Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider estimation of a sparse parameter vector from measurements corrupted by white Gaussian noise. Using the framework of reproducing kernel Hilbert spaces,  derive closed-form expressions of the Barankin bound, i.e., of the minimum locally achievable variance of any estimator with a prescribed bias function, including the unbiased case.  also derive the locally minimum variance (LMV) estimator that achieves the minimum variance, and a necessary and sufficient condition on the prescribed bias function for the existence of finite-variance estimators and, simultaneously, of the LMV estimator. Finally,  present a numerical comparison of the variance of the hard-thresholding estimator with the corresponding minimum achievable variance.
['Sebastian Schmutzhard', 'Alexander Jung', 'Franz Hlawatsch']
I am writing a research paper on a idea Minimum variance estimation for the sparse signal in noise model
[{"from": "human", "value": "I am writing a research paper on a idea Minimum variance estimation for the sparse signal in noise model"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider estimation of a sparse parameter vector from measurements corrupted by white Gaussian noise. Using the framework of reproducing kernel Hilbert spaces,  derive closed-form expressions of the Barankin bound, i.e., of the minimum locally achievable variance of any estimator with a prescribed bias function, including the unbiased case.  also derive the locally minimum variance (LMV) estimator that achieves the minimum variance, and a necessary and sufficient condition on the prescribed bias function for the existence of finite-variance estimators and, simultaneously, of the LMV estimator. Finally,  present a numerical comparison of the variance of the hard-thresholding estimator with the corresponding minimum achievable variance."}]