The wireless network jamming problem

In adversarial environments, disabling the communication capabilities of the enemy is a high priority. We introduce the problem of determining the optimal number and locations for a set of jamming devices in order to neutralize a wireless communication network. This problem is known as the wireless network jamming problem. We develop several mathematical programming formulations based on covering the communication nodes and limiting the connectivity index of the nodes. Two case studies are presented comparing the formulations with the addition of various percentile constraints. Finally, directions of further research are addressed.     

Bootstrap confidence regions computed from autoregressions of arbitrary order

Given a linear time series, e.g. an autoregression of infinite order, we may construct a finite order approximation and use that as the basis for confidence regions. The sieve or autoregressive bootstrap, as this method is often called, is generally seen as a competitor with the better-understood block bootstrap approach. However, in the present paper we argue that, for linear time series, the sieve bootstrap has significantly better performance than blocking methods and offers a wider range of opportunities. In particular, since it does not corrupt second-order properties then it may be used in a double-bootstrap form, with the second bootstrap application being employed to calibrate a basic percentile method confidence interval. This approach confers second-order accuracy without the need to estimate variance. That offers substantial benefits, since variances of statistics based on time series can be difficult to estimate reliably, and—partly because of the relatively small amount of information contained in a dependent process—are notorious for causing problems when used to Studentize. Other advantages of the sieve bootstrap include considerably greater robustness against variations in the choice of the tuning parameter, here equal to the autoregressive order, and the fact that, in contradistinction to the case of the block bootstrap, the percentile t version of the sieve bootstrap may be based on the 'raw' estimator of standard error. In the process of establishing these properties we show that the sieve bootstrap is second order correct.     

Comparing and testing order relations between percentile residual life functions

We consider the problem of comparing and testing order relations between percentile residual life functions. We introduce R-R plots and processes and develop a general approach for this problem.     

Adjusted empirical likelihood models with estimating equations for accelerated life tests

This article proposes an adjusted empirical likelihood estimation (AMELE) method to model and analyze accelerated life testing data. This approach flexibly and rigorously incorporates distribution assumptions and regression structures by estimating equations within a semiparametric estimation framework. An efficient method is provided to compute the empirical likelihood estimates, and asymptotic properties are studied. Real-life examples and numerical studies demonstrate the advantage of the proposed methodology.     

Quantile estimation and comparing two independent groups with an approach based on percentile bootstrap

Although the most common approach for comparing two independent groups is on the basis of some measure of location, determination of the differences in the tails of the groups is often of interest. In this study, Harrell–Davis estimator, Sfakianakis–Verginis estimators and default quantile estimator of R are used in conjunction with a percentile bootstrap method with the aim of comparing two independent groups via the quantiles, and the relative efficiencies of Harrell–Davis and Sfakianakis–Verginis estimators are compared. General performance of Sfakianakis–Verginis estimators was much better than Harrell–Davis estimator in terms of both saving actual type I error and relative efficiency.     

The p-value Function and Statistical Inference

ABSTRACT

This article has two objectives. The first and narrower is to formalize the p-value function, which records all possible p-values, each corresponding to a value for whatever the scalar parameter of interest is for the problem at hand, and to show how this p-value function directly provides full inference information for any corresponding user or scientist. The p-value function provides familiar inference objects: significance levels, confidence intervals, critical values for fixed-level tests, and the power function at all values of the parameter of interest. It thus gives an immediate accurate and visual summary of inference information for the parameter of interest. We show that the p-value function of the key scalar interest parameter records the statistical position of the observed data relative to that parameter, and we then describe an accurate approximation to that p-value function which is readily constructed.     

The percentile residual life up to time t0: Ordering and aging properties

Motivated by practical issues, a new stochastic order for random variables is introduced by comparing all their percentile residual life functions until a certain instant. Some interpretations of these stochastic orders are given, and various properties of them are derived. The relationships to other stochastic orders are studied and also an application in reliability theory is described. Finally, we present some characterization results of the decreasing percentile residual life up to time t₀ aging notion.     

The effect of Monte Carlo approximation on coverage error of double-bootstrap confidence intervals

A double-bootstrap confidence interval must usually be approximated by a Monte Carlo simulation, consisting of two nested levels of bootstrap sampling. We provide an analysis of the coverage accuracy of the interval which takes account of both the inherent bootstrap and Monte Carlo errors. The analysis shows that, by a suitable choice of the number of resamples drawn at the inner level of bootstrap sampling, we can reduce the order of coverage error. We consider also the effects of performing a finite Monte Carlo simulation on the mean length and variability of length of two-sided intervals. An adaptive procedure is presented for the choice of the number of inner level resamples. The effectiveness of the procedure is illustrated through a small simulation study.     

On the Percentile Residual Lifetime of Parallel Systems

In this paper, we consider a parallel system consisting of n components. Then, the percentile residual lifetime of the system given survival of at least n ? r + 1, r = 1, 2, …, n component(s) has been introduced, and some properties of this measure have been investigated. We show that the system accommodates decreasing percentile residual lifetime function, provided the components have increasing hazard rate functions. Different parallel systems have been compared with each other in terms of the introduced measure. Furthermore, behavior of the percentile residual lifetime of the system and the components have been compared in terms of some reliability notions. Also, a characterization result has been presented.     

Simultaneous closeness among order statistics to population quantiles

We derive expressions for the probability that an individual order statistic is closest to the target parameter among the order statistics from a complete random sample. Results are given for random variables with bounded and complete support. We then apply these general results to location-scale parameter families of distributions with specific applications to estimation of percentiles. In this case, simultaneous-closeness probabilities depend upon the parameters through the value of p in the percentile and the sample size, n. Results are finally illustrated with the estimation of percentiles for normal and exponential distributions.