Optimal Composite Markers for Time‐Dependent Receiver Operating Characteristic Curves with Censored Survival Data

Abstract. To increase the predictive abilities of several plasma biomarkers on the coronary artery disease (CAD)‐related vital statuses over time, our research interest mainly focuses on seeking combinations of these biomarkers with the highest time‐dependent receiver operating characteristic curves. An extended generalized linear model (EGLM) with time‐varying coefficients and an unknown bivariate link function is used to characterize the conditional distribution of time to CAD‐related death. Based on censored survival data, two non‐parametric procedures are proposed to estimate the optimal composite markers, linear predictors in the EGLM model. Estimation methods for the classification accuracies of the optimal composite markers are also proposed. In the article we establish theoretical results of the estimators and examine the corresponding finite‐sample properties through a series of simulations with different sample sizes, censoring rates and censoring mechanisms. Our optimization procedures and estimators are further shown to be useful through an application to a prospective cohort study of patients undergoing angiography.     

A Non‐Parametric Estimator of the Spectral Density of a Continuous‐Time Gaussian Process Observed at Random Times

Abstract. In numerous applications data are observed at random times and an estimated graph of the spectral density may be relevant for characterizing and explaining phenomena. By using a wavelet analysis, one derives a non‐parametric estimator of the spectral density of a Gaussian process with stationary increments (or a stationary Gaussian process) from the observation of one path at random discrete times. For every positive frequency, this estimator is proved to satisfy a central limit theorem with a convergence rate depending on the roughness of the process and the moment of random durations between successive observations. In the case of stationary Gaussian processes, one can compare this estimator with estimators based on the empirical periodogram. Both estimators reach the same optimal rate of convergence, but the estimator based on wavelet analysis converges for a different class of random times. Simulation examples and an application to biological data are also provided.     

Testing for order among K populations: theory and examples

Testing for stochastic order among K populations is a common and important problem in statistical practice. It arises in the analysis of both planned experiments and observational studies. The authors develop a new nonparametric test for order among K populations that can accommodate any stochastic ordering. The test is based on a maximally selected chi‐bar‐square statistic. The authors find its limiting distribution and use simulations to derive critical values. Three important examples are used to illustrate the applicability of the general method. The authors find that the new tests outperform the existing methods in many practical cases. The Canadian Journal of Statistics 38: 97–115; 2010 © 2009 Statistical Society of Canada     

On the Validity of the Bootstrap in Non‐Parametric Functional Regression

Abstract. We consider the functional non‐parametric regression model Y= r( χ )+?, where the response Y is univariate, χ is a functional covariate (i.e. valued in some infinite‐dimensional space), and the error ? satisfies E(? | χ ) = 0. For this model, the pointwise asymptotic normality of a kernel estimator of r (·) has been proved in the literature. To use this result for building pointwise confidence intervals for r (·), the asymptotic variance and bias of need to be estimated. However, the functional covariate setting makes this task very hard. To circumvent the estimation of these quantities, we propose to use a bootstrap procedure to approximate the distribution of . Both a naive and a wild bootstrap procedure are studied, and their asymptotic validity is proved. The obtained consistency results are discussed from a practical point of view via a simulation study. Finally, the wild bootstrap procedure is applied to a food industry quality problem to compute pointwise confidence intervals.     

Density Estimation by Total Variation Penalized Likelihood Driven by the Sparsity ℓ1 Information Criterion

Abstract. We propose a non‐linear density estimator, which is locally adaptive, like wavelet estimators, and positive everywhere, without a log‐ or root‐transform. This estimator is based on maximizing a non‐parametric log‐likelihood function regularized by a total variation penalty. The smoothness is driven by a single penalty parameter, and to avoid cross‐validation, we derive an information criterion based on the idea of universal penalty. The penalized log‐likelihood maximization is reformulated as an ?₁‐penalized strictly convex programme whose unique solution is the density estimate. A Newton‐type method cannot be applied to calculate the estimate because the ?₁‐penalty is non‐differentiable. Instead, we use a dual block coordinate relaxation method that exploits the problem structure. By comparing with kernel, spline and taut string estimators on a Monte Carlo simulation, and by investigating the sensitivity to ties on two real data sets, we observe that the new estimator achieves good L ₁ and L ₂ risk for densities with sharp features, and behaves well with ties.     

