Log-likelihood ratio test for detecting transient change

The limit behaviour of scan statistics in a form of maxima of moving sum processes with changing window size for detecting a transient change is studied. Approximate critical values obtained from tail behaviour of the limit variables that are maxima of some locally homogeneous Gaussian fields are compared with critical values obtained by simulation.     

New families of estimators and test statistics in log-linear models

In this paper we consider categorical data that are distributed according to a multinomial, product-multinomial or Poisson distribution whose expected values follow a log-linear model and we study the inference problem of hypothesis testing in a log-linear model setting. The family of test statistics considered is based on the family of ?-divergence measures. The unknown parameters in the log-linear model under consideration are also estimated using ?-divergence measures: Minimum ?-divergence estimators. A simulation study is included to find test statistics that offer an attractive alternative to the Pearson chi-square and likelihood-ratio test statistics.     

A CUSUM test for detecting change in the transfer functions of open loop stochastic systems

A cumulative sum test for detecting change in the transfer function of open loop stochastic systems is proposed. The test is based on the logarithmic transformation of the “evolutionary gain-spectra” estimate. A design relation between the band width parameters of the evolutionary spectral density estimate and the average run length of the cumulative sum test is obtained. This cumulative sum technique has been applied to four simulated systems, one of which is completely time invariant and the other remaining three had change points at different time points.     

Monitoring parameter change in AR(p) time series models

Sequential tests that are generalizations of Page’s CUSUM tests are proposed for detecting an abrupt change in any parameter, or in any collection of parameters of an autoregressive time series model. These tests accommodate nuisance parameters. They are based on large sample approximations to the efficient score vector under the null hypothesis of no change and under the alternative. The empirical power of the tests is evaluated in a simulation study. The new method performs better than the existing ones found in the literature if the criterion is the type I error probability, which can be unacceptably high for methods that minimize the expected value of the reaction time.     

Completely periodic directions and orbit closures of many pseudo-Anosov Teichmueller discs in Q(1,1,1,1)

In this paper, we investigate the closure of a large class of Teichmüller discs in the stratum Q(1, 1, 1, 1){\mathcal{Q}(1, 1, 1, 1)} or equivalently, in a GL⁺₂(\mathbbR){{\rm GL}^+_2(\mathbb{R})} -invariant locus L{\mathcal{L}} of translation surfaces of genus three. We describe a systematic way to prove that the GL⁺₂(\mathbbR){{\rm GL}^+_2(\mathbb{R})} -orbit closure of a translation surface in L{\mathcal{L}} is the whole locus L{\mathcal{L}} . The strategy of the proof is an analysis of completely periodic directions on such a surface and an iterated application of Ratner’s theorem to unipotent subgroups acting on an “adequate” splitting. This analysis applies for example to all Teichmüller discs obtained by the Thurston–Veech’s construction with a trace field of degree three which are moreover “obviously not Veech”. We produce an infinite series of such examples and show moreover that the favourable splitting situation does not arise everywhere on L{\mathcal{L}} , contrary to the situation in genus two. We also study completely periodic directions on translation surfaces in L{\mathcal{L}} . For instance, we prove that completely periodic directions are dense on surfaces obtained by the Thurston–Veech’s construction.     

An adaptation of Page’s CUSUM test for change detection

Summary Page’s CUSUM test for detecting change in a sequence of independent observations is extended to the general parametric model involving nuisance parameters. The test statistic is the standardized efficient score vector. The model of nested random effects is analyzed in detail.     

Asymptotic laws for disparity statistics in product multinomial models

The paper presents asymptotic distributions of φ-disparity goodness-of-fit statistics in product multinomial models, under hypotheses and alternatives assuming sparse and nonsparse cell frequencies. The φ-disparity statistics include the power divergences of Read and Cressie (Goodness-of-fit Statistics for Discrete Multivariate Data, Springer, New York, 1988), the φ-divergences of Ciszár (Studia Sci. Math. Hungar. 2 (1967) 299) and the robust goodness of fit statistics of Lindsay (Ann. Statist. 22 (1994) 1081).     

On the cusum of squares test for variance change in nonstationary and nonparametric time series models

In this paper we consider the problem of testing for a variance change in nonstationary and nonparametric time series models. The models under consideration are the unstable AR(q) model and the fixed design nonparametric regression model with a strong mixing error process. In order to perform a test, we employ the cusum of squares test introduced by Inclán and Tiao (1994,J. Amer. Statist. Assoc.,89, 913–923). It is shown that the limiting distribution of the test statistic is the sup of a standard Brownian bridge as seen in iid random samples. Simulation results are provided for illustration.     

Asymptotics of Bonferroni for dependent normal test statistics

The Bonferroni adjustment is sometimes used to control the familywise error rate (FWE) when the number of comparisons is huge. In genome wide association studies, researchers compare cases to controls with respect to thousands of single nucleotide polymorphisms. It has been claimed that the Bonferroni adjustment is only slightly conservative if the comparisons are nearly independent. We show that the veracity of this claim depends on how one defines “nearly”. Specifically, if the test statistics’ pairwise correlations converge to 0 as the number of tests tend to ∞, the conservatism of the Bonferroni procedure depends on their rate of convergence. The type I error rate of Bonferroni can tend to 0 or 1−exp(−α)≈α, depending on that rate. We show using elementary probability theory what happens to the distribution of the number of errors when using Bonferroni, as the number of dependent normal test statistics gets large. We also use the limiting behavior of Bonferroni to shed light on properties of other commonly used test statistics.     

