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Xinjia Chen

Publications and source records attributed to Xinjia Chen.

At least 37 records · Page 2Linked to original sources
arXiv2012

New Sequential Methods for Detecting Portscanners

In this paper, we propose new sequential methods for detecting port-scan attackers which routinely perform random "portscans" of IP addresses to find vulnerable servers to compromise. In addition to rigorously control the probability of falsely implicating benign remote hosts as malicious, our method performs significantly faster than other current solutions. Moreover, our method guarantees that the maximum amount of observational time is bounded. In contrast to the previous most effective method, Threshold Random Walk Algorithm, which is explicit and analytical in nature, our proposed algorithm involve parameters to be determined by numerical methods. We have developed computational techniques such as iterative minimax optimization for quick determination of the parameters of the new detection algorithm. A framework of multi-valued decision for testing portscanners is also proposed.

stat.AP↗
arXiv2012

New Probabilistic Inequalities from Monotone Likelihood Ratio Property

In this paper, we propose a new approach for deriving probabilistic inequalities. Our main idea is to exploit the information of underlying distributions by virtue of the monotone likelihood ratio property and Berry-Essen inequality. Unprecedentedly sharp bounds for the tail probabilities of some common distributions are established.

math.PR↗
arXiv2012

Sequential Tests of Statistical Hypotheses with Confidence Limits

In this paper, we propose a general method for testing composite hypotheses. Our idea is to use confidence limits to define stopping and decision rules. The requirements of operating characteristic function can be satisfied by adjusting the coefficients of the confidence limits. For common distributions, such adjustment can be done via efficient computation by making use of the monotonicity of the associated operating characteristic function. We show that the problem of testing multiple hypotheses can be cast into the general framework of constructing sequential random intervals with prescribed coverage probabilities. We propose an inclusion principle for constructing multistage testing plans. It is demonstrated that our proposed testing plans can be substantially more efficient than the sequential probability ratio test and its variations. We apply our general methodology to develop an exact approach for testing hypotheses regarding the difference of two binomial proportions.

math.ST↗
arXiv2011

Multistage Hypothesis Tests for the Mean of a Normal Distribution

In this paper, we have developed new multistage tests which guarantee prescribed level of power and are more efficient than previous tests in terms of average sampling number and the number of sampling operations. Without truncation, the maximum sampling numbers of our testing plans are absolutely bounded. Based on geometrical arguments, we have derived extremely tight bounds for the operating characteristic function. To reduce the computational complexity for the relevant integrals, we propose adaptive scanning algorithms which are not only useful for present hypothesis testing problem but also for other problem areas.

math.ST↗
arXiv2011

Coverage Probability of Random Intervals

In this paper, we develop a general theory on the coverage probability of random intervals defined in terms of discrete random variables with continuous parameter spaces. The theory shows that the minimum coverage probabilities of random intervals with respect to corresponding parameters are achieved at discrete finite sets and that the coverage probabilities are continuous and unimodal when parameters are varying in between interval endpoints. The theory applies to common important discrete random variables including binomial variable, Poisson variable, negative binomial variable and hypergeometrical random variable. The theory can be used to make relevant statistical inference more rigorous and less conservative.

math.ST↗
arXiv2009

Multistage Estimation of Bounded-Variable Means

In this paper, we develop a multistage approach for estimating the mean of a bounded variable. We first focus on the multistage estimation of a binomial parameter and then generalize the estimation methods to the case of general bounded random variables. A fundamental connection between a binomial parameter and the mean of a bounded variable is established. Our multistage estimation methods rigorously guarantee prescribed levels of precision and confidence.

math.ST↗
arXiv2009

On Estimation of Finite Population Proportion

In this paper, we study the classical problem of estimating the proportion of a finite population. First, we consider a fixed sample size method and derive an explicit sample size formula which ensures a mixed criterion of absolute and relative errors. Second, we consider an inverse sampling scheme such that the sampling is continue until the number of units having a certain attribute reaches a threshold value or the whole population is examined. We have established a simple method to determine the threshold so that a prescribed relative precision is guaranteed. Finally, we develop a multistage sampling scheme for constructing fixed-width confidence interval for the proportion of a finite population. Powerful computational techniques are introduced to make it possible that the fixed-width confidence interval ensures prescribed level of coverage probability.

math.ST↗
arXiv2008

Robust Estimation of Mean Values

In this paper, we develop a computational approach for estimating the mean value of a quantity in the presence of uncertainty. We demonstrate that, under some mild assumptions, the upper and lower bounds of the mean value are efficiently computable via a sample reuse technique, of which the computational complexity is shown to posses a Poisson distribution.

math.ST↗
arXiv2008

A Theory of Truncated Inverse Sampling

In this paper, we have established a new framework of truncated inverse sampling for estimating mean values of non-negative random variables such as binomial, Poisson, hyper-geometrical, and bounded variables. We have derived explicit formulas and computational methods for designing sampling schemes to ensure prescribed levels of precision and confidence for point estimators. Moreover, we have developed interval estimation methods.

math.ST↗
arXiv2008

Exact Computation of Minimum Sample size for Estimation of Poisson Parameters

In this paper, we develop an approach for the exact determination of the minimum sample size for the estimation of a Poisson parameter with prescribed margin of error and confidence level. The exact computation is made possible by reducing infinite many evaluations of coverage probability to finite many evaluations. Such reduction is based on our discovery that the minimum of coverage probability with respect to a Poisson parameter bounded in an interval is attained at a discrete set of finite many values.

math.ST↗
arXiv2008

Order Statistics and Probabilistic Robust Control

Order statistics theory is applied in this paper to probabilistic robust control theory to compute the minimum sample size needed to come up with a reliable estimate of an uncertain quantity under continuity assumption of the related probability distribution. Also, the concept of distribution-free tolerance intervals is applied to estimate the range of an uncertain quantity and extract the information about its distribution. To overcome the limitations imposed by the continuity assumption in the existing order statistics theory, we have derived a cumulative distribution function of the order statistics without the continuity assumption and developed an inequality showing that this distribution has an upper bound which equals to the corresponding distribution when the continuity assumption is satisfied. By applying this inequality, we investigate the minimum computational effort needed to come up with an reliable estimate for the upper bound (or lower bound) and the range of a quantity. We also give conditions, which are much weaker than the absolute continuity assumption, for the existence of such minimum sample size. Furthermore, the issue of making tradeoff between performance level and risk is addressed and a guideline for making this kind of tradeoff is established. This guideline can be applied in general without continuity assumption.

math.OC↗
arXiv2008

Fast Construction of Robustness Degradation Function

We develop a fast algorithm to construct the robustness degradation function, which describes quantitatively the relationship between the proportion of systems guaranteeing the robustness requirement and the radius of the uncertainty set. This function can be applied to predict whether a controller design based on an inexact mathematical model will perform satisfactorily when implemented on the true system.

math.OC↗