Quantile/expectile regression, and extreme data analysis

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Outline of this document Outline of this document 1 LMS quantile regression 2 Expectile regression 3 Asymmetric MLE 4 Asymmetric Laplace distribution 5 Extreme value data analysis 6 Concluding remarks © T. W. Yee (University of Auckland) Quantile/expectile regression, and extreme data analysis 18 July 2012 @ Cagliari 2/101 2 / 101
LMS quantile regression Introduction to quantile regression I Some motivation Q: Why quantile regression? A: Because there is no information loss: cdf F contains all the information about a random variable, sometimes the tails are of more interest than in the central area. Applications of quantile regression come from many fields. Here are some. Medical examples include investigating height, weight, body mass index (BMI) as a function of age of the person. Historically, the construction of ‘growth charts’ was probably the first example of age-related reference intervals. Another example is Campbell and Newman (1971)—the ultrasonographic assessment of fetal growth has become clinically routine. © T. W. Yee (University of Auckland) Quantile/expectile regression, and extreme data analysis 18 July 2012 @ Cagliari 3/101 3 / 101
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Page 5 and 6: LMS quantile regression Introductio
Page 7 and 8: LMS quantile regression Growth char
Page 9 and 10: LMS quantile regression Three subcl
Page 11 and 12: LMS quantile regression LMS quantil
Page 13 and 14: LMS quantile regression Using the g
Page 15 and 16: LMS quantile regression Box−Cox t
Page 17 and 18: LMS quantile regression VGAM softwa
Page 19 and 20: LMS quantile regression Cole and Gr
Page 21 and 22: LMS quantile regression Example wit
Page 29 and 30: LMS quantile regression Some Poisso
Page 31 and 32: Expectile regression Interpretation
Page 33 and 34: Expectile regression Expectiles I E
Page 35 and 36: Expectile regression Expectiles III
Page 37 and 38: Expectile regression Interrelations
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Page 41 and 42: Expectile regression Expected short
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Page 45 and 46: Asymmetric MLE Asymmetric MLE II an
Page 47 and 48: Asymmetric MLE ALS notes I Here are
Page 49 and 50: Asymmetric MLE ALS notes III ALS qu
Page 51 and 52: Asymmetric MLE Example II 60 ● 20
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Asymmetric MLE Estimation† An ite
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Asymmetric MLE AML Poisson example
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Asymmetric Laplace distribution Asy
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Asymmetric Laplace distribution Two
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Asymmetric Laplace distribution Exa
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Asymmetric Laplace distribution Exa
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Extreme value data analysis Extreme
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Extreme value data analysis © T. W
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Extreme value data analysis Classic
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Extreme value data analysis GEV II
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Extreme value data analysis GEV IV
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Extreme value data analysis GPD I T
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Extreme value data analysis GPD III
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Extreme value data analysis GPD V F
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Extreme value data analysis GPD VII
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Extreme value data analysis GPD IX
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Extreme value data analysis GPD XI
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Extreme value data analysis The Blo
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Extreme value data analysis The Blo
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Extreme value data analysis 20 15 0
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Extreme value data analysis ● 180
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Extreme value data analysis Number
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Extreme value data analysis To chec
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Extreme value data analysis Finally
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Concluding remarks Concluding remar
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