Assessing brand image through communalities and asymmetries in brand-to-attribute and attribute-to-brand associations

Brand image is a key component of customer-based brand equity, and refers to the associations a consumer holds in memory. Such associations are often directional; one should distinguish between brand-to-attribute and attribute-to-brand associations. Information on these associations arise from two ways of collecting data, respectively: brand-by-brand evaluations of all attributes and attribute-by-attributes evaluations of all brands. In this paper, the authors present a methodological approach, namely correspondence analysis of matched matrices, to assess the communalities as well as asymmetries between brand-to-attribute and attribute-to-brand associations. This allows studying whether or not there is match in a brand’s positioning (brand-to-attribute associations) and relative advantage (attribute-to-brand associations). The methodology results in perceptual maps visualizing brand image. The approach is illustrated in an empirical market research project in which two samples of consumers evaluated ten brands of deodorants and eleven attributes. The stability of the solution is examined using bootstrap resampling procedures.     

Computational Tools for Evaluating Phylogenetic and Hierarchical Clustering Trees

This article presents an alternative derivation of the generalized approximate crossvalidation (GACV) score of Xiang and Wahba (1996) for smoothing parameter selection in penalized likelihood regression. The new derivation suggests a simple numerical solution that is stable for all sample sizes. Also suggested is a variant of the score that can be computationally more convenient. Simple simulations are presented to illustrate the effectiveness of the scores.     

A Method for the Computer Calculation of Edgeworth Expansions for Smooth Function Models

Abstract

In this article I describe, in detail, a method for the computer calculation of Edgeworth expansions for a smooth function model accurate in the O(n ^–1) term. For such models, these expansions are an important tool for the analysis of normalizing transformations, the correction of an approximately normally distributed quantity for skewness, and the comparison of bootstrap inference procedures. The method is straightforward and is efficient in a sense described in the article. The implementation of the method in general is clear from its implementation in the Mathematica program (available through StatLib) for the particular case of the studentized mean.     

On the asymptotic accuracy of the bootstrap under arbitrary resampling size

We study the order of convergence of the Kolmogorov-Smirnov distance for the bootstrap of the mean and the bootstrap of quantiles when an arbitrary bootstrap sample size is used. We see that for the bootstrap of the mean, the best order of the bootstrap sample is of the order ofn, wheren is the sample size. In the case of non-lattice distributions and the bootstrap of the sample mean; the bootstrap removes the effect of the skewness of the distribution only when the bootstrap sample equals the sample size. However, for the bootstrap of quantiles, the preferred order of the bootstrap sample isn ^2/3. For the bootstrap of quantiles, if the bootstrap sample is of ordern ² or bigger, the bootstrap is not consistent.     

Bayesian nonparametric predictive inference and bootstrap techniques

We address the question as to whether a prior distribution on the space of distribution functions exists which generates the posterior produced by Efron's and Rubin's bootstrap techniques, emphasizing the connection with the Dirichlet process. We also introduce a new resampling plan which has two advantages: prior opinions are taken into account and the predictive distribution of the future observations is not forced to be concentrated on observed values.     

The effect of objective formulation on retirement decision making

For a retiree who must maintain both investment and longevity risks, we consider the impact on decision making of focusing on an objective relating to the terminal wealth at retirement, instead of a more correct objective relating to a retirement income. Both a shortfall and a utility objective are considered; we argue that shortfall objectives may be inappropriate due to distortion in results with non-monotonically correlated economic factors. The modelling undertaken uses a dynamic programming approach in conjunction with Monte-Carlo simulations of future experience of an individual to make optimal choices. We find that the type of objective targetted can have a significant impact on the optimal choices made, with optimal equity allocations being up to 30% higher and contribution amounts also being significantly higher under a retirement income objective as compared to a terminal wealth objective. The result of these differences can have a significant impact on retirement outcomes.     

An Algorithm for Robust Inference for the Cox Model with Frailties

Abstract

This article proposes a robust method of statistical inference for the Cox's proportional hazards model with frailties. We use the Metropolis—Hastings algorithm and the bootstrap method. We present a computationally efficient algorithm with a customized data structure to implement this method and demonstrate this technique with real data.     

非参数回归函数的稳健Bootstrap

在有异常值的数据中,Bootstrap样本可能比原有样本含有更高的“污染”,这会降低所要做的统计推断的有效性.本文讨论在非参数回归N-W估计中,如何利用影响函数得到重新抽样的概率,使用倾斜的Bootstrap方法得到曲线的拟合,从而达到有效地抵制异常值对回归函数影响的目的,数值模拟的结果表明这种处理方式的有效性.     

On bootstrap estimation of the distribution of the studentized mean

It is shown that bootstrap methods for estimating the distribution of the Studentized mean produce consistent estimators in quite general contexts, demanding not a lot more than existence of finite mean. In particular, neither the sample mean (suitably normalized) nor the Studentized mean need converge in distribution. It is unnecessary to assume that the sampling distribution is in the domain of attraction of any limit law.Now at Michigan State University