Limited Information and Advertising in the U.S. Personal Computer Industry

Traditional discrete‐choice models assume buyers are aware of all products for sale. In markets where products change rapidly, the full information assumption is untenable. I present a discrete‐choice model of limited consumer information, where advertising influences the set of products from which consumers choose to purchase. I apply the model to the U.S. personal computer market where top firms spend over $2 billion annually on advertising. I find estimated markups of 19% over production costs, where top firms advertise more than average and earn higher than average markups. High markups are explained to a large extent by informational asymmetries across consumers, where full information models predict markups of one‐fourth the magnitude. I find that estimated product demand curves are biased toward being too elastic under traditional models. I show how to use data on media exposure to improve estimated price elasticities in the absence of micro ad data.     

Optimal Bandwidth Selection in Heteroskedasticity–Autocorrelation Robust Testing

This paper considers studentized tests in time series regressions with nonparametrically autocorrelated errors. The studentization is based on robust standard errors with truncation lag M=bT for some constant b∈(0, 1] and sample size T. It is shown that the nonstandard fixed‐b limit distributions of such nonparametrically studentized tests provide more accurate approximations to the finite sample distributions than the standard small‐b limit distribution. We further show that, for typical economic time series, the optimal bandwidth that minimizes a weighted average of type I and type II errors is larger by an order of magnitude than the bandwidth that minimizes the asymptotic mean squared error of the corresponding long‐run variance estimator. A plug‐in procedure for implementing this optimal bandwidth is suggested and simulations (not reported here) confirm that the new plug‐in procedure works well in finite samples.     

The Emergence of Service Science: Toward Systematic Service Innovations to Accelerate Co‐Creation of Value

The current growth of the service sector in global economies is unparalleled in human history—by scale and speed of labor migration. Even large manufacturing firms are seeing dramatic shifts in percent revenue derived from services. The need for service innovations to fuel further economic growth and to raise the quality and productivity levels of services has never been greater. Services are moving to center stage in the global arena, especially knowledge‐intensive business services aimed at business performance transformation. One challenge to systematic service innovation is the interdisciplinary nature of service, integrating technology, business, social, and client (demand) innovations. This paper describes the emergence of service science, a new interdisciplinary area of study that aims to address the challenge of becoming more systematic about innovating in service.     

Care: A Critical Review of Theory,Policy and Practice

‘Care’ is a source of critical tension in current social theory, and the policy and practice implications of that tension are evidenced in its current prominence on the political agenda of developed welfare states. This article critically appraises current developments in the theory, policy and practice of care, drawing on interdisciplinary developments in political theory, sociology and social policy. Developing feminist and disability‐rights theories, it explores a critical synthesis of conflicting normative and theoretical positions regarding the giving and receiving of care, and of the ethics and justice of care. It examines case studies of current comparative policy developments across a range of different welfare regimes, including the marketization/commodification and de/re‐familiaization of care, exploring ideological and normative trends in the design of contemporary policies. It discusses the impact of theory and policy on the practice of care, looking particularly at the issue of long‐term care for disabled and older adults. Finally, the authors argue for the development of a citizenship‐based approach to care that decouples it from individualistic and paternalistic paradigms that disempower those who give and receive care.     

Black‐market Medicine and Public Opinion Towards the Welfare State: Evidence from Israel

Based on a survey and interviews, this article presents and analyses Israeli public opinion toward black‐market medicine (BMM) and the welfare state. In addition to providing quantitative and qualitative evidence of the existence of under‐the‐table payments in Israel, we suggest various insights into this phenomenon. While most citizens admit that they would consider making under‐the‐table payments in order to receive preferential medical treatment, when the questions mention words such as ‘illegal’ or ‘bribe’, respondents tend to be less tolerant of such activities. We find that, first, there is a basic willingness among Israeli citizens to use BMM. Second, despite this predilection, Israeli citizens are reluctant to articulate their willingness to engage in such illegal activities. This reluctance implies the existence of a moral barrier among the population as far as identifying themselves with illegal behaviour is concerned. We may infer the existence of a gap between declared attitudes and behaviour. Third, the fact that people's willingness to engage in BMM is greater than their willingness to adopt black‐market strategies in other areas signifies the special nature of health care. Finally, by connecting the phenomenon of BMM to public opinion regarding the welfare state, we point to a possible gap between normative attitudes and preferences produced by structural conditions.