A generalization of the Solis–Wets method

Abstract

a b s t r a c tIn this paper we focus on the application of global stochastic optimization methods to extremum estimators. We propose a general stochastic method-the master method -which includes several stochastic optimization algorithms as a particular case. The proposed method is sufficiently general to include the Solis-Wets method, the improving hit-and-run algorithm, and a stochastic version of the zigzag algorithm. A matrix formulation of the master method is presented and some specific results are given for the stochastic zigzag algorithm. Convergence of the proposed method is established under a mild set of conditions, and a simple regression model is used to illustrate the method.

Confidence intervals for the minimum of a function using extreme value statistics

“…Our computational experiments suggest that it is preferable to consider a larger number of observations than a larger number of replications. To state this differently, we recommend a one shot Table 2 (1 − p) interval estimates for p = 0.10/0.05/0.01; LB and UB respectively denote the lower and upper bound of the confidence zone constructed according with (4). The values in parentheses denote sample variances defined according to (6) and 7 run with a larger number of observations than averaging over several trials with a smaller number of observations.…”

“…Theoretical applications of Theorem 2.3 can be found, for instance, in Romeijn and Smith (1994) and Carvalho (2010). We follow de Haan's general recommendation to set the parameter α = k/2, where k denotes the number of dimensions of the problem of interest.…”

A flexible and tractable class of one-factor copulas

“…In principle, several runs with different starting points should be tested to ensure that the global minimizer is reached. Also, formal statistical procedures can be performed to test wether the given minimizer is indeed the global minimizer; see, e.g., (de Carvalho 2011(de Carvalho , 2012Veall 1990). We found that a single run was enough to find what appeared to be the global optimum.…”

A dimension reduction technique for estimation in linear mixed models

“…In effect, this simplified problem endows us with the means to obtain estimates of variance components with large computational savings. In addition, given that the search domain of the simplified problem is compact, we can rely the analysis over stochastic optimization methods well qualified for closed bounded domains (Spall 2003;Carvalho 2010). …”