I have a set of observations. When I do an OLS I get a $\beta$. After I remove some values I also get a $\beta$. Now I want to test if the properties of two betas are the same? Please give me a hint how to do that?
What exactly are you trying to find out? One way to approach this would be to look at the problem differently: Simply add a predictor (0 for regular observations, 1 for observations you would remove) and estimate/test the interaction between this new predictor and the other term of interest.