Applied Stochastic Models and Data Analysis

Yashin, Anatoli I.; Manton, Kenneth G.; Lowrimore, Gene R.

1997 Applied Stochastic Models and Data Analysis

doi: 10.1002/(SICI)1099-0747(199703)13:1<1::AID-ASM289>3.0.CO;2-E

The use of maximum likelihood methods in analysing times to failure in the presence of unobserved randomly changing covariates requires constrained optimization procedures. An alternative approach using a generalized version of the EM‐algorithm requires smoothed estimates of covariate values. Similar estimates are needed in evaluating past exposures to hazardous chemicals, radiation or other toxic materials when health effects only become evident long after their use. In this paper, two kinds of equation for smoothing estimates of unobserved covariates in survival problems are derived. The first shows how new information may be used to update past estimates of the covariates' values. The second can be used to project the covariates' trajectory from the present to the past. If the hazard function is quadratic in form, both types of smoothing equation can be derived in a closed analytical form. Examples of both types of equation are presented. Use of these equations in the extended EM‐algorithm, and in estimating past exposures to hazardous materials, are discussed. © 1997 by John Wiley & Sons, Ltd.

Pentzaropoulos, G. C.; Giokas, D. I.

1997 Applied Stochastic Models and Data Analysis

doi: 10.1002/(SICI)1099-0747(199703)13:1<15::AID-ASM290>3.0.CO;2-2

The problem of achieving near‐optimality in homogeneous central‐server queueing networks is investigated by means of a composite approach based on approximate operational analysis and goal programming procedures. A near‐optimal solution is shown to exist: this includes the expected overall waiting time, the overall throughput rate, as well as the distribution of queue length values. The need to maintain a balanced network flow and the desire to minimize the overall waiting time are expressed as complimentary objectives. Numerical results, based on past measurements from a multi‐server computing facility, indicate that the performance gains obtained by the application of the present methodology are quite significant throughout the network's feasible population scale. © 1997 by John Wiley & Sons, Ltd.

Sengupta, Jati K.

1997 Applied Stochastic Models and Data Analysis

doi: 10.1002/(SICI)1099-0747(199703)13:1<29::AID-ASM291>3.0.CO;2-N

Problems of estimating parameters in a linear programming model and using it in production planning are discussed here. An empirical application illustrates the various aspects of the estimation problem. © 1997 by John Wiley & Sons, Ltd.

Saoudi, S.; Ghorbel, F.; Hillion, A.

1997 Applied Stochastic Models and Data Analysis

doi: 10.1002/(SICI)1099-0747(199703)13:1<39::AID-ASM292>3.0.CO;2-J

The kernel density estimation method is not so attractive when the density has its support confined to a bounded space U of Rd. In a recent paper, we suggested a new nonparametric probability density function (p.d.f.) estimator called the ‘kernel‐diffeomorphism estimator’, which suppressed border convergence difficulties by using an appropriate regular change of variable. The present paper gives more asymptotic theory (uniform consistency, normality). An invariance criterion for p.d.f. estimators is discussed. The invariance of the kernel diffeomorphism estimator under special affine motion (a translation followed by any member of the special linear group SL(d, R) is proved. © 1997 by John Wiley & Sons, Ltd.