Counterfeit versus original patronage: Do emotional brand attachment, brand involvement, and past experience matter?

To enhance brand performance and to protect original brands from the unprecedented upsurge of counterfeits, marketers are continuously looking for effective anti-counterfeiting methods. Developing and maintaining emotional brand attachment and brand involvement with consumers have become a strategic marketing endeavor of luxury brands. A significant question bearing both theoretical and practical implications, however, is whether emotional brand attachment or brand involvement is more apposite to warrant a luxury brand’s performance and to safeguard the original brand from counterfeits, which remains unanswered. To address this knowledge gap, a survey was conducted. On the basis of an empirical study, this paper reveals that emotional brand attachment is a more prominent influencer than brand involvement to escalate original brand patronage although the effect of brand involvement is also significant. However, while improved brand involvement pushes consumers to patronize counterfeits, higher emotional brand attachment does not result in increased counterfeit patronage. These effects do not vary as a function of previous experience of either originals or counterfeits. Findings of this research contribute to brand literature by presenting empirical evidence of distinct influence of emotional brand attachment over brand involvement, which represents significant practical implications in relation to strategic brand management and anti-counterfeiting strategies

Asymptotic Generalization Bound of Fisher's Linear Discriminant Analysis

Fisher's linear discriminant analysis (FLDA) is an important dimension reduction method in statistical pattern recognition. It has been shown that FLDA is asymptotically Bayes optimal under the homoscedastic Gaussian assumption. However, this classical result has the following two major limitations: 1) it holds only for a fixed dimensionality $D$, and thus does not apply when $D$ and the training sample size $N$ are proportionally large; 2) it does not provide a quantitative description on how the generalization ability of FLDA is affected by $D$ and $N$. In this paper, we present an asymptotic generalization analysis of FLDA based on random matrix theory, in a setting where both $D$ and $N$ increase and $D/N\longrightarrow\gamma\in[0,1)$. The obtained lower bound of the generalization discrimination power overcomes both limitations of the classical result, i.e., it is applicable when $D$ and $N$ are proportionally large and provides a quantitative description of the generalization ability of FLDA in terms of the ratio $\gamma=D/N$ and the population discrimination power. Besides, the discrimination power bound also leads to an upper bound on the generalization error of binary-classification with FLDA

Turnpike Property and Convergence Rate for an Investment Model with General Utility Functions

In this paper we aim to address two questions faced by a long-term investor with a power-type utility at high levels of wealth: one is whether the turnpike property still holds for a general utility that is not necessarily differentiable or strictly concave, the other is whether the error and the convergence rate of the turnpike property can be estimated. We give positive answers to both questions. To achieve these results, we first show that there is a classical solution to the HJB equation and give a representation of the solution in terms of the dual function of the solution to the dual HJB equation. We demonstrate the usefulness of that representation with some nontrivial examples that would be difficult to solve with the trial and error method. We then combine the dual method and the partial differential equation method to give a direct proof to the turnpike property and to estimate the error and the convergence rate of the optimal policy when the utility function is continuously differentiable and strictly concave. We finally relax the conditions of the utility function and provide some sufficient conditions that guarantee the turnpike property and the convergence rate in terms of both primal and dual utility functions.Comment: 29 page