Time integrated least squares estimators of regression parameters of independent stochastic processes

Industrial processes may be continuously monitored by instruments under control of microprocessors. Thus the data are usually obtained in the form of sets of (continuous) curves over certain time intervals. This paper presents a method of estimating regression parameters in terms of the sample paths from independent stochastic processes. Time integrated least squares estimators of the parameters are obtained which are unbiased, translation invariant, consistent and asymptotically jointly normal. Since technically it is difficult to compute these estimators, using analog-to-digital conversion of continuous processes which are time sampled at regular intervals, optimal approximations of the estimators are considered which are very easily computable and their asymptotic properties are appended.