Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  studies the limiting behavior of Tyler's M-estimator for the scatter matrix, in the regime that the number of samples n and their dimension p both go to infinity, and p / n converges to a constant y with 0 < y < 1 .  prove that when the data samples x 1 , ź , x n are identically and independently generated from the Gaussian distribution N ( 0 , I ) , the operator norm of the difference beten a properly scaled Tyler's M-estimator and ź i = 1 n x i x i ź / n tends to zero. As a result, the spectral distribution of Tyler's M-estimator converges akly to the Marcenko-Pastur distribution.
['Teng Zhang', 'Xiuyuan Cheng', 'Amit Singer']
I am writing a research paper on a idea Marčenko-Pastur law for Tyler's M-estimator
[{"from": "human", "value": "I am writing a research paper on a idea Mar\u010denko-Pastur law for Tyler's M-estimator"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  studies the limiting behavior of Tyler's M-estimator for the scatter matrix, in the regime that the number of samples n and their dimension p both go to infinity, and p / n converges to a constant y with 0 < y < 1 .  prove that when the data samples x 1 , \u017a , x n are identically and independently generated from the Gaussian distribution N ( 0 , I ) , the operator norm of the difference beten a properly scaled Tyler's M-estimator and \u017a i = 1 n x i x i \u017a / n tends to zero. As a result, the spectral distribution of Tyler's M-estimator converges akly to the Marcenko-Pastur distribution."}]