Monte Carlo Simulation in Quantile Regression Parameter for Sparsity Estimate

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Monte Carlo is a method used to generate data according to the distribution and resampling until the parameters of the method used became convergen. The purpose of this simulation is first to prove that quantile regression with the estimated sparsity function parameter can model the data according to the non-uniform distribution of the data. Secondly, it’s to prove that the quantile regression is a developed method from the linear regression. The pattern of data which is not uniform is generally referred to as heterogeneous data, while the pattern of uniform data distribution is called homogeneous data. Data in this study will be generated for small and large samples on homogeneous and heterogeneous data. Uniformity of variance will be carried out on both heterogeneous and homogeneous data types, namely 0.25,1 and 4. The parameter estimation process and data generation will be resampled 1000 times. Thus, in conclusion of the simulation studies was the parameter estimates in the classical regression will be the same as the parameter estimates in the quantile regression at quantile 0.5. In the simulation, it is decided that the quantile regression method can be used on heterogeneous and homogeneous data to the unconstrained number of samples and variances.