De-noised Least Squares Estimators: an Application to Estimating Advertising Eeectiveness

It is known in marketing science that an advertiser under-or overspends millions of dollars on advertising because the estimation of advertising eeectiveness is biased. This bias is induced by measurement noise in advertising variables, such as awareness and television rating points, which are provided by commercial market research rms based on small-sample survey of consumers. In this paper, we propose a de-noised regression approach to deal with the problem of noisy variables. We show that de-noised least squares estimators are consistent. Simulation results indicate that the de-noised regression approach outperforms the classical regression approach. A marketing example is presented to illustrate the use of de-noised least squares estimators.