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Optimality of AIC in Inference About Brownian Motion

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An Erratum to this article was published on 15 November 2006

Abstract

In the usual Gaussian White-Noise model, we consider the problem of estimating the unknown square-integrable drift function of the standard Brownian motion using the partial sums of its Fourier series expansion generated by an orthonormal basis. Using the squared L 2 distance loss, this problem is known to be the same as estimating the mean of an infinite dimensional random vector with l 2 loss, where the coordinates are independently normally distributed with the unknown Fourier coefficients as the means and the same variance. In this modified version of the problem, we show that Akaike Information Criterion for model selection, followed by least squares estimation, attains the minimax rate of convergence.

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Authors and Affiliations

  1. Applied Statistics Unit, Indian Statistical Institute, 203 B.T. Road, Calcutta, 700108, India

    Arijit Chakrabarti

  2. Department of Statistics, Purdue University, 150 North University Street, West Lafayette, IN, 47907-2067, USA

    Jayanta K. Ghosh

  3. Statistics and Mathematics Unit, Indian Statistical Institute, 203 B.T.Road, Calcutta, 700108, India

    Jayanta K. Ghosh

Authors
  1. Arijit Chakrabarti
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  2. Jayanta K. Ghosh
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Corresponding author

Correspondence to Arijit Chakrabarti.

Additional information

An erratum to this article can be found at http://dx.doi.org/10.1007/s10463-006-0092-2

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Chakrabarti, A., Ghosh, J.K. Optimality of AIC in Inference About Brownian Motion. Ann Inst Stat Math 58, 1–20 (2006). https://doi.org/10.1007/s10463-005-0007-7

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  • DOI: https://doi.org/10.1007/s10463-005-0007-7

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