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In this thesis, we are going to study the consistency properties of one of the most well-known linear estimators – LASSO estimator. First, we bring up some necessary background for introducing this estimator. Then, we are able to introduce primary and secondary forms of LASSO estimator. After that, we prove that primary form of the LASSO estimator is weakly consistent under certain weak conditions. We, also, prove a much stronger statement about the secondary form. We prove that the secondary form is strongly consistent. What’s more, with extra assumptions, we specify the convergence rate of the estimator. Finally, we propose a method for determining free parameter of primary form of LASSO,... 

In recent years, optimization via simulation for the systemswhose objective function has stochastic characteristic and doesn’t explicitly exist in closed form, has attracted considerable interest.Simulation of this kind of systems at times may be veryexpensive. In this research, the constraint simulation optimization problem is considered for solving problems with stochastic features based on metamodels. For this purpose, stochastic Kriging is used as a metamodel. In this method, first, a few feasible points in the solution space are identified by thek-optimal design of experiment and then the simulation runs are performed. In the next step, a metamodel is fitted to all the stochastic...