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

Tiee-Jian Wu and M. T. Wasan

Stochastic Processes and their Applications, 1996, vol. 64, issue 2, 273-286

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.

Keywords: Continuous-time multiple linear regression Stochastic processes with orthogonal increments Gauss-Markov theorem; consistency (search for similar items in EconPapers)
Date: 1996
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