Bootstrap tests for multivariate directional alternatives

Tests on multivariate means that are hypothesized to be in a specified direction have received attention from both theoretical and applied points of view. One of the most common procedures used to test this cone alternative is the likelihood ratio test (LRT) assuming a multivariate normal model for the data. However, the resulting test for an ordered alternative is biased in that the only usable critical values are bounds on the null distribution. The present paper provides empirical evidence that bootstrapping the null distribution of the likelihood ratio statistic results in a bootstrap test (BT) with comparable power properties without the additional burden of assuming multivariate normality. Additionally, the tests based on the LRT statistic can reject the null hypothesis in favor of the alternative even though the true means are far from the alternative region. The BT also has similar properties for normal and nonnormal data. This anomalous behavior is due to the formulation of the null hypothesis and a possible remedy is to reformulate the null to be the complement of the alternative hypothesis. We discuss properties of a BT for the modified set of hypotheses (MBT) based on a simulation study. The resulting test is conservative in general and in some specific cases has power estimates comparable to those for existing methods. The BT has higher sensitivity but relatively lower specificity, whereas the MBT has higher specificity but relatively lower sensitivity.     

Residential Segregation on the Island: The Role of Race and Class in Puerto Rican Neighborhoods

In this paper, we use racial data from Census 2000, available for the first time in 50 years, to examine the links among race, socioeconomic status, and residential location on the island of Puerto Rico. Puerto Ricans overwhelmingly chose white as their race, and they chose only one race, not a combination of races that would seem more in keeping with the ideology of mestizaje. Overall, segregation by race is modest compared with residential segregation in the United States. In keeping with the Puerto Rican claim that class is more important than race, we find that segregation by race is generally lower than segregation between the lowest and highest income categories in all metro areas, but that the results for education and occupational status differ by metropolitan area. In San Juan-Bayamón, the most diverse metropolitan area on the island, we find that as percent black increases, neighborhood socioeconomic status decreases, though the changes are not that stark, except in Loiza, a community of black Puerto Ricans and in some Dominican neighborhoods, though there are relatively few of these neighborhoods.     

An Evaluation of Conditional Manding Using a Four-Component Multiple Schedule

Most verbal behavior curricula for children with autism spectrum disorder (ASD) focus on teaching multiple mands during the early stages of training (e.g., picture exchange communication system; Bondy & Frost, 1994). However, few, if any, of those curricula train children with ASD to differentially mand only for reinforcers that are reasonable for a caregiver to deliver in a given context (e.g., mands to cuddle at bedtime) and to refrain from manding for reinforcers that would be inappropriate to deliver in that context (e.g., mands to play outside at bedtime). In this study, we first taught a boy with ASD two initial mands. Immediately thereafter we brought those mands under the conditional discriminative control of a four-component multiple schedule with (a) S¹ correlated with one reinforcer available (i.e., edibles), (b) S² correlated with both reinforcers available (i.e., edibles or drink), (c) S³ correlated with another reinforcer available (i.e., drink), and (d) S^Δ correlated with no reinforcer available. Following treatment, the child displayed conditionally discriminated manding in accordance with each of the four components of the schedule. We discuss these findings relative to the potential benefits of bringing mands under both evocative and discriminative control.

     

Bounds for the error in an approximation to the distribution of continuous random vectors with bounded supports

An approximation for the distributions of m-dimensional random variables with absolutely continuous cumulative distribution functions and bounded supports is presented. In addition, two easily computed bounds for the error in using the approximation rather than the actual distribution are provided for any measurable region.     

A semiparametric estimator of the distribution function of a variable measured with error

The estimation of the distribution functon of a random variable X measured with error is studied. Let the i-th observation on X be denoted by Y_iX_i+ε_i where ε_i is the measuremen error. Let {Y_i} (i=1,2,…,n) be a sample of independent observations. It is assumed that {X_i} and {∈_i} are mutually independent and each is identically distributed. As is standard in the literature for this problem, the distribution of e is assumed known in the development of the methodology. In practice, the measurement error distribution is estimated from replicate observations.

