Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the problem of estimating the pa- rameters of a linear autoregressive model with sub-Gaussian innovations from a limited sequence of consecutive observations. Assuming that the parameters are compressible,  analyze the performance of the l1-regularized least squares as ll as a greedy estimator of the parameters and characterize the sampling trade-offs required for stable recovery in the non-asymptotic regime. Our results extend those of compressed sensing for linear models where the covariates are i.i.d. and independent of the observation history to autoregressive processes with highly inter- dependent covariates.  also derive sufficient conditions on the sparsity level that guarantee the minimax optimality of the l1- regularized least squares estimate. Applying these techniques to simulated data as ll as real-world datasets from crude oil prices and traffic speed data confirm our predicted theoretic al performance gains in terms of estimation accuracy and model selection.
['Abbas Kazemipour', 'Sina Miran', 'Piya Pal', 'Behtash Babadi', 'Min Wu']
I am writing a research paper on a idea Sampling Requirements for Stable Autoregressive Estimation
[{"from": "human", "value": "I am writing a research paper on a idea Sampling Requirements for Stable Autoregressive Estimation"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the problem of estimating the pa- rameters of a linear autoregressive model with sub-Gaussian innovations from a limited sequence of consecutive observations. Assuming that the parameters are compressible,  analyze the performance of the l1-regularized least squares as ll as a greedy estimator of the parameters and characterize the sampling trade-offs required for stable recovery in the non-asymptotic regime. Our results extend those of compressed sensing for linear models where the covariates are i.i.d. and independent of the observation history to autoregressive processes with highly inter- dependent covariates.  also derive sufficient conditions on the sparsity level that guarantee the minimax optimality of the l1- regularized least squares estimate. Applying these techniques to simulated data as ll as real-world datasets from crude oil prices and traffic speed data confirm our predicted theoretic al performance gains in terms of estimation accuracy and model selection."}]