Asymptotics of estimators in a heteroscedastic regression model with strong mixing errors
Abstract:
Consider the model Yni = g(xni)
+ σ niε ni, i = 1, …, n,
where σ ni2 = f(uni),
the design points (xni, uni)
are known and nonrandom, g(·)
and f(·) are unknown functions
defined on [0, 1], and the random
errors { ε ni, 1 ≤ i ≤ n}
are assumed to have the same distribution as { ε i, 1 ≤ i ≤ n},
which is a sequence of identically distributed α -mixing random variables with mean
zero. Estimators of f(·) and
g(·) are constructed by the
G-M method and their rth
(r > 2) mean consistency
and strong consistency are obtained under appropriate conditions. To
demonstrate the validity of theoretical results, finite sample behaviors
of the estimators are considered via a simulation study.
2010 AMS Mathematics Subject Classification: Primary 60G05; Secondary 62G20.
Keywords and phrases: heteroscedastic regression model,
strong mixing random variables, G-M estimator, consistency.
