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Testing nonparametric statistical functionals with applications to rank tests [J. Statist. Plann. Inference 81 (1999) 71–93]
Journal of Statistical Planning and Inference 92 (2001) 297
www.elsevier.com/locate/jspi
Erratum
Testing nonparametric statistical functionals with applications to rank tests [J. Statist. Plann. Inference 81 (1999) 71–93] Arnold Janssen Mathematical Institute, University of Dusseldorf, D-40225 Dusseldorf, Germany
I am grateful to Prof. Helmut Rieder who pointed out that my recent paper is incomplete and the notation may be misleading whenever the tangent cone is not a linear space. The following modiÿcations cover the remaining case. 1. P. 74. Substitute the last seven lines by: There exists a unique gradient Ę ∈ L02 (P0 ) with smallest L2 (P0 )-norm such that Ä˙ = Ę + (Ä˙ − Ä) ˜ and (Ä˙ − Ä) ˜ is orthogonal with respect to {g − h : g; h ∈ T (P0 ; P)}. Actually, Ę is the orthogonal projection of Ä˙ on the L2 (P0 )-closure of the latter space. 2. In Theorem 3(b), Corollary 3.3, and A(ii), p. 78 the following assumption is needed (which trivially holds for all concrete examples under consideration). Suppose that Ę ∈ T (P0 ; P) holds.
PII of original article: S0378-3758(99)00009-9 E-mail address: [email protected] (A. Janssen)
c 2001 Elsevier Science B.V. All rights reserved. 0378-3758/01/$ - see front matter PII: S 0 3 7 8 - 3 7 5 8 ( 0 0 ) 0 0 0 7 1 - 9
www.elsevier.com/locate/jspi
Erratum
Testing nonparametric statistical functionals with applications to rank tests [J. Statist. Plann. Inference 81 (1999) 71–93] Arnold Janssen Mathematical Institute, University of Dusseldorf, D-40225 Dusseldorf, Germany
I am grateful to Prof. Helmut Rieder who pointed out that my recent paper is incomplete and the notation may be misleading whenever the tangent cone is not a linear space. The following modiÿcations cover the remaining case. 1. P. 74. Substitute the last seven lines by: There exists a unique gradient Ę ∈ L02 (P0 ) with smallest L2 (P0 )-norm such that Ä˙ = Ę + (Ä˙ − Ä) ˜ and (Ä˙ − Ä) ˜ is orthogonal with respect to {g − h : g; h ∈ T (P0 ; P)}. Actually, Ę is the orthogonal projection of Ä˙ on the L2 (P0 )-closure of the latter space. 2. In Theorem 3(b), Corollary 3.3, and A(ii), p. 78 the following assumption is needed (which trivially holds for all concrete examples under consideration). Suppose that Ę ∈ T (P0 ; P) holds.
PII of original article: S0378-3758(99)00009-9 E-mail address: [email protected] (A. Janssen)
c 2001 Elsevier Science B.V. All rights reserved. 0378-3758/01/$ - see front matter PII: S 0 3 7 8 - 3 7 5 8 ( 0 0 ) 0 0 0 7 1 - 9