A rate of convergence for the set compound estimation in a family of certain retracted distributions
Summary This paper is concerned with the set compound squared-error loss estimation problem. Here, the author obtains Lévy consistent estimate$$\hat G_n $$ of the empiric distributionGn of the parameters $ θ_{1} $,...,$ θ_{n} $ for a more general family of retracted distributions on the interval [θ,...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Nogami, Yoshiko [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1982 |
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| Schlagwörter: |
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| Anmerkung: |
© The Institute of Statistical Mathematics, Tokyo 1982 |
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| Übergeordnetes Werk: |
Enthalten in: Annals of the Institute of Statistical Mathematics - Kluwer Academic Publishers-Plenum Publishers, 1949, 34(1982), 2 vom: 01. Dez., Seite 241-257 |
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| Übergeordnetes Werk: |
volume:34 ; year:1982 ; number:2 ; day:01 ; month:12 ; pages:241-257 |
| Links: |
|---|
| DOI / URN: |
10.1007/BF02481025 |
|---|
| Katalog-ID: |
OLC2071676815 |
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| 520 | |a Summary This paper is concerned with the set compound squared-error loss estimation problem. Here, the author obtains Lévy consistent estimate$$\hat G_n $$ of the empiric distributionGn of the parameters $ θ_{1} $,...,$ θ_{n} $ for a more general family of retracted distributions on the interval [θ, θ+1) than the uniform on [θ, θ+1) as in R. Fox (1970,Ann. Math. Statist.,41, 1845–1852; 1978,Ann. Statist.,6, 846–853) and exhibits a decision procedure based on$$\hat G_n $$ with a convergence rateO((n−1 logn)1/4) for the mofified regret uniformly in ($ θ_{1} $, $ θ_{2} $, ..., $ θ_{n} $ ∈ $ Ω^{n} $ with bounded Ω. The author also gives a counterexample to the convergence of the modified regret for Ω=(−∞, ∞). | ||
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10.1007/BF02481025 doi (DE-627)OLC2071676815 (DE-He213)BF02481025-p DE-627 ger DE-627 rakwb eng 510 VZ Nogami, Yoshiko verfasserin aut A rate of convergence for the set compound estimation in a family of certain retracted distributions 1982 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Institute of Statistical Mathematics, Tokyo 1982 Summary This paper is concerned with the set compound squared-error loss estimation problem. Here, the author obtains Lévy consistent estimate$$\hat G_n $$ of the empiric distributionGn of the parameters $ θ_{1} $,...,$ θ_{n} $ for a more general family of retracted distributions on the interval [θ, θ+1) than the uniform on [θ, θ+1) as in R. Fox (1970,Ann. Math. Statist.,41, 1845–1852; 1978,Ann. Statist.,6, 846–853) and exhibits a decision procedure based on$$\hat G_n $$ with a convergence rateO((n−1 logn)1/4) for the mofified regret uniformly in ($ θ_{1} $, $ θ_{2} $, ..., $ θ_{n} $ ∈ $ Ω^{n} $ with bounded Ω. The author also gives a counterexample to the convergence of the modified regret for Ω=(−∞, ∞). Decision Procedure Lipschitz Condition Empiric Distribution Function Component Procedure Component Problem Enthalten in Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers-Plenum Publishers, 1949 34(1982), 2 vom: 01. Dez., Seite 241-257 (DE-627)129934658 (DE-600)390313-8 (DE-576)015492907 0020-3157 nnns volume:34 year:1982 number:2 day:01 month:12 pages:241-257 https://doi.org/10.1007/BF02481025 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_24 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2012 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4305 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4316 GBV_ILN_4323 GBV_ILN_4324 AR 34 1982 2 01 12 241-257 |
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10.1007/BF02481025 doi (DE-627)OLC2071676815 (DE-He213)BF02481025-p DE-627 ger DE-627 rakwb eng 510 VZ Nogami, Yoshiko verfasserin aut A rate of convergence for the set compound estimation in a family of certain retracted distributions 1982 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Institute of Statistical Mathematics, Tokyo 1982 Summary This paper is concerned with the set compound squared-error loss estimation problem. Here, the author obtains Lévy consistent estimate$$\hat G_n $$ of the empiric distributionGn of the parameters $ θ_{1} $,...,$ θ_{n} $ for a more general family of retracted distributions on the interval [θ, θ+1) than the uniform on [θ, θ+1) as in R. Fox (1970,Ann. Math. Statist.,41, 1845–1852; 1978,Ann. Statist.,6, 846–853) and exhibits a decision procedure based on$$\hat G_n $$ with a convergence rateO((n−1 logn)1/4) for the mofified regret uniformly in ($ θ_{1} $, $ θ_{2} $, ..., $ θ_{n} $ ∈ $ Ω^{n} $ with bounded Ω. The author also gives a counterexample to the convergence of the modified regret for Ω=(−∞, ∞). Decision Procedure Lipschitz Condition Empiric Distribution Function Component Procedure Component Problem Enthalten in Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers-Plenum Publishers, 1949 34(1982), 2 vom: 01. Dez., Seite 241-257 (DE-627)129934658 (DE-600)390313-8 (DE-576)015492907 0020-3157 nnns volume:34 year:1982 number:2 day:01 month:12 pages:241-257 https://doi.org/10.1007/BF02481025 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_24 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2012 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4305 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4316 GBV_ILN_4323 GBV_ILN_4324 AR 34 1982 2 01 12 241-257 |
