development.
منابع مشابه
Hessian Stochastic Ordering in the Family of multivariate Generalized Hyperbolic Distributions and its Applications
In this paper, random vectors following the multivariate generalized hyperbolic (GH) distribution are compared using the hessian stochastic order. This family includes the classes of symmetric and asymmetric distributions by which different behaviors of kurtosis in skewed and heavy tail data can be captured. By considering some closed convex cones and their duals, we derive some necessary and s...
متن کاملCesaro Supermodular Order and Archimedean Copulas
In this paper, we introduce a new kind of order, Cesaro supermodular order, which includes supermodular order and stochastic order. For this new order, we show that it almost fulfils all desirable properties of a multivariate positive dependence order that have been proposed by Joe (1997). Also, we obtain some relations between it with other orders. Finally, we consider different issues related...
متن کاملMultivariate Counting Processes: Copulas and beyond By
Multivariate stochastic processes with Poisson marginals are of interest in insurance and finance; they can be used to model the joint behaviour of several claim arrival processes, for example. We discuss various methods for the construction of such models, with particular emphasis on the use of copulas. An important class of multivariate counting processes with Poisson marginals arises if the ...
متن کاملOn Multivariate Likelihood Ratio Ordering among Generalized Order Statistics and their Spacings
The most of the results obtained about stochastic properties of generalized order statistics and their spacings in the literature are based on equal model parameters. In this paper, with less restrictive conditions on the model parameters, we prove some new multivariate likelihood ratio ordering results between two sub-vectors of GOS's as well as two sub-vectors of $p$-spacings based on two con...
متن کاملDeterministic and Stochastic Root Finding in One Dimension for Increasing Convex Functions
We study the one-dimensional root finding problem for increasing convex functions, both in the case where the function can be evaluated exactly and where the function must be simulated so that only confidence interval estimates are available. The algorithms studied are gradient-free and do not depend upon any additional smoothness conditions. We provide a performance guarantee in the determinis...
متن کامل