Tests for the variance parameter in the Fay–Herriot model

The Fay–Herriot model is a linear mixed model that plays a relevant role in small area estimation (SAE). Under the SAE set-up, tools for selecting an adequate model are required. Applied statisticians are often interested on deciding if it is worthwhile to use a mixed effect model instead of a simpler fixed-effect model. This problem is not standard because under the null hypothesis the random effect variance is on the boundary of the parameter space. The likelihood ratio test and the residual likelihood ratio test are proposed and their finite sample distributions are derived. Finally, we analyse their behaviour under simulated scenarios and we also apply them to real data.     

On Box–Muller Transformation and Simulation of Normal Record Data

Record data are commonly encountered in many fields such as sports, geography, finance, and reliability. In this article, we use the well-known Box–Muller transformation to develop an efficient method of simulating record data from the normal distribution. Another method based on exponential records is also discussed. Then, the performance of these algorithms is compared with some standard simulation methods.     

What Happens When Manufacturers Perform The Retailing Functions?

This study examines the effects of a relatively new channel structure on prices and sales in a large department store, which in recent years has switched the management of many of its product categories from a traditional retailer‐managed system to a manufacturer‐managed system. We find that the change caused overall retail prices to decrease. However, there was significant heterogeneity in the response across brands. In the cell phone category, brands with high market shares and inelastic demand did not change prices. In the watch category, the retail prices of relatively low‐end brands decreased while the prices of premium brands increased substantially after the switch. In addition to sales increases due to lower prices, we find that the channel structure change further caused sales to increase by 9–10% in the cell phone category and by 11–17% in the watch category. These results are consistent with previous theoretical predictions. We believe that our results provide important academic and managerial implications due to the increasing prevalence of manufacturer‐managed systems in the retail industry.