testing of statistical significance of parameters which are under the restriction, base on T test can be correct? if not, how can I make inference about estimated parameter?
This paper is a good start to answer your question http://www.jstor.org/stable/1912529
A Bayesian analysis using an appropriate prior would be a possibility.
An example of a parameter which is under constraint is the standard deviation just like every other measure of dispersion. Dispersion is a distance and therefore cannot be negative. The test of significance of a standard deviation can be based on the sampling distribution of the variance which is chi-square. In garch modelling alpha is constrained to be less than 1 for stationarity to be attained and positive for positive residual variance. In spite of this constraint, statistical significance of the alpha coefficient might be tested by a t-test of the mean value (within the limits of the constraint). Therefore the use of the t-distribution for the test of significance of a constrained parameter is acceptable where applicable.
here is the link of my article it can be useful for you
https://www.researchgate.net/publication/325058733_SVM_Multi-Classification_of_Induction_Machine's_bearings_defects_using_Vibratory_Analysis_based_on_Empirical_Mode_Decomposition/stats
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