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Weighted least squares estimates in linear regression models for processes with uncorrelated increments

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  • Wu, Tiee-Jian
  • Wasan, M. T.

Abstract

Due to the advances in computer technology a lot of industrial, biological, and medical processes are continuously monitored by instruments under the control of microprocessors. Thus, our data is a set of curves defined on certain time intervals, i.e., sample paths of continuous-time stochastic processes. The multiple linear regression models with non-random regressors and with error processes having orthogonal increments are considered. Based on the sample path(s) of such process(es) the weighted least-squares estimates of regression parameters and the variance parameter are obtained. For gaining insights of the continuous-time least-squares procedure, the rationale are discussed in details. Furthermore, under minimal conditions, the quadratic mean- as well as the strong-consistency of the estimates are established.

Suggested Citation

  • Wu, Tiee-Jian & Wasan, M. T., 1996. "Weighted least squares estimates in linear regression models for processes with uncorrelated increments," Stochastic Processes and their Applications, Elsevier, vol. 64(2), pages 273-286, November.
    • Handle: RePEc:eee:spapps:v:64:y:1996:i:2:p:273-286
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    References listed on IDEAS

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    Cited by:

    1. Henderson, D. & Kovalenko, A. & Pizio, O. & Wasan, D., 1997. "The effective interaction between colloidal hard sphere particles in a polymerizing solvent. Application of Wertheim's theory of association," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 276-296.
    2. Ibarrola, P. & Pérez-Palomares, A., 2003. "Linear sufficiency and linear admissibility in a continuous time Gauss-Markov model," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 315-327, November.

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