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This paper focuses on pricing and vertical cooperative advertising decisions in a two-tier supply chain. Using a Stackelberg game model where the manufacturer acts as the game leader and the retailer acts as the game follower, we obtain closed-form equilibrium solution and explicitly show how pricing and advertising decisions are made. When market demand decreases exponentially with respect to the retail price and increases with respect to national and local advertising expenditures in an additive way, the manufacturer benefits from providing percentage reimbursement for the retailer’s local advertising expenditure when demand price elasticity is large enough. Whether the manufacturer benefits from cooperative advertising is also closely related to supply chain member’s relative advertising efficiency. In the decision for adopting coop advertising strategy, it is critical for the manufacturer to identify how market demand depends on national and local advertisements. The findings from this research can enhance our understanding of cooperative advertising decisions in a two-tier supply chain with price-dependent demand.

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This work is concerned with marginal sure independence feature screening for ultrahigh dimensional discriminant analysis. The response variable is categorical in discriminant analysis. This enables us to use the conditional distribution function to construct a new index for feature screening. In this article, we propose a marginal feature screening procedure based on empirical conditional distribution function. We establish the sure screening and ranking consistency properties for the proposed procedure without assuming any moment condition on the predictors. The proposed procedure enjoys several appealing merits. First, it is model-free in that its implementation does not require specification of a regression model. Second, it is robust to heavy-tailed distributions of predictors and the presence of potential outliers. Third, it allows the categorical response having a diverging number of classes in the order of O(n^κ ) with some κ ≥ 0. We assess the finite sample property of the proposed procedure byMonte Carlo simulation studies and numerical comparison.We further illustrate the proposed methodology by empirical analyses of two real-life datasets. Supplementary materials for this article are available online.

Consider an age-dependent, single-species branching process defined by a progeny number distribution, and a lifetime distribution associated with each independent particle. In this paper, we focus on the associated inverse problem where one wishes to formally solve for the progeny number distribution or the lifetime distribution that defines the Bellman-Harris branching process. We derive results for the existence and uniqueness (the identifiability) of these two distributions given one of two types of information: the extinction time probability of the entire process (extinction time distribution), or the distribution of the total number of particles at one fixed time. We demonstrate that perfect knowledge of the distribution of extinction times allows us to formally determine either the progeny number distribution or the lifetime distribution. Furthermore, we show that these constructions are unique. We then consider “data” consisting of a perfectly known total number distribution given at one specific time. For a process with known progeny number distribution and exponentially distributed lifetimes, we show that the rate parameter is identifiable. For general lifetime distributions, we also show that the progeny distribution is globally unique. Our results are presented through four theorems, each describing the constructions in the four distinct cases.