There are discussions about variable selection when sample size and dimension
fixed, but few dealing with n fixed and . Recently, high dimensional data, such as
Microarray, exhibits very high dimension and much smaller sample size . In the present
paper, we consider data set with fixed sample size n and growing dimension . 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.