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Multivariate Probability Density and Regression Functions Estimation of Continuous-Time Stationary Processes from Discrete-Time Data

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Stochastic Processes and Related Topics

Part of the book series: Trends in Mathematics ((TM))

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Abstract

Let be a real-valued continuous-time jointly stationary processes and let tj be a renewal point process on [0,00], with finite mean rate independent of (Y,X). Given the observations and a measurable function, we estimate the multivariate probability density and the regression function of given X(0) = xo, X(T) = XI, …, X(r m ) = x m for arbitrary lags m. We present consistency and asymptotic normality results for appropriate estimates of f and r.

Research partially supported by NSF Grant DMS-97-03876

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Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of California, San Diego, La Jolla, CA, 92093-0407, USA

    Elias Masry

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  1. Elias Masry
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Editor information

Editors and Affiliations

  1. Departments of Mathematics & Statistics, Columbia University, New York, NY, 10027-0010, UK

    Ioannis Karatzas

  2. Department of Mathematics, University of Tennessee, Knoxville, TN, 37996-1300, USA

    Balram S. Rajput

  3. Department of Mathematics, Boston University, Boston, MA, 02215-2411, USA

    Murad S. Taqqu

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To the memory of Stamatis: A lifelong friend, research collaborator, and colleague

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© 1998 Springer Science+Business Media New York

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Masry, E. (1998). Multivariate Probability Density and Regression Functions Estimation of Continuous-Time Stationary Processes from Discrete-Time Data. In: Karatzas, I., Rajput, B.S., Taqqu, M.S. (eds) Stochastic Processes and Related Topics. Trends in Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-2030-5_17

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  • DOI: https://doi.org/10.1007/978-1-4612-2030-5_17

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-7389-9

  • Online ISBN: 978-1-4612-2030-5

  • eBook Packages: Springer Book Archive

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