Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In practical communication environments, it is frequently observed that the underlying noise distribution is not Gaussian and may vary in a wide range from short-tailed to heavy-tailed forms. To describe partially known noise distribution densities, a distribution class characterized by the upper-bounds upon a noise variance and a density dispersion in the central part is used. The results on the minimax variance estimation in the Huber sense are applied to the problem of asymptotically minimax detection of a ak signal. The least favorable density minimizing Fisher information over this class is called the ber-Hermite density and it has the Gaussian and Laplace densities as limiting cases. The subsequent minimax detector has the following form: i) with relatively small variances, it is the minimum L 2 -norm distance rule; ii) with relatively large variances, it is the L 1  -norm distance rule; iii) it is a compromise beten these extremes with relatively moderate variances. It is shown that the proposed minimax detector is robust and close to Huber's for heavy-tailed distributions and more efficient than Huber's for short-tailed ones both in asymptotics and on finite samples
['Georgy Shevlyakov', 'Kiseon Kim']
I am writing a research paper on a idea Robust minimax detection of a weak signal in noise with a bounded variance and density value at the center of symmetry
[{"from": "human", "value": "I am writing a research paper on a idea Robust minimax detection of a weak signal in noise with a bounded variance and density value at the center of symmetry"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In practical communication environments, it is frequently observed that the underlying noise distribution is not Gaussian and may vary in a wide range from short-tailed to heavy-tailed forms. To describe partially known noise distribution densities, a distribution class characterized by the upper-bounds upon a noise variance and a density dispersion in the central part is used. The results on the minimax variance estimation in the Huber sense are applied to the problem of asymptotically minimax detection of a ak signal. The least favorable density minimizing Fisher information over this class is called the ber-Hermite density and it has the Gaussian and Laplace densities as limiting cases. The subsequent minimax detector has the following form: i) with relatively small variances, it is the minimum L 2 -norm distance rule; ii) with relatively large variances, it is the L 1  -norm distance rule; iii) it is a compromise beten these extremes with relatively moderate variances. It is shown that the proposed minimax detector is robust and close to Huber's for heavy-tailed distributions and more efficient than Huber's for short-tailed ones both in asymptotics and on finite samples"}]