A semiparametric estimation procedure of dependence parameters in multivariate families of distributions

This paper investigates the properties of a semiparametric methodfor estimating the dependence parameters in a family of multivariatedistributions. The proposed estimator, obtained as a solutionof a pseudo-likelihood equation, is shown to be consistent,asymptotically normal and fully efficient at independence. Anatural estimator of its asymptotic variance is proved to beconsistent. Comparisons are made with alternative semiparametricestimators in the special case of Clayton's model for associationin bivariate data.     

Conditional properties of unconditional parametric bootstrap procedures for inference in exponential families

Higher-order inference about a scalar parameter in the presenceof nuisance parameters can be achieved by bootstrapping, incircumstances where the parameter of interest is a componentof the canonical parameter in a full exponential family. Theoptimal test, which is approximated, is a conditional one basedon conditioning on the sufficient statistic for the nuisanceparameter. A bootstrap procedure that ignores the conditioningis shown to have desirable conditional properties in providingthird-order relative accuracy in approximation of p-values associatedwith the optimal test, in both continuous and discrete models.The bootstrap approach is equivalent to third-order analyticalapproaches, and is demonstrated in a number of examples to givevery accurate approximations even for very small sample sizes.     

Relative index of inequality: definition, estimation, and inference

The relative index of inequality (RII) is a commonly used measure of the extent to which the occurrence of an outcome such as chronic illness or early death varies with socioeconomic status or some other background variable. The standard RII estimator applies only to linear variation in incidence rates. In this paper a general definition of the RII is introduced, alternative approaches to point estimation are considered, and a parametric bootstrap method is suggested for the construction of approximate confidence intervals. Estimation based on cubic splines fitted by maximum penalized likelihood is developed in some detail, and the proposed approach handles naturally the commonly needed adjustment for a 'standardizing' covariate such as age. Death rates in a large longitudinal study in England and Wales from 1996-2000 are analyzed in order to illustrate the various methods. A small simulation study explores the relative merits of different estimators. The approach based on cubic splines is found to reduce bias substantially, at the expense of some increase in variance, when variation in incidence rates is nonlinear.     

Comparison of Resubstitution,Data Splitting,the Bootstrap,and the Jackknife as Methods for Estimating Validity Indices of New Marker Tests: A Monte Carlo Study

Estimating the diagnostic efficiency of marker tests on the basis of the training set is an intricate problem of discriminant analysis for which no analytical solution exists. The paper outline the problem, describes various popular estimation procedures and presents the results of computer simulations comparing the estimators with respect to both bias and variance.     

Analysis of relation between virologic responses and immunologic responses, patient's factors in AIDS clinical trials using a semiparametric mixed-effects model

In this article we propose to use a semiparametric mixed-effects model based on an exploratory analysis of clinical trial data for a study of the relation between virologic responses and immunologic markers such as CD4+ and CD8 counts, and host-specific factors in AIDS clinical trials. The regression spline technique, used for inference for parameters in the model, reduces the unknown nonparametric components to parametric functions. It is simple and straightforward to implement the procedures using readily available software, and parameter inference can be developed from standard parametric models. We apply the model and the proposed method to an AIDS clinical study. Our findings indicate that viral load level is positively related to baseline viral load level, negatively related to CD4+ cell counts, but unrelated to CD8 cell counts and patient's age neither.     

Independence and interdependence in collective decision making: an agent-based model of nest-site choice by honeybee swarms

Condorcet''s jury theorem shows that when the members of a group have noisy but independent information about what is best for the group as a whole, majority decisions tend to outperform dictatorial ones. When voting is supplemented by communication, however, the resulting interdependencies between decision makers can strengthen or undermine this effect: they can facilitate information pooling, but also amplify errors. We consider an intriguing non-human case of independent information pooling combined with communication: the case of nest-site choice by honeybee (Apis mellifera) swarms. It is empirically well documented that when there are different nest sites that vary in quality, the bees usually choose the best one. We develop a new agent-based model of the bees'' decision process and show that its remarkable reliability stems from a particular interplay of independence and interdependence between the bees.     

