Hypothesis testing and variable selection in Ridge regression

There are discussions about variable selection when sample size n \rightarrow 1 and dimension p
fixed, but few dealing with n fixed and p \rightarrow 1. Recently, high dimensional data, such as
Microarray, exhibits very high dimension p and much smaller sample size n. In the present
paper, we consider data set with fixed sample size n and growing dimension p \rightarrow 1. We
also conduct a hypothesis testing for variable selection in ridge regression. We also prove
the consistency of the variable selection method for data with fixed sample size and infinite
number of variables.