The proposed semiparametric estimator is derived by estimating the quantises of X on a set of n transformed V-values and smoothing the estimated quantiles using a spline function. The number of parameters of the spline function is determined by the data with a simple criterion, such as AIC. In a simulation study, the semiparametric estimator dominates an optimal kernel estimator and a normal mixture estimator for a wide class of densities.

The proposed estimator is applied to estimate the distribution function of the mean pH value in a field plot. The density function of the measurement error is estimated from repeated measurements of the pH values in a plot, and is treated as known for the estimation of the distribution function of the mean pH value.     

A Comparison of Unit-Root Test Criteria

During the past 15 years, the ordinary least squares estimator and the corresponding pivotal statistic have been widely used for testing the unit-root hypothesis in autoregressive processes. Recently, several new criteria, based on maximum likelihood estimators and weighted symmetric estimators, have been proposed. In this article, we describe several different test criteria. Results from a Monte Carlo study that compares the power of the different criteria indicate that the new tests are more powerful against the stationary alternative. Of the procedures studied, the weighted symmetric estimator and the unconditional maximum likelihood estimator provide the most powerful tests against the stationary alternative. As an illustration, the weekly series of one-month treasury-bill rates is analyzed.     

Hanging Out With Which Friends? Friendship‐Level Predictors of Unstructured and Unsupervised Socializing in Adolescence

Companions are central to explanations of the risky nature of unstructured and unsupervised socializing, yet we know little about whom adolescents are with when hanging out. We examine predictors of how often friendship dyads hang out via multilevel analyses of longitudinal friendship‐level data on over 5,000 middle schoolers. Adolescents hang out most with their most available friends and their most generally similar friends, not with their most at‐risk or similarly at‐risk friends. These findings vary little by gender and wave. Together, the findings suggest that the risks of hanging out stem from the nature of hanging out as an activity, not the nature of adolescents' companions, and that hanging out is a context for friends' mutual reinforcement of preexisting characteristics.     

Adjusting the degrees of freedom for the jackknife

The rule of thumb given by Mosteller and Tukey for obtaining the degrees of freedom which are appropriate for the approximate t-statistic associated with the jackknife is discussed.Examples of possible misapplication of this rule are given.     

Bi‐Criteria Scheduling of Surgical Services for an Outpatient Procedure Center

Uncertainty in the duration of surgical procedures can cause long patient wait times, poor utilization of resources, and high overtime costs. We compare several heuristics for scheduling an Outpatient Procedure Center. First, a discrete event simulation model is used to evaluate how 12 different sequencing and patient appointment time‐setting heuristics perform with respect to the competing criteria of expected patient waiting time and expected surgical suite overtime for a single day compared with current practice. Second, a bi‐criteria genetic algorithm (GA) is used to determine if better solutions can be obtained for this single day scheduling problem. Third, we investigate the efficacy of the bi‐criteria GA when surgeries are allowed to be moved to other days. We present numerical experiments based on real data from a large health care provider. Our analysis provides insight into the best scheduling heuristics, and the trade‐off between patient and health care provider‐based criteria. Finally, we summarize several important managerial insights based on our findings.     

Reflecting on attention-deficient hyperactivity disorder and disablement in education with Eric Fromm

Drawing upon the thought of Eric Fromm, this paper argues that efforts to understand and counter behaviour that causes difficulties in education should begin in a critical and reflective engagement with both the conditions of human freedom and the character of educational institutions and society as a whole. Fromm’s critique of dominating ideas about good mental health within capitalistic societies is examined in relation to disablement and attention-deficient hyperactivity disorder. A study of a sixth-form college in the south of England elucidates connections between Fromm’s insights into social psychology and disablement as a process of oppression.