In the linear regression setting, we propose a general framework, termed weighted orthogonal components regression (WOCR), which encompasses many known methods as special cases, including ridge regression and principal components regression. WOCR makes use of the monotonicity inherent in orthogonal components to parameterize the weight function. The formulation allows for efficient determination of tuning parameters and hence is computationally advantageous. Moreover, WOCR offers insights for deriving new better variants. Specifically, we advocate assigning weights to components based on their correlations with the response, which may lead to enhanced predictive performance. Both simulated studies and real data examples are provided to assess and illustrate the advantages of the proposed methods.
It is widely acknowledged that the reported numbers of infected cases with COVID-19 were not complete. A structured approach is proposed where we distinguish cases reflected later in the numbers of confirmed cases and those with mild or no symptoms thus not captured by any systems at all. The number of infected cases in the US is estimated to be 220.54% of that reported as of Apr 20, 2020. This implies an overall infection ratio of 0.53%, and a case mortality rate at 2.85% which is close to the 3.4% suggested by WHO in March 2020.