The asymptotic regularity of a generalization of a linear regression model with a nonmonotonous link function

Rok, strany: 1999, 37 - 44

Consider the nonlinear regression model $E(y_i)=g(x_i^Tθ)$, $i=1,…, n$, where $y_i$ is a random vector of observations, $g$ is a differentiable, not necessarily monotonous real function, $θ$ is a parameter from some parameter space $Θsubseteq Bbb R^m$, and $x_i$ are $m$-dimensional vectors. Next, consider a sequence of such models corresponding to adding observations $(n o∞)$, and assume that the $x_i$ are random. In the article, we formulate conditions, under which the sequence of (random) models is asymptotically regular almost surely in the local and in the global sense. More precisely, we give conditions which ensure us that: 1. For given $θ^*$, a natural number $m$ exists with probability one, such that, starting from the $m$ th observation, we shall get models that are regular in $θ^*$. 2. A natural number $m$ exists with probability one, such that from the $m$th observation, we shall get models that are regular on the whole of $Θ$.

ISO 690:

Harman, R. 1999. The asymptotic regularity of a generalization of a linear regression model with a nonmonotonous link function. In Tatra Mountains Mathematical Publications, vol. 17, no.3, pp. 37-44. 1210-3195.

APA:

Harman, R. (1999). The asymptotic regularity of a generalization of a linear regression model with a nonmonotonous link function. Tatra Mountains Mathematical Publications, 17(3), 37-44. 1210-3195.