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Potthoff-Roy�任������ֱ�任.

Growth curve model is a general multivariable
linear model. It plays an important role in modern statistics. In this
paper, firstly, we define the penalized least squares for growth curve
model, after transforming it by the Potthoff-Roy transformation. By
using adaptive LASSO we can get corresponding estimation, as well as
achieve the variable selection. Then, the penalized least squares
estimation of the growth curve model is presented with a unified expression
of approximate estimation. In addition, we discuss the properties of
the penalized least squares estimations of the growth curve model,
which is transformed by Potthoff-Roy transformation, and the properties,
which are Oracle properties, are proved in this paper. By using the
criteria to measure estimation and variable selection, we compare
several penalized least squares estimations and the effect of variable
selection of different penalty functions. The result shows that the
adaptive LASSO performs better in parameter estimation and variable
selection. Besides, we compare different transformations. Results
indicate that Potthoff-Roy transformation performs better than matrix
stacking transformation when considering variable selection and
parameter estimation comprehensively.