Comparison of Different Methodologies of Parameter-Estimation From Extreme Values

This letter deals with the case where parameter estimation is required, but only observations of extreme values (i.e., the minimum observed value and/or the maximum observed value per interval) are available. We describe the theoretical grounds of the three leading methodologies of estimation from extremes, discuss the relations between them, and analyze the tradeoffs of the different methodologies with respect to the performance (accuracy), complexity, and robustness of the estimates. We then demonstrate our evaluations via a specially designed simulation, which validates our results.

[1]  Eric P. Smith,et al.  An Introduction to Statistical Modeling of Extreme Values , 2002, Technometrics.

[2]  W. Marsden.  I and J , 2012 .

[3]  Daniel Lemire,et al.  Streaming Maximum-Minimum Filter Using No More than Three Comparisons per Element , 2006, Nord. J. Comput..

[4]  Narayanaswamy Balakrishnan,et al.  Approximate MLEs for the location and scale parameters of the extreme value distribution with censoring , 1991 .

[5]  J. R. Wallis,et al.  Estimation of the generalized extreme-value distribution by the method of probability-weighted moments , 1985 .

[6]  S. Nadarajah,et al.  Extreme Value Distributions: Theory and Applications , 2000 .

[7]  Demetris Koutsoyiannis,et al.  Statistics of extremes and estimation of extreme rainfall: II. Empirical investigation of long rainfall records / Statistiques de valeurs extrêmes et estimation de précipitations extrêmes: II. Recherche empirique sur de longues séries de précipitations , 2004 .

[8]  J. Raynal.  Moment estimators of the GEV distribution for the minima , 2013, Applied Water Science.

[9]  I. J. Myung,et al.  Tutorial on maximum likelihood estimation , 2003 .

[10]  M. Parlange,et al.  Statistics of extremes in hydrology , 2002 .

[11]  R. Jain,et al.  Records , 1973, Tempo.

[12]  J. Hosking.  L‐Moments: Analysis and Estimation of Distributions Using Linear Combinations of Order Statistics , 1990 .

[13]  Enrique Castillo.  Extreme value theory in engineering , 1988 .

[14]  Hagit Messer,et al.  A New Approach to Precipitation Monitoring: A critical survey of existing technologies and challenges , 2015, IEEE Signal Processing Magazine.

[15]  Stuart G. Coles,et al.  Bayesian methods in extreme value modelling: a review and new developments. , 1996 .

[16]  Francisco J. Samaniego,et al.  On estimating population characteristics from record‐breaking observations. i. parametric results , 1988 .

[17]  Jafar Ahmadi,et al.  On the Fisher information in record values , 2001 .

[18]  Jonatan Ostrometzky,et al.  Accumulated Mixed Precipitation Estimation Using Measurements from Multiple Microwave Links , 2015 .

[19]  J. R. Wallis,et al.  Probability weighted moments compared with some traditional techniques in estimating Gumbel Parameters and quantiles , 1979 .

[20]  E. Gumbel,et al.  Statistics of extremes , 1960 .

[21]  Jonatan Ostrometzky,et al.  Accumulated rainfall estimation using maximum attenuation of microwave radio signal , 2014, 2014 IEEE 8th Sensor Array and Multichannel Signal Processing Workshop (SAM).

[22]  L. Haan,et al.  On the block maxima method in extreme value theory: PWM estimators , 2013, 1310.3222.

[23]  Peter I. Corke,et al.  Environmental Wireless Sensor Networks , 2010, Proceedings of the IEEE.

[24]  Hidde Leijnse,et al.  Measuring urban rainfall using microwave links from commercial cellular communication networks , 2011 .

[25]  J. Stedinger,et al.  Generalized maximum‐likelihood generalized extreme‐value quantile estimators for hydrologic data , 2000 .

[26]  Luis R. Pericchi,et al.  Anticipating catastrophes through extreme value modelling , 2003 .

[27]  G. Baskerville,et al.  Rapid Estimation of Heat Accumulation from Maximum and Minimum Temperatures , 1969 .

[28]  Fisher information in record data , 2003 .

[29]  Scott A. Sisson,et al.  A fully probabilistic approach to extreme rainfall modeling , 2003 .

[30]  E. H. Lloyd.  LEAST-SQUARES ESTIMATION OF LOCATION AND SCALE PARAMETERS USING ORDER STATISTICS , 1952 .

[31]  Marco Borga,et al.  Regional frequency analysis of extreme precipitation in the eastern Italian Alps and the August 29, 2003 flash flood , 2007 .

[32]  David Walshaw,et al.  Getting the Most From Your Extreme Wind Data: A Step by Step Guide , 1994, Journal of research of the National Institute of Standards and Technology.

[33]  Jui-pin Wang,et al.  The distribution of annual maximum earthquake magnitude around Taiwan and its application in the estimation of catastrophic earthquake recurrence probability , 2011 .

[34]  Steven Kay,et al.  Fundamentals Of Statistical Signal Processing , 2001 .

[35]  A. Walden,et al.  Maximum likelihood estimation of the parameters of the generalized extreme-value distribution , 1980 .

[36]  B. Arnold,et al.  A first course in order statistics , 2008 .

[37]  Henry D. I. Abarbanel,et al.  Statistics of extreme events with application to climate , 1992 .

[38]  Herbert A. David,et al.  Order Statistics , 2011, International Encyclopedia of Statistical Science.

[39]  Kenneth C. Smith,et al.  Microelectronic circuits, 2nd ed. , 1987 .