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Patient unpunctuality significantly disrupts the operations of healthcare facilities, reduces provider productivity, and increases healthcare costs. To alleviate the negative impact of unpunctual patients, this study addresses the appointment scheduling (AS) in the simultaneous presence of unpunctual patients, multiple servers, and no-shows. To determine the appointment schedule, we propose a two-stage stochastic mixed-integer programming model to minimise the total cost incurred by patient waiting and clinic overtime. It becomes challenging for a standard solver to solve this model due to the dynamic patient-to-server assignment decisions that are proactively anticipated in the determination of appointment times. To deal with this problem, a stochastic approximation algorithm is proposed under unbiased gradient estimators. The effectiveness and efficiency of this algorithm are validated in extensive numerical experiments that compare it with Benders decomposition and a heuristic algorithm. Further, the features of the optimal appointment schedule are analysed: (i) the shape of the appointment intervals relies on the number of servers; (ii) the length of intervals is sensitive to no-shows; (iii) the initial block size is greatly affected by patient unpunctuality. Managerial insights are also provided for hospital managers to schedule unpunctual patients in practice. [ABSTRACT FROM AUTHOR]

In this paper, we propose and investigate a new kernel regression estimators based on the two-time-scale stochastic approximation algorithm in the case of independent functional data. We study the properties of the proposed recursive estimators and compare them with the recursive estimators based on single-time-scale stochastic algorithm proposed by Slaoui and to the non-recursive estimator proposed by Slaoui. It turns out that, with an adequate choice of the parameters, the proposed two-time-scale estimators perform better than the recursive estimators constructed using single-time-scale stochastic algorithm. We corroborate these theoretical results through some simulations and two real datasets. [ABSTRACT FROM AUTHOR]

Sliced inverse regression (SIR) is a recommended method to identify and estimate the central dimension reduction (CDR) subspace. CDR subspace is at the base to describe the conditional distribution of the response Y given a d-dimensional predictor vector X. To estimate this space, two versions are very popular: the slice version and the kernel version. A recursive method of the slice version has already been the subject of a systematic study. In this paper, we propose to study the kernel version. It's a recursive method based on a stochastic approximation algorithm of the kernel version. The asymptotic normality of the proposed estimator is also proved. A simulation study that not only shows the good numerical performance of the proposed estimate and which also allows to evaluate its performance with respect to existing methods is presented. A real dataset is also used to illustrate the approach. [ABSTRACT FROM AUTHOR]

In this paper, we consider an extension of the generalized class of recursive regression estimators to the case of strong mixing data. Then, we study the properties of these estimators and compare them with the well known Nadaraya-Watson estimator. The Bias, variance and Mean Integrated Square Error are computed explicitly. Using a selected bandwidth and a special stepsize, we showed that the proposed recursive estimators allowed us to obtain quite better results compared to the non-recursive regression estimator under α-mixing condition in terms of estimation error and much better in terms of computational costs. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the problem of the regression estimation near the edges under censoring. For this purpose, we consider a new recursive estimator based on the stochastic approximation algorithm and Bernstein polynomials of the regression function when the response random variable is subject to random right censoring. We give the central limit theorem and the strong pointwise convergence rate for our proposed nonparametric recursive estimators under some mild conditions. Finally, we provide pointwise moderate deviation principles (MDP) for the proposed estimators. We corroborate these theoretical results through simulations as well as the analysis of a real data set. [ABSTRACT FROM AUTHOR]

In this article, we aim to solve Bayesian Risk Optimization (BRO), which is a recently proposed framework that formulates simulation optimization under input uncertainty. In order to efficiently solve the BRO problem, we derive nested stochastic gradient estimators and propose corresponding stochastic approximation algorithms. We show that our gradient estimators are asymptotically unbiased and consistent, and that the algorithms converge asymptotically. We demonstrate the empirical performance of the algorithms on a two-sided market model. Our estimators are of independent interest in extending the literature of stochastic gradient estimation to the case of nested risk measures. [ABSTRACT FROM AUTHOR]

In this paper, we propose two kernel distribution estimators based on a data transformation. We study the properties of these estimators and we compare them with two conventional estimators. It appears that with an appropriate choice of the parameters of the two proposed estimators, the convergence rate of two estimators will be faster than that of the two conventional estimators and the Mean Integrated Square Error will be smaller than the two conventional estimators. We corroborate these theoretical results through simulations as well as a real data set. [ABSTRACT FROM AUTHOR]

In this paper, we propose a relative recursive regression estimator for censored data defined by the stochastic approximation algorithm to deal with the presence of outliers or when the response is usually positive. We give the central limit theorem and the strong pointwise convergence rate for our proposed nonparametric relative recursive estimators under some mild conditions. We finally developed a second generation plug-in bandwidth selection procedure. [ABSTRACT FROM AUTHOR]

In this article we propose an automatic selection of the bandwidth of the recursive kernel density estimators for spatial data defined by the stochastic approximation algorithm. We showed that, using the selected bandwidth and the stepsize which minimize the MWISE (Mean Weighted Integrated Squared Error), the recursive estimator will be quite similar to the nonrecursive one in terms of estimation error and much better in terms of computational costs. In addition, we obtain the central limit theorem for the nonparametric recursive density estimator under some mild conditions. [ABSTRACT FROM AUTHOR]

We propose a computational framework for real-time risk assessment and prioritising for random outcomes without prior information on probability distributions. The basic model is built based on satisficing measure (SM) which yields a single index for risk comparison. Since SM is a dual representation for a family of risk measures, we consider problems constrained by general convex risk measures and specifically by conditional value-at-risk. Starting from offline optimisation, we apply sample average approximation technique and argue the convergence rate and validation of optimal solutions. In online stochastic optimisation case, we develop primal-dual stochastic approximation algorithms respectively for general risk constrained problems, and derive their regret bounds. For both offline and online cases, we illustrate the relationship between risk ranking accuracy with sample size (or iterations). [ABSTRACT FROM AUTHOR]

We present a method to solve constrained convex stochastic optimization problems when the objective is a finite sum of convex functions. Our method is based on Incremental Stochastic Subgradient Algorithms and String-Averaging techniques, with an assumption that the subgradient directions are affected by random errors in each iteration. Our analysis allows the method to perform approximate projections onto the feasible set in each iteration. We provide convergence results for the case where a diminishing step-size rule is used. We test our method in a large set of random instances of a stochastic convex programming problem and we compare its performance with the robust mirror descent stochastic approximation algorithm proposed in Nemirovski et al. (Robust stochastic approximation approach to stochastic programming, SIAM J Optim 19 (2009), pp. 15741609). [ABSTRACT FROM AUTHOR]

Many mathematical and physical problems are led to find a root of a real functionf. This kind of equation is an inverse problem and it is difficult to solve it. Especially in engineering sciences, the analytical expression of the functionfis unknown to the experimenter, but it can be measured at each pointxkwithM(xk) as expected value and induced error ξk. The aim is to approximate the unique root θ under some assumptions on the functionfand errors ξk. We use a stochastic approximation algorithm that constructs a sequence (xk)k ⩾ 1. We establish the almost complete convergence of the sequence (xk)kto the exact root θ by considering the errors (ξk)kquasi-associated and we illustrate the method by numerical examples to show its efficiency. [ABSTRACT FROM AUTHOR]