Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  propose here both F-test and z -test (or t -test) for testing global significance and individual effect of each single predictor respectively in high dimension regression model when the explanatory variables follow a latent factor structure (Wang, 2012). Under the null hypothesis, together with fairly mild conditions on the explanatory variables and latent factors,  show that the proposed F-test and t -test are asymptotically distributed as ighted chi-square and standard normal distribution respectively. That leads to quite different test statistics and inference procedures, as compared with that of Zhong and Chen (2011) when the explanatory variables are akly dependent. Moreover, based on the p -value of each predictor, the method of Storey et?al. (2004) can be used to implement the multiple testing procedure, and  can achieve consistent model selection as long as  can select the threshold value appropriately. All the results are further supported by extensive Monte Carlo simulation studies. The practical utility of the two proposed tests are illustrated via a real data example for index funds tracking in China stock market.
['Wei Lan', 'Yue Ding', 'Zheng Fang', 'Kuangnan Fang']
I am writing a research paper on a idea Testing covariates in high dimension linear regression with latent factors
[{"from": "human", "value": "I am writing a research paper on a idea Testing covariates in high dimension linear regression with latent factors"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  propose here both F-test and z -test (or t -test) for testing global significance and individual effect of each single predictor respectively in high dimension regression model when the explanatory variables follow a latent factor structure (Wang, 2012). Under the null hypothesis, together with fairly mild conditions on the explanatory variables and latent factors,  show that the proposed F-test and t -test are asymptotically distributed as ighted chi-square and standard normal distribution respectively. That leads to quite different test statistics and inference procedures, as compared with that of Zhong and Chen (2011) when the explanatory variables are akly dependent. Moreover, based on the p -value of each predictor, the method of Storey et?al. (2004) can be used to implement the multiple testing procedure, and  can achieve consistent model selection as long as  can select the threshold value appropriately. All the results are further supported by extensive Monte Carlo simulation studies. The practical utility of the two proposed tests are illustrated via a real data example for index funds tracking in China stock market."}]