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Winning the Hand of the Princess Saralinda
princesses dukes asymptotics tandem queues infi nite-server queues in series
2015/7/8
Suitors come to the castle in order to try to win the hand of the Princess Saralinda. The first suitor to perform n amazing feats will succeed. If the number n of feats is large and the times to perfo...
One may consider a discrete-event simulation as a Markov chain evolving on a suitably rich state space. One way that regenerative cycles may be constructed for general state-space Markov chains is to ...
Estimating Tail Probabilities in Queues via Extremal Statistics
Extreme values queues regenerative processes rare events estimation asymptotics
2015/7/8
We study the estimation of tail probabilities in a queue via a semi-parametric estimator based on the maximum value of the workload, observed over the sampled time interval. Logarithmic consistency an...
On the Maximum Workload of a Queue Fed by Fractional Brownian Motion
Long-range dependence queues fractional Brownian motion extreme values
2015/7/8
Consider a queue with a stochastic fluid input process modeled as fractional Brownian motion (fBM). When the queue is stable, we prove that the maximum of the workload process observed over an interva...
On the Validity of Long-Run Estimation Methods for Discrete-Event Systems
Validity Long-Run Estimation Methods Discrete-Event Systems
2015/7/8
On the Validity of Long-Run Estimation Methods for Discrete-Event Systems.
A Large Deviations Perspective on Ordinal Optimization
Large Deviations Perspective Ordinal Optimization
2015/7/6
We consider the problem of optimal allocation of computing budget to maximize the probability of correct selection in the ordinal optimization setting. This problem has been studied in the literature ...
On Functional Central Limit Theorems for Semi-Markov and Related Processes
Semi-Markov processes Markov chains Central limit theorem Martingales Discrete-event systems
2015/7/6
The semi-Markov process (SMP) has long been used as a model for the underlying process of a discrete-event stochastic system. Important refinements of this model include the continuous-time Markov cha...
In this paper, we introduce a new approach to constructing unbiased estimators when computing expectations of path functionals associated with stochastic differential equations (SDEs). Our randomizati...
The Cross-Entropy Method for Estimation
cross-entropy estimation rare events importance sampling adaptive Monte Carlo zero-variance distribution
2015/7/6
This chapter describes how difficult statistical estimation problems can often be solved efficiently by means of the cross-entropy (CE) method. The CE method can be viewed as an adaptive importance sa...
The Dantzig selector:statistical estimation when p is much larger than n
Statistical linear model model selection ideal estimation oracle inequalities sparse solutions to underdetermined systems `1-minimization linear programming restricted orthonormality geometry in high dimensions random matrices
2015/6/17
In many important statistical applications, the number of variables or parameters p is much larger than the number of observations n. Suppose then that we have observations y = Xβ + z, where β ∈ Rp is...
Modern statistical estimation via oracle inequalities
Modern statistical estimation oracle inequalities
2015/6/17
A number of fundamental results in modern statistical theory involve thresholding estimators. This survey paper aims at reconstructing the history of how thresholding rules came to be popular in stati...
REJOINDER: THE DANTZIG SELECTOR:STATISTICAL ESTIMATION WHEN P IS MUCH LARGER THAN N
DANTZIG SELECTOR STATISTICAL ESTIMATION MUCH LARGER THAN N
2015/6/17
First of all, we would like to thank all the discussants for their interest and comments, as well as for their thorough investigation. The comments all underlie the importance and timeliness of the to...
Supplementary materials for Statistical Estimation and Testing via the Sorted 1 Norm
Supplementary materials Statistical Estimation Sorted 1 Norm
2015/6/17
In this note we give a proof showing that even though the number of false discoveries and the total number of discoveries are not continuous functions of the parameters, the formulas we obtain for the...
Controlling the False Discovery Rate via Knockoffs
Variable selection false discovery rate (FDR) sequential hypothesis testing martingale theory permutation methods Lasso
2015/6/17
In many fields of science, we observe a response variable together with a large number of potential explanatory variables, and would like to be able to discover which variables are truly associated wi...
EigenPrism:Inference for High-Dimensional Signal-to-Noise Ratios
EigenPrism High-Dimensional Signal Noise Ratios
2015/6/17
Consider the following three important problems in statistical inference, namely, constructing confidence intervals for (1) the error of a high-dimensional (p > n) regression estimator, (2) the linear...