P-splines regression smoothing and difference type of penalty

P-splines regression provides a flexible smoothing tool. In this paper we consider difference type penalties in a context of nonparametric generalized linear models, and investigate the impact of the order of the differencing operator. Minimizing Akaike’s information criterion we search for a possible best data-driven value of the differencing order. Theoretical derivations are established for the normal model and provide insights into a possible ‘optimal’ choice of the differencing order and its interrelation with other parameters. Applications of the selection procedure to non-normal models, such as Poisson models, are given. Simulation studies investigate the performance of the selection procedure and we illustrate its use on real data examples.     

Food Safety in the Domestic Environment: The Effect of Consumer Risk Information on Human Disease Risks

The improvement of food safety in the domestic environment requires a transdisciplinary approach, involving interaction between both the social and natural sciences. This approach is applied in a study on risks associated with Campylobacter on broiler meat. First, some web-based information interventions were designed and tested on participant motivation and intentions to cook more safely. Based on these self-reported measures, the intervention supported by the emotion "disgust" was selected as the most promising information intervention. Its effect on microbial cross-contamination was tested by recruiting a set of participants who prepared a salad with chicken breast fillet carrying a known amount of tracer bacteria. The amount of tracer that could be recovered from the salad revealed the transfer and survival of Campylobacter and was used as a measure of hygiene. This was introduced into an existing risk model on Campylobacter in the Netherlands to assess the effect of the information intervention both at the level of exposure and the level of human disease risk. We showed that the information intervention supported by the emotion "disgust" alone had no measurable effect on the health risk. However, when a behavioral cue was embedded within the instruction for the salad preparation, the risk decreased sharply. It is shown that a transdisciplinary approach, involving research on risk perception, microbiology, and risk assessment, is successful in evaluating the efficacy of an information intervention in terms of human health risks. The approach offers a novel tool for science-based risk management in the area of food safety.     

Heterogeneity's Ruses: Some Surprising Effects of Selection on Population Dynamics

As a cohort of people, animals, or machines ages, the individuals at highest risk tend to die or exit first. This differential selection can produce patterns of mortality for the population as a whole that are surprisingly different from the patterns for subpopulations or individuals. Naive acceptance of observed population patterns may lead to erroneous policy recommendations if an intervention depends on the response of individuals. Furthermore, because patterns at the individual level may be simpler than composite population patterns, both theoretical and empirical research may be unnecessarily complicated by failure to recognize the effects of heterogeneity.     

Federal Statistics in a Complex Environment: The Case of the 1980 Census

The taking and the interpretation of something as big and as complicated as the national census is more than an exercise in statistical thinking. It involves other diverse fields such as ethics, epistemology, law, and politics. This article shows that a national census is more akin to so-called ill-structured problems. Unlike well-structured problems, the formulation of an ill-structured problem varies from field to field and from person to person, and the various aspects of an ill-structured problem (i.e., ethics, epistemology, etc.) cannot be clearly separated from one another. The 1980 census is discussed as an ill-structured problem, and a method for treating such problems is presented, within which statistical information is only one component.     

Examples of Differing Weighted and Unweighted Estimates from a Sample Survey

Unweighted estimators using data collected in a sample survey can be badly biased, whereas weighted estimators are approximately unbiased for population parameters. We present four examples using data from the 1988 National Maternal and Infant Health Survey to demonstrate that weighted and unweighted estimators can be quite different, and to show the underlying causes of such differences.     

Searching for differential expression: a non-parametric approach

Microarray experiments are being widely used in medical and biological research. The main features of these studies are the large number of variables (genes) involved and the low number of replicates (arrays). It seems clear that the most appropriate models, when looking for detecting differences in gene expression are those that exploit the most useful information to compensate for the lack of replicates. On the other hand, the control of the error in the decision process plays an important role for the high number of simultaneous statistical tests (one for each gene), so that concepts such as the false discovery rate (FDR) take a special importance. One of the alternatives for the analysis of the data in these experiments is based on the calculation of statistics derived from modifications of the classical methods used in this type of problems (moderated-t, B-statistic). Nonparametric techniques have been also proposed [B. Efron, R. Tibshirani, J.D. Storey, and V. Tusher, Empirical Bayes analysis of a microarray experiment, J. Amer. Stat. Assoc. 96 (2001), pp. 1151–1160; W. Pan, J. Lin, and C.T. Le, A mixture model approach to detecting differentially expressed genes with microarray data, Funct. Integr. Genomics 3 (2003), pp. 117–124], allowing the analysis without assuming any prior condition about the distribution of the data, which make them especially suitable in such situations. This paper presents a new method to detect differentially expressed genes based on non-parametric density estimation by a class of functions that allow us to define a distance between individuals in the sample (characterized by the coordinates of the individual (gene) in the dual space tangent to the manifold of parameters) [A. Miñarro and J.M. Oller, Some remarks on the individuals-score distance and its applications to statistical inference, Qüestiió, 16 (1992), pp. 43–57]. From these distances, we designed the test to determine the rejection region based on the control of FDR.     

Generation of d–optimal designs in a finite design space

This paper presents some considerations about the numerical procedures for generating D–optimal design in a finite design space. The influence of starting procedures and the finite set of points on the design efficiency is considered. Some modifications of the existing procedures for D–optimal designs generation are described. It is shown that for large number of factors the sequential procedures are more appropriate than the nonsequential ones     

Concordance of Complete or Right-Censored Rankings Based on Spearman's Footrule

A right-censored ranking is what results when a judge ranks only the “top K” of M objects. Complete uncensored rankings constitute a special case. We present two measures of concordance among the rankings of N ≥ 2 such judges, both based on Spearman's footrule. One measure is unweighted, while the other gives greatest weight to the first rank, less to the second, and so on. We consider methods for calculating or estimating the P-values of the corresponding tests of the hypothesis of random ranking.     

Risk and time preferences of entrepreneurs: evidence from a Danish field experiment

To understand how small business entrepreneurs respond to government policy one has to know their risk and time preferences. Are they risk averse, or have high discount rates, such that they are hard to motivate? We have conducted a set of field experiments in Denmark that will allow a direct characterization of small business entrepreneurs in terms of these traits. We build on experimental tasks that are well established in the literature. The results do not suggest that small business entrepreneurs are more or less risk averse than the general population under the assumption of Expected Utility Theory. However, we generally find an S-shaped probability weighting function for both small business entrepreneurs and non-entrepreneurs, with entrepreneurs being more optimistic about the chance of occurrence for the best outcome in lotteries with real monetary outcomes. The results also point to a significant difference in individual discount rates between entrepreneurs and non-entrepreneurs: entrepreneurs are willing to wait longer for certain rewards than the general population.     

Decision Makers as Statisticians: Diversity,Ambiguity, and Learning

I study individuals who use frequentist models to draw uniform inferences from independent and identically distributed data. The main contribution of this paper is to show that distinct models may be consistent with empirical evidence, even in the limit when data increases without bound. Decision makers may then hold different beliefs and interpret their environment differently even though they know each other's model and base their inferences on the same evidence. The behavior modeled here is that of rational individuals confronting an environment in which learning is hard, rather than individuals beset by cognitive limitations or behavioral biases.