On robustness of the Shiryaev–Roberts change-point detection procedure under parameter misspecification in the post-change distribution

The gist of the quickest change-point detection problem is to detect the presence of a change in the statistical behavior of a series of sequentially made observations, and do so in an optimal detection-speed-versus-“false-positive”-risk manner. When optimality is understood either in the generalized Bayesian sense or as defined in Shiryaev's multi-cyclic setup, the so-called Shiryaev–Roberts (SR) detection procedure is known to be the “best one can do”, provided, however, that the observations’ pre- and post-change distributions are both fully specified. We consider a more realistic setup, viz. one where the post-change distribution is assumed known only up to a parameter, so that the latter may be misspecified. The question of interest is the sensitivity (or robustness) of the otherwise “best” SR procedure with respect to a possible misspecification of the post-change distribution parameter. To answer this question, we provide a case study where, in a specific Gaussian scenario, we allow the SR procedure to be “out of tune” in the way of the post-change distribution parameter, and numerically assess the effect of the “mistuning” on Shiryaev's (multi-cyclic) Stationary Average Detection Delay delivered by the SR procedure. The comprehensive quantitative robustness characterization of the SR procedure obtained in the study can be used to develop the respective theory as well as to provide a rational for practical design of the SR procedure. The overall qualitative conclusion of the study is an expected one: the SR procedure is less (more) robust for less (more) contrast changes and for lower (higher) levels of the false alarm risk.     

基于solaris平台的DNS服务器侦测和阻止DOS攻击的实现

DNS服务器所面临的威胁集中表现出了互连网的脆弱性,针对DNS服务器的拒绝服务攻击是DNS服务器面临的最大威胁.提出了一种针对查询攻击进行侦测和阻止的思路,并且在solaris的平台上用perl语言来实现,能够保证DNS服务器有效地抵御常规攻击,为正常用户提供及时的服务.同时,本文也对伪造源IP的分布式拒绝服务攻击提出了一种解决方案.     

“It's the Beast Thing”

This article examines the representations of men and masculinities in contemporary crime narratives featuring a female protagonist. These “chick dick” stories (which adapt elements from the hardboiled detective novel, film noir, chick lit, and chick flicks) repeatedly engage with the gendered power dynamics made visible and problematic through the intersection of “chick” and crime genres, most particularly the sexualization of violence. In these narratives, popular masculinities operate as deployable concepts to dramatize contemporary gender relations. By tapping into the popular sentiment of a “crisis in masculinity,” chick dick texts also mobilize a rhetoric of unrepresentable male victimization and individual male pathologies. This strategy highlights the spaces and places in which masculinities are made vulnerable at the same time as it offers simplistic and individualized explanations for the systemic sexualized violence that dominate these narratives.     

Asymptotic behaviour of a test statistic for detection of change in mean of vectors

The paper gives an asymptotic distribution of a test statistic for detecting a change in a mean of random vectors with dependent components. The studied test statistic has a form of a maximum of a square Euclidean norms of vectors with components being standardized partial cumulative sums of deviations from means. The limit distribution was obtained using a result of Piterbarg [1994. High deviations for multidimensional stationary Gaussian processes with independent components. In: Zolotarev, V.M. (Ed.), Stability Problems for Stochastic Models, pp. 197–210].     

A single-featured EWMA-X control chart for detecting shifts in process mean and standard deviation

The combined EWMA-X chart is a commonly used tool for monitoring both large and small process shifts. However, this chart requires calculating and monitoring two statistics along with two sets of control limits. Thus, this study develops a single-featured EWMA-X (called SFEWMA-X) control chart which has the ability to simultaneously monitor both large and small process shifts using only one set of statistic and control limits. The proposed SFEWMA-X chart is further extended to monitoring the shifts in process standard deviation. A set of simulated data are used to demonstrate the proposed chart's superior performance in terms of average run length compared with that of the traditional charts. The experimental examples also show that the SFEWMA-X chart is neater and easier to visually interpret than the original EWMA-X chart.     

On Calculations Involving the Maximum Cell Frequency

We describe a method of computing the cumulative distribution function of the maximum and minimum cell frequencies in sampling distributions commonly encountered in the analysis of categorical data.The procedure is efficient for exact or approximate calculation in both homogeneous and non-homogeneous cases, is non-recursive, and does not require Dirichlet integrals.Some related statistical problems are also discussed.     

On Approximability of Boolean Formula Minimization

For a Boolean function given by a Boolean formula (or a binary circuit) S we discuss the problem of building a Boolean formula (binary circuit) of minimal size, which computes the function g equivalent to , or -equivalent to , i.e., . In this paper we prove that if P NP then this problem can not be approximated with a good approximation ratio by a polynomial time algorithm.     

Modified Wald statistics for generalized linear models

Summary: Wald statistics in generalized linear models are asymptotically ² distributed. The asymptotic chi–squared law of the corresponding quadratic form shows disadvantages with respect to the approximation of the finite–sample distribution. It is shown by means of a comprehensive simulation study that improvements can be achieved by applying simple finite–sample size approximations to the distribution of the quadratic form in generalized linear models. These approximations are based on a ² distribution with an estimated degree of freedom that generalizes an approach by Patnaik and Pearson. Simulation studies confirm that nominal level is maintained with higher accuracy compared to the Wald statistics.     

Center and Distinguisher for Strings with Unbounded Alphabet

Consider two sets and of strings of length L with characters from an unbounded alphabet , i.e., the size of is not bounded by a constant and has to be taken into consideration as a parameter for input size. A closest string s* of is a string that minimizes the maximum of Hamming¹ distance(s, s*) over all string s : s . In contrast, a farthest string t* from maximizes the minimum of Hamming distance(t*,t) over all elements t: t . A distinguisher of from is a string that is close to every string in and far away from any string in . We obtain polynomial time approximation schemes to settle the above problems.     

Estimating population size with truncated sampling

Let X₁, X₂,…,X_n be independent, indentically distributed random variables with density f(x,θ) with respect to a σ-finite measure μ. Let R be a measurable set in the sample space X. The value of X is observable if X ? (X?R) and not otherwise. The number J of observable X’s is binomial, N, Q, Q = 1?P(X ? R). On the basis of J observations, it is desired to estimate N and θ. Estimators considered are conditional and unconditional maximum likelihood and modified maximum likelihood using a prior weight function to modify the likelihood before maximizing. Asymptotic expansions are developed for the [Ncirc]’s of the form [Ncirc] = N + α√N + β + o_p(1), where α and β are random variables. All estimators have the same α, which has mean 0, variance σ² (a function of θ) and is asymptotically normal. Hence all are asymptotically equivalent by the usual limit distributional theory. The β’s differ and Eβ can be considered an “asymptotic bias”. Formulas are developed to compare the asymptotic biases of the various estimators. For a scale parameter family of absolutely continuous distributions with X = (0,∞) and R = (T,∞), special formuli are developed and a best estimator is found.