We study sample average approximations under adaptive importance sampling. Based on a Banach-space-valued martingale strong law of large numbers, we establish uniform convergence of the sample average approximation to the function being approximated. In the optimization context, we obtain convergence of the optimal value and optimal solutions of the sample average approximation.

To incorporate uncertainties in empty container repositioning problem, we formulate a two-stage stochastic programming model with random demand, supply, ship weight capacity and ship space capacity. The Sample Average Approximation (SAA) method is applied to approximate the expected value function. Several non-independent and identically distributed sampling schemes are considered to enhance th...

Abstract. The stochastic variational inequality (SVI) has been used widely, in engineering and economics, as an effective mathematical model for a number of equilibrium problems involving uncertain data. This paper presents a new expected residual minimization (ERM) formulation for a class of SVI. The objective of the ERM-formulation is Lipschitz continuous and semismooth which helps us guarant...

People often estimate the average duration of several events (e.g., on average, how long does it take to drive from one's home to his or her office). While there is a great deal of research investigating estimates of duration for a single event, few studies have examined estimates when people must average across numerous stimuli or events. The current studies were designed to fill this gap by e...

AIM To assess the conclusiveness of the Cochrane Neonatal Reviews (CNRs). We tested the hypotheses that: 1) the majority of the reviews is inconclusive; 2) the majority of reviews recognizes the need for further studies; 3) the ability to reach a conclusion is dependent upon both the number of studies and the number of patients. We also aimed to determine whether the conclusiveness of the CNRs ...

We propose a sample average approximation (SAA) method for stochastic programming problems involving an expected value constraint. Such problems arise, for example, in portfolio selection with constraints on conditional value-at-risk (CVaR). Our contributions include an analysis of the convergence rate and a statistical validation scheme for the proposed SAA method. Computational results using ...

In this paper, we prove a result for the asymptotic distribution of the sample average value-at-risk (AVaR) under certain regularity assumptions. The asymptotic distribution can be used to derive asymptotic confidence intervals when AV aR2(X) is calculated by the Monte Carlo method which is adopted in many risk management systems. We study the effect of the tail behavior of the random variable ...

Sample-average approximations (SAA) are a practical means of finding approximate solutions of stochastic programming problems involving an extremely large (or infinite) number of scenarios. SAA can also be used to find estimates of a lower bound on the optimal objective value of the true problem which, when coupled with an upper bound, provides confidence intervals for the true optimal objectiv...