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10.1007/BF02481025 doi (DE-627)OLC2071676815 (DE-He213)BF02481025-p DE-627 ger DE-627 rakwb eng 510 VZ Nogami, Yoshiko verfasserin aut A rate of convergence for the set compound estimation in a family of certain retracted distributions 1982 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Institute of Statistical Mathematics, Tokyo 1982 Summary This paper is concerned with the set compound squared-error loss estimation problem. Here, the author obtains Lévy consistent estimate$$\hat G_n $$ of the empiric distributionGn of the parameters $ θ_{1} $,...,$ θ_{n} $ for a more general family of retracted distributions on the interval [θ, θ+1) than the uniform on [θ, θ+1) as in R. Fox (1970,Ann. Math. Statist.,41, 1845–1852; 1978,Ann. Statist.,6, 846–853) and exhibits a decision procedure based on$$\hat G_n $$ with a convergence rateO((n−1 logn)1/4) for the mofified regret uniformly in ($ θ_{1} $, $ θ_{2} $, ..., $ θ_{n} $ ∈ $ Ω^{n} $ with bounded Ω. The author also gives a counterexample to the convergence of the modified regret for Ω=(−∞, ∞). Decision Procedure Lipschitz Condition Empiric Distribution Function Component Procedure Component Problem Enthalten in Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers-Plenum Publishers, 1949 34(1982), 2 vom: 01. Dez., Seite 241-257 (DE-627)129934658 (DE-600)390313-8 (DE-576)015492907 0020-3157 nnns volume:34 year:1982 number:2 day:01 month:12 pages:241-257 https://doi.org/10.1007/BF02481025 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_24 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2012 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4305 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4316 GBV_ILN_4323 GBV_ILN_4324 AR 34 1982 2 01 12 241-257 |
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10.1007/BF02481025 doi (DE-627)OLC2071676815 (DE-He213)BF02481025-p DE-627 ger DE-627 rakwb eng 510 VZ Nogami, Yoshiko verfasserin aut A rate of convergence for the set compound estimation in a family of certain retracted distributions 1982 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Institute of Statistical Mathematics, Tokyo 1982 Summary This paper is concerned with the set compound squared-error loss estimation problem. Here, the author obtains Lévy consistent estimate$$\hat G_n $$ of the empiric distributionGn of the parameters $ θ_{1} $,...,$ θ_{n} $ for a more general family of retracted distributions on the interval [θ, θ+1) than the uniform on [θ, θ+1) as in R. Fox (1970,Ann. Math. Statist.,41, 1845–1852; 1978,Ann. Statist.,6, 846–853) and exhibits a decision procedure based on$$\hat G_n $$ with a convergence rateO((n−1 logn)1/4) for the mofified regret uniformly in ($ θ_{1} $, $ θ_{2} $, ..., $ θ_{n} $ ∈ $ Ω^{n} $ with bounded Ω. The author also gives a counterexample to the convergence of the modified regret for Ω=(−∞, ∞). Decision Procedure Lipschitz Condition Empiric Distribution Function Component Procedure Component Problem Enthalten in Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers-Plenum Publishers, 1949 34(1982), 2 vom: 01. Dez., Seite 241-257 (DE-627)129934658 (DE-600)390313-8 (DE-576)015492907 0020-3157 nnns volume:34 year:1982 number:2 day:01 month:12 pages:241-257 https://doi.org/10.1007/BF02481025 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_24 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2012 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4305 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4316 GBV_ILN_4323 GBV_ILN_4324 AR 34 1982 2 01 12 241-257 |
