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Consider the heteroscedastic regression model Y(j)(xin, tin) = tinβ + g(xin) + σine(j)(xin), 1 ≤ j ≤ m, 1 ≤ i ≤ n, where $${\sigma_{in}^{2}=f(u_{in})}$$ , (xin, tin, uin) are fixed design points, β is an unknown parameter, g(·) and f(·) are unknown functions, and the errors {e(j)(xin)} are mean zero NA random variables. The moment consistency for least-squares...
In applied statistics a finite dimensional parameter involved in the distribution function of the observed random variable is very often constrained by a number of nonlinear inequalities. This paper is devoted to studying the likelihood ratio test for and against the hypothesis that the parameter is restricted by some nonlinear inequalities. The asymptotic null distributions of the likelihood ratio...
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