Estimation in multiple linear regression Berkson model for processes with uncorrelated increments

This paper presents a method of estimating the regression and variance parameters in the multiple linear regression Berkson model for a continuous-time stochastic process with uncorrelated increments. Under minimal conditions, we establish (i) the Gauss-Markov theorem and the quadratic mean-as well as the strong consistency of the proposed estimate of the regression parameter and (ii) the weak consistency of the proposed estimate of the variance parameter.