Significance thresholds of onesided tests for means of bivariate normally distributed variables

Tests at hypotheses on the expectation vaiues ot normally distributed bivdriaU random variables, which arc based on single component tests, require the determination of the relation between the single significance thresholds and the overall error of the first kind probability. It is shown that a simple approximation can be applied to negatively correlated variables even if only the ratio of the variances is known. Numerical calculations are presented for the general case. Two examples are given.     

Estimation of a nonparametric regression spectrum for multivariate time series

Estimation of a nonparametric regression spectrum based on the periodogram is considered. Neither trend estimation nor smoothing of the periodogram is required. Alternatively, for cases where spectral estimation of phase shifts fails and the shift does not depend on frequency, a time domain estimator of the lag-shift is defined. Asymptotic properties of the frequency and time domain estimators are derived. Simulations and a data example illustrate the methods.     

Detection of intrusions in information systems by sequential change-point methods

Sequential multi-chart detection procedures for detecting changes in multichannel sensor systems are developed. In the case of complete information on pre-change and post-change distributions, the detection algorithm represents a likelihood ratio-based multichannel generalization of Page’s cumulative sum (CUSUM) test that is applied to general stochastic models that may include correlated and nonstationary observations. There are many potential application areas where it is necessary to consider multichannel generalizations and general statistical models. In this paper our main motivation for doing so is network security: rapid anomaly detection for an early detection of attacks in computer networks that lead to changes in network traffic. Moreover, this kind of application encourages the development of a nonparametric multichannel detection test that does not use exact pre-change (legitimate) and post-change (attack) traffic models. The proposed nonparametric method can be effectively applied to detect a wide variety of attacks such as denial-of-service attacks, worm-based attacks, port-scanning, and man-in-the-middle attacks. In addition, we propose a multichannel CUSUM procedure that is based on binary quantized data; this procedure turns out to be more efficient than the previous two algorithms in certain scenarios. All proposed detection algorithms are based on the change-point detection theory. They utilize the thresholding of test statistics to achieve a fixed rate of false alarms, while allowing changes in statistical models to be detected “as soon as possible”. Theoretical frameworks for the performance analysis of detection procedures, as well as results of Monte Carlo simulations for a Poisson example and results of detecting real flooding attacks, are presented.     

Procedures for investigating outliers when estimating in the general univariate linear situation-nonfull rank case

This paper is a continuation of GGD = Golub, Guttman and Dutter (1973) and DG = Dutter and Guttman (1974a), and will deal with the problem of how to handle outliers in the general univariate linear model situation y = Xθ + ?, ? = N(0, σ²I).when X is not of full rank, and where interest is in the estimation of τ = Bθ, where τ is assumed to be estimable. The special case B = X, that is, interest is in η = Xθ, is discussed.