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Estimating prediction error: cross-validation vs. accumulated prediction error
Umeå universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
Umeå universitet, Samhällsvetenskapliga fakulteten, Statistiska institutionen.
2010 (Engelska)Ingår i: Communications in statistics. Simulation and computation, ISSN 0361-0918, E-ISSN 1532-4141, Vol. 39, nr 5, s. 880-898Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

We study the validation of prediction rules such as regression models and classification algorithms through two out-of-sample strategies, cross-validation and accumulated prediction error. We use the framework of Efron (1983) where measures of prediction errors are defined as sample averages of expected errors and show through exact finite sample calculations that cross-validation and accumulated prediction error yield different smoothing parameter choices in nonparametric regression. The difference in choice does not vanish as sample size increases.

Ort, förlag, år, upplaga, sidor
Informa plc. , 2010. Vol. 39, nr 5, s. 880-898
Nyckelord [en]
Local polynomial regression, Nonparametric regression, Out-of-sample validation, Smoothing parameter
Nationell ämneskategori
Sannolikhetsteori och statistik
Forskningsämne
statistik
Identifikatorer
URN: urn:nbn:se:umu:diva-34149DOI: 10.1080/03610911003650409ISI: 000277568500002Scopus ID: 2-s2.0-77952385264OAI: oai:DiVA.org:umu-34149DiVA, id: diva2:319164
Tillgänglig från: 2010-05-14 Skapad: 2010-05-14 Senast uppdaterad: 2023-03-24Bibliografiskt granskad
Ingår i avhandling
1. Selection of smoothing parameters with application in causal inference
Öppna denna publikation i ny flik eller fönster >>Selection of smoothing parameters with application in causal inference
2011 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
Abstract [en]

This thesis is a contribution to the research area concerned with selection of smoothing parameters in the framework of nonparametric and semiparametric regression. Selection of smoothing parameters is one of the most important issues in this framework and the choice can heavily influence subsequent results. A nonparametric or semiparametric approach is often desirable when large datasets are available since this allow us to make fewer and weaker assumptions as opposed to what is needed in a parametric approach. In the first paper we consider smoothing parameter selection in nonparametric regression when the purpose is to accurately predict future or unobserved data. We study the use of accumulated prediction errors and make comparisons to leave-one-out cross-validation which is widely used by practitioners. In the second paper a general semiparametric additive model is considered and the focus is on selection of smoothing parameters when optimal estimation of some specific parameter is of interest. We introduce a double smoothing estimator of a mean squared error and propose to select smoothing parameters by minimizing this estimator. Our approach is compared with existing methods.The third paper is concerned with the selection of smoothing parameters optimal for estimating average treatment effects defined within the potential outcome framework. For this estimation problem we propose double smoothing methods similar to the method proposed in the second paper. Theoretical properties of the proposed methods are derived and comparisons with existing methods are made by simulations.In the last paper we apply our results from the third paper by using a double smoothing method for selecting smoothing parameters when estimating average treatment effects on the treated. We estimate the effect on BMI of divorcing in middle age. Rich data on socioeconomic conditions, health and lifestyle from Swedish longitudinal registers is used.

Ort, förlag, år, upplaga, sidor
Umeå: Statistiska institutionen, Umeå universitet, 2011. s. 27
Serie
Statistical studies, ISSN 1100-8989 ; 44
Nyckelord
Smoothing parameter selection, Nonparametric regression, Semiparametric additive model, Double smoothing, Causal inference, BMI, Divorce
Nationell ämneskategori
Sannolikhetsteori och statistik
Forskningsämne
statistik
Identifikatorer
urn:nbn:se:umu:diva-39614 (URN)978-91-7459-147-7 (ISBN)
Disputation
2011-03-04, Norra Beteendevetarhuset Hörsal 1031, Umeå universitet, Umeå, 10:15 (Engelska)
Opponent
Handledare
Tillgänglig från: 2011-02-11 Skapad: 2011-02-02 Senast uppdaterad: 2018-06-08Bibliografiskt granskad

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Häggström, Jennyde Luna, Xavier

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Communications in statistics. Simulation and computation
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Totalt: 564 träffar
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