Local Asymptotic Normality of Ranks and Covariates in Transformation Models

P. J. Bickel and Y. Ritov
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P. J. Bickel: University of California
Y. Ritov: The Hebrew University of Jerusalem

Chapter 3 in Festschrift for Lucien Le Cam, 1997, pp 43-54 from Springer

Abstract: Abstract Le Cam & Yang (1988) addressed broadly the following question: Given observations X (n) = (X1n,…, Xnn) distributed according to P θ (n) ; θ∈R k such that the family of probability measures {P θ (n) ;}has a locally asymptotically normal (LAN) structure at θ0 and a statistic $$ {{Y}^{{\left( n \right)}}} = {{g}_{{\left( n \right)}}}\left( {{{X}^{{\left( n \right)}}}} \right) $$ : (i) (i) When do the distributions of Y(n) also have an LAN structure at θ0? (ii) When is there no loss in information about B in going from X (n) to Y (n)?

Keywords: Transformation Model; Semiparametric Model; Monotone Transformation; Local Asymptotic Normality; Semiparametric Transformation Model (search for similar items in EconPapers)
Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-1880-7_3

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DOI: 10.1007/978-1-4612-1880-7_3

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