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10.1007/BF02481025 doi (DE-627)OLC2071676815 (DE-He213)BF02481025-p DE-627 ger DE-627 rakwb eng 510 VZ Nogami, Yoshiko verfasserin aut A rate of convergence for the set compound estimation in a family of certain retracted distributions 1982 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Institute of Statistical Mathematics, Tokyo 1982 Summary This paper is concerned with the set compound squared-error loss estimation problem. Here, the author obtains Lévy consistent estimate$$\hat G_n $$ of the empiric distributionGn of the parameters $ θ_{1} $,...,$ θ_{n} $ for a more general family of retracted distributions on the interval [θ, θ+1) than the uniform on [θ, θ+1) as in R. Fox (1970,Ann. Math. Statist.,41, 1845–1852; 1978,Ann. Statist.,6, 846–853) and exhibits a decision procedure based on$$\hat G_n $$ with a convergence rateO((n−1 logn)1/4) for the mofified regret uniformly in ($ θ_{1} $, $ θ_{2} $, ..., $ θ_{n} $ ∈ $ Ω^{n} $ with bounded Ω. The author also gives a counterexample to the convergence of the modified regret for Ω=(−∞, ∞). Decision Procedure Lipschitz Condition Empiric Distribution Function Component Procedure Component Problem Enthalten in Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers-Plenum Publishers, 1949 34(1982), 2 vom: 01. Dez., Seite 241-257 (DE-627)129934658 (DE-600)390313-8 (DE-576)015492907 0020-3157 nnns volume:34 year:1982 number:2 day:01 month:12 pages:241-257 https://doi.org/10.1007/BF02481025 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_24 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2012 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4305 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4316 GBV_ILN_4323 GBV_ILN_4324 AR 34 1982 2 01 12 241-257 |
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A rate of convergence for the set compound estimation in a family of certain retracted distributions |
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A rate of convergence for the set compound estimation in a family of certain retracted distributions |
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Nogami, Yoshiko |
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Annals of the Institute of Statistical Mathematics |
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1982 |
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Nogami, Yoshiko |
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Aufsätze |
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Nogami, Yoshiko |
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10.1007/BF02481025 |
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510 |
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a rate of convergence for the set compound estimation in a family of certain retracted distributions |
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A rate of convergence for the set compound estimation in a family of certain retracted distributions |
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Summary This paper is concerned with the set compound squared-error loss estimation problem. Here, the author obtains Lévy consistent estimate$$\hat G_n $$ of the empiric distributionGn of the parameters $ θ_{1} $,...,$ θ_{n} $ for a more general family of retracted distributions on the interval [θ, θ+1) than the uniform on [θ, θ+1) as in R. Fox (1970,Ann. Math. Statist.,41, 1845–1852; 1978,Ann. Statist.,6, 846–853) and exhibits a decision procedure based on$$\hat G_n $$ with a convergence rateO((n−1 logn)1/4) for the mofified regret uniformly in ($ θ_{1} $, $ θ_{2} $, ..., $ θ_{n} $ ∈ $ Ω^{n} $ with bounded Ω. The author also gives a counterexample to the convergence of the modified regret for Ω=(−∞, ∞). © The Institute of Statistical Mathematics, Tokyo 1982 |
| abstractGer |
Summary This paper is concerned with the set compound squared-error loss estimation problem. Here, the author obtains Lévy consistent estimate$$\hat G_n $$ of the empiric distributionGn of the parameters $ θ_{1} $,...,$ θ_{n} $ for a more general family of retracted distributions on the interval [θ, θ+1) than the uniform on [θ, θ+1) as in R. Fox (1970,Ann. Math. Statist.,41, 1845–1852; 1978,Ann. Statist.,6, 846–853) and exhibits a decision procedure based on$$\hat G_n $$ with a convergence rateO((n−1 logn)1/4) for the mofified regret uniformly in ($ θ_{1} $, $ θ_{2} $, ..., $ θ_{n} $ ∈ $ Ω^{n} $ with bounded Ω. The author also gives a counterexample to the convergence of the modified regret for Ω=(−∞, ∞). © The Institute of Statistical Mathematics, Tokyo 1982 |
| abstract_unstemmed |
Summary This paper is concerned with the set compound squared-error loss estimation problem. Here, the author obtains Lévy consistent estimate$$\hat G_n $$ of the empiric distributionGn of the parameters $ θ_{1} $,...,$ θ_{n} $ for a more general family of retracted distributions on the interval [θ, θ+1) than the uniform on [θ, θ+1) as in R. Fox (1970,Ann. Math. Statist.,41, 1845–1852; 1978,Ann. Statist.,6, 846–853) and exhibits a decision procedure based on$$\hat G_n $$ with a convergence rateO((n−1 logn)1/4) for the mofified regret uniformly in ($ θ_{1} $, $ θ_{2} $, ..., $ θ_{n} $ ∈ $ Ω^{n} $ with bounded Ω. The author also gives a counterexample to the convergence of the modified regret for Ω=(−∞, ∞). © The Institute of Statistical Mathematics, Tokyo 1982 |
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A rate of convergence for the set compound estimation in a family of certain retracted distributions |
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