The BLUE's covariance matrix revisited: A review

In this paper we comment on and review some unexpected but interesting features of the BLUE (best linear unbiased estimator) of the expectation vector in the general linear model and in particular, the BLUE's covariance matrix. Most of these features appear in the literature but are rather scattered or hidden.     

Experimental designs when there are one or more factor constraints

In response surface methodology, designs of orders one or two are often needed such that some or all the factor levels satisfy one or more linear constraints. A method is discussed for obtaining such designs by projection of a standard design onto the constraint hyperplane. It is shown that a projected design obtained from a rotatable design is also rotatable, and for a rotatable design that is also orthogonal (in particular any orthogonal first-order design) a least squares analysis carried out on the generating design supplies a least squares solution for the constrained design subject to the constraints. Some useful properties of the generating design, such as orthogonal blocking and fractionation are retained in the projected design. Some second-order mixture designs generated by two-level factorials are discussed.     

A New Proof of Murthy's Estimator which Applies to Sequential Sampling

Murthy's estimator has been used for constructing an unbiased estimator of a population total or mean from a sample of fixed size when there is unequal probability sampling without replacement. Traditionally, the estimator is derived by constructing an unordered version of Raj's ordered unbiased estimator. This paper presents an elementary proof of Murthy's estimator which applies the Rao–Blackwell theorem to a very simple estimator. This proof includes any sequential sampling scheme, thus extending the usefulness of Murthy's estimator. We demonstrate this extension by deriving unbiased estimators for inverse sampling.     

Choice Bracketing

When making many choices, a person can broadly bracket them by assessing the consequences of all of them taken together, or narrowly bracket them by making each choice in isolation. We integrate research conducted in a wide range of decision contexts which shows that choice bracketing is an important determinant of behavior. Because broad bracketing allows people to take into account all the consequences of their actions, it generally leads to choices that yield higher utility. The evidence that we review, however, shows that people often fail to bracket broadly when it would be feasible for them to do so. In addition to documenting the diverse effects of bracketing, we also discuss factors that determine whether people bracket narrowly or broadly. We conclude with a discussion of normative aspects of bracketing and argue that there are some situations in which narrower bracketing results in superior decision making.     

Shame, Embarrassment, and Formal Sanction Threats: Extending the Deterrence/Rational Choice Model to Academic Dishonesty

Following the lead of Grasmick and Bursik (1990), we propose that significant others and conscience both function as agents of social control to deter illicit behavior in a manner similar to that provided by the law and more formal, bureaucratic organizations. All three–conscience, significant others, and formal organizations–entail potential threats and costs (i.e., shame, embarrassment, and formal sanctions). Actors consider these potential threats and costs, and assess the certainty and severity of them, in deciding whether or not to engage in criminal or deviant behavior. In the research reported here, data from a sample of undergraduate students are employed to examine the effects of perceived certainty and severity of shame, embarrassment, and formal sanction threats of the self-reported prevalence of involvement in a variety of forms of academic dishonesty. The results suggest rather limited support for the deterrence/rational choice model, nearly all of which is due to the influence of conscience (shame).     

Book Reviews

Qualitative Sociology -     

Effect of shoe type on descending a curb

The aim of this study was to evaluate the effect of shoe type on the performance of women during curb descent. Performance during curb stepping may be explained by biomechanical research that has evaluated the kinematics of overground walking and stair ascent and descent. Studies have reported that women exhibit performance differences when wearing high heels, flip flops and sneakers during overground walking and stair ascent and descent. Thus, in addition to features of the curb, the type of shoe being worn may also affect performance. Although several studies have investigated curb stepping, no known studies have investigated the effects of different types of footwear on curb descent performance. This research was conducted in a real-world environment where participants wore three different types of shoes and performed a series of activities that involved curb stepping. The subjects were videotaped while descending a curb, allowing for observation of changes in gait parameters. Results of this study indicate that wearing high heels leads to performance differences as compared to wearing flip flops or sneakers.     

Flexible empirical Bayes estimation for wavelets

Wavelet shrinkage estimation is an increasingly popular method for signal denoising and compression. Although Bayes estimators can provide excellent mean-squared error (MSE) properties, the selection of an effective prior is a difficult task. To address this problem, we propose empirical Bayes (EB) prior selection methods for various error distributions including the normal and the heavier-tailed Student t -distributions. Under such EB prior distributions, we obtain threshold shrinkage estimators based on model selection, and multiple-shrinkage estimators based on model averaging. These EB estimators are seen to be computationally competitive with standard classical thresholding methods, and to be robust to outliers in both the data and wavelet domains. Simulated and real examples are used to illustrate the flexibility and improved MSE performance of these methods in a wide variety of settings.