Stochastic models for fractal processes

This paper considers the situation where a stochastic process may display both long-range dependence (LRD) and intermittency. The existence of such a process is established in Anh et al. (1999). Existing works have commonly paid attention either to LRD or intermittency quite separately. This paper offers a convenient framework to study both effects simultaneously. A method is given to estimate and separate the two effects. The wavelet theory plays an essential role in this procedure. Numerical experiments on fractional Brownian motion and multiplicative cascade processes confirm the power of the method.     

Minimum contrast estimation of random processes based on information of second and third orders

This paper presents the results on consistency and asymptotic normality of a class of minimum contrast estimators for random processes with short- or long-range dependence based on the second- and third-order cumulant spectra. Asymptotic properties of sample spectral functionals of second and third orders, which are of independent interest in view of their possible use for nonparametric estimation of processes with short- or long-range dependence, are also provided.     

On LSE in regression model for long-range dependent random fields on spheres

We study the asymptotic behaviour of least squares estimators (LSE) in regression models for long-range dependent random fields observed on spheres. The LSE can be given as a weighted functional of long-range dependent random fields. It is known that in this scenario the limits can be non-Gaussian. We derive the limit distribution and the corresponding rate of convergence for the estimators. The results were obtained under rather general assumptions on the random fields. Simulation studies were conducted to support theoretical findings.     

Continuous-Time Stochastic Processes with Cyclical Long-Range Dependence

This paper introduces continuous‐time random processes whose spectral density is unbounded at some non‐zero frequencies. The discretized versions of these processes have asymptotic properties similar to those of discrete‐time Gegenbauer processes. The paper presents some properties of the covariance function and spectral density as well as a theory of statistical estimation of the mean and covariance function of such processes. Some directions for further generalizations of the results are indicated.     

Lone mothers' time allocations: choices and satisfactions

This paper uses the 2006 Australian Time Use Survey to examine the allocation of time to personal care, employment‐related activities, home duties, leisure and child care of lone mothers, in comparison to the time allocations of single women, women in childless couples and partnered mothers. Both primary and secondary time allocations are considered. The satisfactions that women report concerning their current time allocations are also analysed. The time use and satisfaction data are described using both tabulations and multiple regression methods. Lone mothers are shown to have similar time allocations as the other types of households, even though they have different financial and time resources. This raises the concern that lone mothers' desire or need to maintain such time allocations may lead to task overload. Consistent with this, lone mothers are found to be less satisfied with the way they allocate their time than single women and partnered mothers. The tensions associated with time use among lone mothers discussed in the literature are real, and important.     

A linear programming duality approach to analyzing strictly nonblocking <Emphasis Type="Italic">d</Emphasis>-ary multilog networks under general crosstalk constraints

When a switching network topology is used for constructing optical cross-connects, as in the circuit switching case, no two routes are allowed to share a link. However, if two routes share too many switching elements, then crosstalk introduced at those switching elements degrades signal quality. Vaez and Lea (IEEE Trans. Commun. 48:(2)316–323, 2000) introduced a parameter c which is the maximum number of distinct switching elements a route can share with other routes in the network. This is called the general crosstalk constraint. This paper presents a new method of analyzing strictly nonblocking multi-log networks under this general crosstalk constraint using linear programming duality.     

Joint chance-constrained staffing optimization in multi-skill call centers

This paper concerns the staffing optimization problem in multi-skill call centers. The objective is to find a minimal cost staffing solution while meeting a target level for the quality of service (QoS) to customers. We consider a staffing problem in which joint chance constraints are imposed on the QoS of the day. Our joint chance-constrained formulation is more rational capturing the correlation between different call types, as compared to separate chance-constrained versions considered in previous studies. We show that, in general, the probability functions in the joint-chance constraints display S-shaped curves, and the optimal solutions should belong to the concave regions of the curves. Thus, we propose an approach combining a heuristic phase to identify solutions lying in the concave part and a simulation-based cut generation phase to create outer-approximations of the probability functions. This allows us to find good staffing solutions satisfying the joint-chance constraints by simulation and linear programming. We test our formulation and algorithm using call center examples of up to 65 call types and 89 agent groups, which shows the benefits of our joint-chance constrained formulation and the advantage of our algorithm over standard ones.

     

A pragmatic adaptive enrichment design for selecting the right target population for cancer immunotherapies

One of the challenges in the design of confirmatory trials is to deal with uncertainties regarding the optimal target population for a novel drug. Adaptive enrichment designs (AED) which allow for a data-driven selection of one or more prespecified biomarker subpopulations at an interim analysis have been proposed in this setting but practical case studies of AEDs are still relatively rare. We present the design of an AED with a binary endpoint in the highly dynamic setting of cancer immunotherapy. The trial was initiated as a conventional trial in early triple-negative breast cancer but amended to an AED based on emerging data external to the trial suggesting that PD-L1 status could be a predictive biomarker. Operating characteristics are discussed including the concept of a minimal detectable difference, that is, the smallest observed treatment effect that would lead to a statistically significant result in at least one of the target populations at the interim or the final analysis, respectively, in the setting of AED.     

Family size and children’s education in Vietnam

Data from the nationally representative 1994 Inter-Censal Demographic Survey are used to examine the association between family size and children s schooling in Vietnam. The data provide information on several education measures for all children over age 10, including children no longer residing in the household. Although a clear inverse bivariate association between family size and children s school attendance and educational attainment is evident, multivariate analysis controlling for urban/rural residence, region, parents’ education, household wealth, and child’s age, reveals that much of this association, especially that predicting educational attainment, is attributable to these other influences. Moreover, much of the effect that remains after statistical adjustment for the other influences is seen mainly at the largest family sizes. We consider the implications of these findings for current population policy in Vietnam and the possible features of the Vietnamese context that might account for the modest association.