Asymptotic results for jump probabilities associated to the multiple scan statistic

2017 ◽  
Vol 70 (5) ◽  
pp. 951-968 ◽  
Author(s):  
Markos V. Koutras ◽  
Demetrios P. Lyberopoulos
Keyword(s):  
Scan Statistic ◽  
Asymptotic Results ◽  
Multiple Scan

Asymptotic results for the multiple scan statistic

2017 ◽  
Vol 54 (1) ◽  
pp. 320-330 ◽  
Author(s):  
M. V. Boutsikas ◽  
M. V. Koutras ◽  
F. S. Milienos
Keyword(s):  
Random Walk ◽  
Real Life ◽  
Poisson Approximation ◽  
Scan Statistics ◽  
Bernoulli Trials ◽  
Scan Statistic ◽  
Asymptotic Results ◽  
Compound Poisson Approximation ◽  
Multiple Scan ◽  
Random Walk Theory

AbstractThe contribution of the theory of scan statistics to the study of many real-life applications has been rapidly expanding during the last decades. The multiple scan statistic, defined on a sequence of n Bernoulli trials, enumerates the number of occurrences of k consecutive trials which contain at least r successes among them (r≤k≤n). In this paper we establish some asymptotic results for the distribution of the multiple scan statistic, as n,k,r→∞ and illustrate their accuracy through a simulation study. Our approach is based on an appropriate combination of compound Poisson approximation and random walk theory.

scholarly journals On the asymptotic distribution of the discrete scan statistic

2006 ◽  
Vol 43 (04) ◽  
pp. 1137-1154 ◽  
Author(s):  
Michael V. Boutsikas ◽  
Markos V. Koutras
Keyword(s):  
Quality Control ◽  
Molecular Biology ◽  
Null Hypothesis ◽  
Success Probability ◽  
Poisson Approximation ◽  
Scan Statistic ◽  
Asymptotic Results ◽  
Compound Poisson Approximation ◽  
Extreme Value Theorem ◽  
Positive Integers

The discrete scan statistic in a binary (0-1) sequence of n trials is defined as the maximum number of successes within any k consecutive trials (n and k, n ≥ k, being two positive integers). It has been used in many areas of science (quality control, molecular biology, psychology, etc.) to test the null hypothesis of uniformity against a clustering alternative. In this article we provide a compound Poisson approximation and subsequently use it to establish asymptotic results for the distribution of the discrete scan statistic as n, k → ∞ and the success probability of the trials is kept fixed. An extreme value theorem is also provided for the celebrated Erdős-Rényi statistic.

scholarly journals On the asymptotic distribution of the discrete scan statistic

2006 ◽  
Vol 43 (4) ◽  
pp. 1137-1154 ◽  
Author(s):  
Michael V. Boutsikas ◽  
Markos V. Koutras
Keyword(s):  
Quality Control ◽  
Molecular Biology ◽  
Null Hypothesis ◽  
Success Probability ◽  
Poisson Approximation ◽  
Scan Statistic ◽  
Asymptotic Results ◽  
Compound Poisson Approximation ◽  
Extreme Value Theorem ◽  
Positive Integers

The discrete scan statistic in a binary (0-1) sequence of n trials is defined as the maximum number of successes within any k consecutive trials (n and k, n ≥ k, being two positive integers). It has been used in many areas of science (quality control, molecular biology, psychology, etc.) to test the null hypothesis of uniformity against a clustering alternative. In this article we provide a compound Poisson approximation and subsequently use it to establish asymptotic results for the distribution of the discrete scan statistic as n, k → ∞ and the success probability of the trials is kept fixed. An extreme value theorem is also provided for the celebrated Erdős-Rényi statistic.

Asymptotic for LS estimators in the EV regression model for dependent errors

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4845-4856
Author(s):  
Konrad Furmańczyk
Keyword(s):  
Regression Model ◽  
Functional Dependence ◽  
Dependent Data ◽  
Errors In Variables ◽  
Mixing Conditions ◽  
Asymptotic Results ◽  
Dependence Measure ◽  
Wide Range ◽  
Ev Regression Model ◽  
Linear And Nonlinear

We study consistency and asymptotic normality of LS estimators in the EV (errors in variables) regression model under weak dependent errors that involve a wide range of linear and nonlinear time series. In our investigations we use a functional dependence measure of Wu [16]. Our results without mixing conditions complete the known asymptotic results for independent and dependent data obtained by Miao et al. [7]-[10].

Standard Asymptotic Theory

2017 ◽  
Author(s):  
Russell Cheng
Keyword(s):  
Asymptotic Theory ◽  
Asymptotic Variance ◽  
Statistical Significance ◽  
Regularity Conditions ◽  
Parameter Estimates ◽  
Asymptotic Results ◽  
Ml Estimation ◽  
True Parameter ◽  
Log Likelihood ◽  
Ml Estimator

This book relies on maximum likelihood (ML) estimation of parameters. Asymptotic theory assumes regularity conditions hold when the ML estimator is consistent. Typically an additional third derivative condition is assumed to ensure that the ML estimator is also asymptotically normally distributed. Standard asymptotic results that then hold are summarized in this chapter; for example, the asymptotic variance of the ML estimator is then given by the Fisher information formula, and the log-likelihood ratio, the Wald and the score statistics for testing the statistical significance of parameter estimates are all asymptotically equivalent. Also, the useful profile log-likelihood then behaves exactly as a standard log-likelihood only in a parameter space of just one dimension. Further, the model can be reparametrized to make it locally orthogonal in the neighbourhood of the true parameter value. The large exponential family of models is briefly reviewed where a unified set of regular conditions can be obtained.

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