Quantile/expectile regression, and extreme data analysis

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LMS quantile regression lms. functions I > args(lms.bcn) function (percentiles = c(25, 50, 75), zero = c(1, 3), llambda = "identity", lmu = "identity", lsigma = "loge", elambda = list(), emu = list(), esigma = list(), dfmu.init = 4, dfsigma.init = 2, ilambda = 1, isigma = NULL, expectiles = FALSE) NULL > args(lms.bcg) function (percentiles = c(25, 50, 75), zero = c(1, 3), llambda = "identity", lmu = "identity", lsigma = "loge", elambda = list(), emu = list(), esigma = list(), dfmu.init = 4, dfsigma.init = 2, ilambda = 1, isigma = NULL) NULL > args(lms.yjn) function (percentiles = c(25, 50, 75), zero = c(1, 3), llambda = "identity", lsigma = "loge", elambda = list(), esigma = list(), dfmu.init = 4, dfsigma.init = 2, ilambda = 1, isigma = NULL, rule = c(10, 5), yoffset = NULL, diagW = FALSE, iters.diagW = 6) NULL © T. W. Yee (University of Auckland) Quantile/expectile regression, and extreme data analysis 18 July 2012 @ Cagliari 18/101/ 101
LMS quantile regression Cole and Green (1992) advocated estimation by penalized likelihood using splines. Their penalized log-likelihood was n∑ l i − 1 2 λ λ i=1 which is a special case of ∫ {λ ′′ (t) } ∫ 2 1 {µ dt − 2 λ µ ′′ (t) } ∫ 2 1 {σ dt − 2 λ σ ′′ (t) } 2 dt, n∑ i=1 l i − 1 2 p∑ M∑ k=1 j=1 λ (j)k ∫ { f ′′ (j)k (x k)} 2 dxk . (3) This is exactly the VGAM framework! Of the three functions, it is often a good idea to allow µ(x) to be more flexible and/or set λ and σ to be an intercept term only, e.g., s(x2, df = c(1, 4, 1)) or lms.bcn(zero = c(1, 3)). © T. W. Yee (University of Auckland) Quantile/expectile regression, and extreme data analysis 18 July 2012 @ Cagliari 19/101/ 101
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Page 3 and 4: LMS quantile regression Introductio
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
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Page 15 and 16: LMS quantile regression Box−Cox t
Page 17: LMS quantile regression VGAM softwa
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
Page 39 and 40: Expectile regression Interrelations
Page 41 and 42: Expectile regression Expected short
Page 43 and 44: Expectile regression Expected short
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
Page 53 and 54: Asymmetric MLE Estimation† An ite
Page 55 and 56: Asymmetric MLE AML Poisson example
Page 57 and 58: Asymmetric Laplace distribution Asy
Page 59 and 60: Asymmetric Laplace distribution Two
Page 61 and 62: Asymmetric Laplace distribution Exa
Page 63 and 64: Asymmetric Laplace distribution Exa
Page 65 and 66: Extreme value data analysis Extreme
Page 67 and 68: 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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Quantile/expectile regression, and extreme data analysis

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