In the applications of COX regression models, we always encounter data
sets that contain too many variables that
only a few of them contribute to the model. Therefore, it will waste
much more samples to estimate the “noneffective” variables in the inference. In
this paper, we use a sequential procedure for constructingthe
fixed size confidence set for the “effective” parameters to the model based on
an adaptive shrinkage estimate such that the “effective” coefficients can be
efficiently identified with the minimum sample size. Fixed design is considered
for numerical simulation. The strong consistency, asymptotic distributions and
convergence rates of estimates under the fixed design are obtained. In addition,
the sequential procedure is shown to be asymptotically optimal in the sense of
Chow and Robbins (1965).
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