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

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.