Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  consider a generalized multivariate regression problem where the responses are some functions of linear transformations of predictors.  assume that these functions are strictly monotonic, but their form and parameters are unknown.  propose a semi-parametric estimator based on the ordering of the responses which is invariant to the functional form of the transformation function as long as it is strictly monotonic.  prove that our estimator, which maximizes the rank similarity beten responses and linear transformations of predictors, is a consistent estimator of the true coefficient matrix.  also identify the rate of convergence and show that the squared estimation error decays with a rate of o(1/n).  then propose a greedy algorithm to maximize the highly non-smooth objective function of our model and examine its performance through extensive simulations. Finally,  compare our algorithm with traditional multivariate regression algorithms over synthetic and real data.
['Milad Kharratzadeh', 'Mark Coates']
I am writing a research paper on a idea Semi-parametric Order-based Generalized Multivariate Regression
[{"from": "human", "value": "I am writing a research paper on a idea Semi-parametric Order-based Generalized Multivariate Regression"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  consider a generalized multivariate regression problem where the responses are some functions of linear transformations of predictors.  assume that these functions are strictly monotonic, but their form and parameters are unknown.  propose a semi-parametric estimator based on the ordering of the responses which is invariant to the functional form of the transformation function as long as it is strictly monotonic.  prove that our estimator, which maximizes the rank similarity beten responses and linear transformations of predictors, is a consistent estimator of the true coefficient matrix.  also identify the rate of convergence and show that the squared estimation error decays with a rate of o(1/n).  then propose a greedy algorithm to maximize the highly non-smooth objective function of our model and examine its performance through extensive simulations. Finally,  compare our algorithm with traditional multivariate regression algorithms over synthetic and real data."}]