Systems and Means of Informatics
2021, Volume 31, Issue 4, pp 27-37
DISTRIBUTIONS OF LIKELIHOOD RATIO STATISTICS FOR MONOTONE TREND DETECTION
Abstract
The problem of analyzing a monotonic trend is considered. The model is based on the change in the mean of the normal distribution, for which the distributions of the likelihood ratio statistics are mixtures of chi-square or beta distributions with weights determined through the Stirling numbers of the first kind. The questions of approximation of these distributions are investigated. An effective method for calculating significance criteria by discarding insignificant elements of a mixture is proposed which makes it possible to reduce the complexity of calculations by several orders of magnitude. The issues of expanding the criteria for analyzing the trend of the mean normal distribution to procedures for identifying stochastic ordering are discussed. For these purposes, the authors apply the monotonic trend criterion for the averaged ranks, the statistics of which, in the absence of changes, is distributed as a mixture of chi-square distributions.
The use of a graded assessment structure was of fundamental importance: it was possible not only to obtain original results, but also to ensure the viability of the proposed solutions.
[+] References (9)
- Fitzmaurice, G. M., N. M. Laird, and J. H. Ware. 2011. Applied longitudinal analysis. 2nd ed. Hoboken, NJ: Wiley. 701 p.
- Fernandez, N. B., J. Aiken, and J. T. Smith. 2011. Use of maximal spanning trees and the gamma test of monotone trend in the development and assessment of teams. Procd. Soc. Behv. 26:147-158.
- Roth, M., G. Jongbloed, and A. Buishand. 2019. Monotone trends in the distribution of climate extremes. Theor. Appl. Climatol. 136(3-4): 1175-1184.
- Kliestik, T., K. Valaskova, E. Nica, M. Kovacova, and G. Lazaroiu. 2020. Advanced methods of earnings management: Monotonic trends and change-points under spotlight in the Visegrad countries. Oeconomia Copernicana 11 (2):371-400.
- Barlow, R. Å., D. J. Bartholomew, J. M. Bremmer, and H. D. Brunk. 1972. Statistical inference under order restrictions: The theory and application of isotonic regression. London, New York, Sydney, Toronto: Wiley. 388 ð.
- Krivenko, M.P., and I. V. Mackevich. 1988. Properties of elements of an estimate of monotonous trend. Theor. Probab. Appl. 33(2):316-329.
- Krivenko, M. P., and K. V. Streltsov. 1996. On the distribution of the number of steps in an estimate of monotone trend. Theor. Probab. Appl. 41(1):25-34.
- Chacko, V.J. 1963. Testing homogeneity against ordered alternatives. Ann. Math. Stat. 34(3):945-956.
- Miles, R. E. 1959. The complete amalgamation into blocks, by weighted means, of a finite set of real numbers. Biometrika 46(3):317-327.
[+] About this article
Title
DISTRIBUTIONS OF LIKELIHOOD RATIO STATISTICS FOR MONOTONE TREND DETECTION
Journal
Systems and Means of Informatics
Volume 31, Issue 4, pp 27-37
Cover Date
2021-12-10
DOI
10.14357/08696527210403
Print ISSN
0869-6527
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
monotone trend; likelihood ratio test; nonparametric trend detection; asymptotic distribution; probability distribution approximation
Authors
M. P. Krivenko 
Author Affiliations
Federal Research Center "Computer Science and Control", Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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