Exponential Sample Clauses

Exponential m(x) = 2 + exp(3x)/400. Bump. m(x) = 10 + 2(x − 1.5) + 5exp(−200(x − 1.5)2). Cycle. m(x) = 10 + 10 sin(2πx); Population values of y in small area i = 1,... , 200 are generated under the random intercepts model yi = m(x) + ui + εi with x drawn from a Uniform distribution [0, 3], the area effects ui drawn from N(0, 1) and the error effects εi independently generated from N(0, 1). The linear case represents a situation in which the EBLUP is based on a good representation of the true model, while the NPEBLUP may be too complex and overparametrized. The jump model is a discontinuous function for which EBLUP and NPEBLUP are based on a misspecified model; the Exponential, Bump and Cycle models define increasingly more complicated structures of the relationship between y and x. For each of the five generated populations a total of T = 250 simulations were carried out. For each sample the EBLUP and the NPEBLUP estimators have been used to estimate the small area means y¯i, i = 1,... , 200. Then, for each estimator and for each small area we computed the Monte Carlo estimate of the Bias −T
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