Page 125 - Contributed Paper Session (CPS) - Volume 5

CPS1141 Mahdi Roozbeh

In the following, similar to approaches by Saleh (2006) and Yuzbashi and
Ahmed (2015), some asymptotic distributional results involving the proposed
estimators are given.
Lemma 3.1. Under the regularity conditions (A1)-(A3) and local
alternatives {K(n)}

The following result is a direct conclusion of Proposition 3.2 and Lemma 3.1.
Theorem 3.1. Under the regularity conditions (A1)-(A3) and local
alternatives {K(n)}, £n is asymptotically distributed according to a non-central
chi-square distribution with p2 degrees of freedom and noncentrality
1
parameter ∆∗, where
2

4. Improved Estimation Strategies
In many practical situations, along with the model one may suspect that
belongs to the sub-space defined by = 0. In such situation one combines
2
the estimate of and the test-statistic to obtain improved estimators of .
First, we consider the preliminary test partially generalized restricted ridge
estimator (PTPGRRE) defined by

where () is the upper α-level critical value (0 < α < 1) from the central
2
2
chi-square distribution and I(A) is the indicator function of the set A. The
PTPGRRE has the disadvantage that it depends on α, the level of significance,
̂
̂
and also it yields the extreme results, namely GR1(k) and G1(k) depending on
the outcome of the test. Later, we will discuss in detail of the Stein-type
partially generalized restricted ridge estimator (SPGRRE) defined by

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