Statistica Sinica 10(2000), 1231-1241

DENOISED LEAST SQUARES ESTIMATORS: AN APPLICATION

TO ESTIMATING ADVERTISING EFFECTIVENESS

Zongwu Cai$^*$, Prasad A. Naik$^\dagger$ and Chih-Ling Tsai$^\dagger$

$^*$University of North Carolina and $^\dagger$University of California

Abstract: It is known in marketing science that an advertiser under- or overspends millions of dollars on advertising because the estimation of advertising effectiveness 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 firms based on small-sample surveys of consumers. In this paper, we propose a denoised regression approach to deal with the problem of noisy variables. We show that denoised least squares estimators are consistent. Simulation results indicate that the denoised regression approach outperforms the classical regression approach. A marketing example is presented to illustrate the use of denoised least squares estimators.

Key words and phrases: Advertising, linear smoother, noisy data, threshold, wavelets.