An experimental test of alternative models of bidding in ascending auctions

The theory and behavior of the clock version of the ascending auction has been well understood for at least 20 years. The more widely used oral outcry version of the ascending auction that allows bidders to submit their own bids has been the subject of some recent controversy mostly in regard to whether or not jump bidding, i.e. bidders submitting bids higher than required by the auctioneer, should be allowed. Isaac, Salmon & Zillante (2005) shows that the standard equilibrium for the clock auction does not apply to the non-clock format and constructs an equilibrium bid function intended to match with field data on ascending auctions. In this study, we will use economic experiments to provide a direct empirical test of that model while simultaneously providing empirical evidence to resolve the policy disputes centered around the place of jump bidding in ascending auctions.Received: March 2005The authors would like to thank Florida State University for providing the funding for the experiments in this paper and Bradley Andrews for programming assistance.     

Development of effective algorithms for detecting breakdowns in models of systems

For a linear dynamic system with undetermined parameters we discuss the construction of algorithms and programs to exhibit breakdown criteria for breakdowns using Kalman filtering and sequential statistical analysis. Translated fromAlgoritmy Upravleniya i Identifikatsii, pp. 118–128, 1997.     

Using algebraic models of programs for detecting metamorphic malwares

Polymorphic and metamorphic viruses are the most sophisticated malicious programs that give a lot of trouble to virus scanners. Each time when these viruses infect new executables or replicate themselves, they completely modify (obfuscate) their signature to avoid being detected. This contrivance poses a serious threat to antivirus software that relies on classical virus-detection techniques: such viruses do not have any stable specific sequence of instructions that one looks for. In the ultimate case, the only characteristic that remains invariable for all generations of the same virus is their functionality (semantics). To all appearance, the only way to detect for sure a metamorphic malicious code is to look for a pattern that has the same semantics as (i.e., equivalent to) some representative sample of the virus. Thus, metamorphic virus detection is closely related to the equivalence-checking problem for programs. In this paper, we outline some new automata-theoretic framework for the designing of virus detectors. Our approach is based on the equivalence-checking techniques in algebraic models of sequential programs. An algebraic model of programs is an abstract model of computation, where programs are viewed as finite automata operating on Kripke structures. Models of this kind make it possible to focus on those properties of program instructions that are widely used in obfuscating transformations. We give a survey (including the latest results) on the complexity of equivalence-checking problem in various algebraic models of programs and estimate thus the resilience of some obfuscating transformation commonly employed by metamorphic viruses.     

APPROXIMATE POWER OF HETEROSCEDASTICITY TEST IN NONLINEAR MODELS WITH ARIMA（0,1,0） ERRORS

This paper presents an approach for estimating power of the score test, based on an asymptotic approximation to the power of the score test under contiguous alternatives. The method is applied to the problem of power calculations for the score test of heteroscedasticity in European rabbit data （Ratkowsky, 1983）. Simulation studies are presented which indicate that the asymptotic approximation to the finite-sample situation is good over a wide range of parameter configurations.     

Lower bounds for the distributions of certain multivariate test statistics

A lower (upper) bound is given for the distribution of each d_j, j = k + 1, …, p (j = 1, …, s), the jth latent root of AB^?1, where A and B are independent noncentral and central Wishart matrices having $\text{W}{}_{\mathrm{p}}\text{(q, Σ; Ω)}$ with rank $\text{(Ω) ≤ k = p ? s}$ and W_p(n, Σ), respectively. Similar bound are also given for the distributions of noncentral means and canonical correlations. The results are applied to obtain lower bounds for the null distributions of some multivariate test statistics in Tintner's model, MANOVA and canonical analysis.     

Asymptotic properties of pseudo maximum likelihood estimators and test in semi-parametric copula models with multiple change points

The main purpose of the present paper is to establish the asymptotic properties of pseudo maximum likelihood estimators of the parameters of a multiple change-point model in the multivariate copula models when marginal distributions are unspecified but the copula function is parametrized. A pseudo likelihood ratio-type statistic is proposed for testing a sequence of observations for no change in the copula parameter against possible changes. Finally, a weighted bootstrap procedure that aims at evaluating the limiting distributions is examined.     

A sign test for detecting the equivalence of Sylvester Hadamard matrices

In this paper we show that every matrix in the class of Sylvester Hadamard matrices of order 2 ^k under H-equivalence can have full row and column sign spectrum, meaning that tabulating the numbers of sign interchanges along any row (or column) gives all integers 0,1,...,2 ^k  − 1 in some order. The construction and properties of Yates Hadamard matrices are presented and is established their equivalence with the Sylvester Hadamard matrices of the same order. Finally, is proved that every normalized Hadamard matrix has full column or row sign spectrum if and only if is H-equivalent to a Sylvester Hadamard matrix. This provides us with an efficient criterion identifying the equivalence of Sylvester Hadamard matrices.     

A test for detecting the outlying observations in a multivariate normal family

One presents a test for the detection of outlaying observations in the multivariate normal case; it is a generalization of a test due to Bol'shev [1], intended for the one-dimensional case.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 97, pp. 176–180, 1980.     

Robust test for structural instability in dynamic factor models

Annals of the Institute of Statistical Mathematics - In this paper, we consider a robust test for structural breaks in dynamic factor models. The proposed framework considers structural changes...