An Extension of the Gauss-Markov Theorem for Mixed Linear Regression Models with Non-Stationary Stochastic Parameters
The presence of fixed and stochastic parameters in a mixed linear regression model has been dealt with for the case where the stochastic parameters follow a stationary process. The solution is given either by Generalized Least Squares (e.g. Rao, 1965, p. 192) or by a recursive state space estimation procedure such as the Kalman filter and smoother (e.g. Sallas and Harville 1981). The estimation of non-stationary stochastic parameters has been mainly approached in the state space framework, either as an initial condition problem (see among others, Ansley and Kohn, 1985, 1989; Kohn and Ansley, 1986; Bell and Hillmer, 1991 and De Jong, 1989, 1991); or as a hierarchical model with “fixed” effects in the hierarchy given a flat prior distribution (see Sallas and Harville, 1981, 1988; Tsimikas and Ledolter, 1994).
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