Abstract
In this paper we examine some of the statistical properties of the estimate of the solution to a random boundary value problem. We treat an acoustic propagation problem in which part of the boundary data is unknown but is instead measured at discrete points. Non-parametric regression is used to smooth the boundary data, and then the PDE is solved by Fourier series. The bias and variance of this estimate is analyzed and an analysis of the effect of incomplete sampling is given.
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References
Arfken, G. (1970) Mathematical Methods for Physicists, 2nd ed., Academic Press.
Cheney, E. W. (1964) Introduction to Approximation Theory, McGraw-Hill Book Company.
Clay, C. S. and Medwin, H. (1977) Acoustical Oceanography, John Wiley & Sons.
Rice, J. and Rosenblatt, M. (1981) ‘Integrated Mean Squared Error of a Smoothing Spline’, J. Approx. Thy., 33, 4, 353–369.
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© 1993 Springer Science+Business Media Dordrecht
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Hobbs, S.L. (1993). Non-Parametric Estimation and Statistical Properties of an Ocean Acoustic Pressure Field. In: Moura, J.M.F., Lourtie, I.M.G. (eds) Acoustic Signal Processing for Ocean Exploration. NATO ASI Series, vol 388. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1604-6_5
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DOI: https://doi.org/10.1007/978-94-011-1604-6_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4699-2
Online ISBN: 978-94-011-1604-6
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