Pitfalls of hypothesis tests and model selection on bootstrap samples: Causes and consequences in biometrical applications

The bootstrap method has become a widely used tool applied in diverse areas where results based on asymptotic theory are scarce. It can be applied, for example, for assessing the variance of a statistic, a quantile of interest or for significance testing by resampling from the null hypothesis. Recently, some approaches have been proposed in the biometrical field where hypothesis testing or model selection is performed on a bootstrap sample as if it were the original sample. P‐values computed from bootstrap samples have been used, for example, in the statistics and bioinformatics literature for ranking genes with respect to their differential expression, for estimating the variability of p‐values and for model stability investigations. Procedures which make use of bootstrapped information criteria are often applied in model stability investigations and model averaging approaches as well as when estimating the error of model selection procedures which involve tuning parameters. From the literature, however, there is evidence that p‐values and model selection criteria evaluated on bootstrap data sets do not represent what would be obtained on the original data or new data drawn from the overall population. We explain the reasons for this and, through the use of a real data set and simulations, we assess the practical impact on procedures relevant to biometrical applications in cases where it has not yet been studied. Moreover, we investigate the behavior of subsampling (i.e., drawing from a data set without replacement) as a potential alternative solution to the bootstrap for these procedures.     

Testing mate choice and overdominance at MH in natural families of Atlantic salmon Salmo salar

This study aimed to test mate choice and selection during early life stages on major histocompatibility (MH) genotype in natural families of Atlantic salmon Salmo salar spawners and juveniles, using nine microsatellites to reconstruct families, one microsatellite linked to an MH class I gene and one minisatellite linked to an MH class II gene. MH‐based mate choice was only detected for the class I locus on the first year, with lower expected heterozygosity in the offspring of actually mated pairs than predicted under random mating. The genotype frequencies of MH‐linked loci observed in the juveniles were compared with frequencies expected from Mendelian inheritance of parental alleles to detect selection during early life stages. No selection was detected on the locus linked to class I gene. For the locus linked to class II gene, observed heterozygosity was higher than expected in the first year and lower in the second year, suggesting overdominance and underdominance, respectively. Within family, juveniles' body size was linked to heterozygosity at the same locus, with longer heterozygotes in the first year and longer homozygotes in the second year. Selection therefore seems to differ from one locus to the other and from year to year.     

Endpoint error in smoothing and differentiating raw kinematic data: An evaluation of four popular methods

‘Endpoint error’ describes the erratic behavior at the beginning and end of the computed acceleration data which is commonly observed after smoothing and differentiating raw displacement data. To evaluate endpoint error produced by four popular smoothing and differentiating techniques, Lanshammar's (1982, J. Biomechanics 15, 99–105) modification of the Pezzack et al. (1977, J. Biomechanics, 10, 377–382) raw angular displacement data set was truncated at three different locations corresponding to the major peaks in the criterion acceleration curve. Also, for each data subset, three padding conditions were applied. Each data subset was smoothed and differentiated using the Butterworth digital filter, cubic spline, quintic spline, and Fourier series to obtain acceleration values. RMS residual errors were calculated between the computed and criterion accelerations in the endpoint regions. Although no method completely eliminated endpoint error, the results demonstrated clear superiority of the quintic spline over the other three methods in producing accurate acceleration values close to the endpoints of the modified Pezzack et al. (1977) data set. In fact, the quintic spline performed best with non-padded data (cumulative error=48.0 rad s⁻²). Conversely, when applied to non-padded data, the Butterworth digital filter produced wildly deviating values beginning more than the 10 points from the terminal data point (cumulative error=226.6 rad s⁻²). Each of the four methods performed better when applied to data subsets padded by linear extrapolation (average cumulative error=68.8 rad s⁻²) than when applied to analogous subsets padded by reflection (average cumulative error=86.1 rad s⁻²).     

Joint effect of nitrogen and phosphorous on glucose oxidase production by Aspergillus niger: Discussion of an experimental design with a risk of co-linearity

The combined effects of nitrogen and phosphorous on the production of glucose oxidase and gluconic acid by Aspergillus niger cannot be adequately described with Monod-type model, neither do they fit well to linear equations with interactions N × P, nor quadratic with N² and P² terms. On the other hand, the interactions of type N²P and NP², although common in real cases such as enzymatic kinetics in the presence of inhibitors, should be verified – if included in empiric models – by means of designs that can lead to artefactual results derived from the co-linearity. To avoid this risk we propose a procedure, based on the ‘bootstrap’ algorithm, which provided consistent results in the mentioned bioproductions. Applied together with methods of response surface and gradient, said procedure allowed to optimize the enzyme production as a function of the concentrations of N and P, to quintuple the initially obtained levels, and to explain other culture behaviours related with the sources of these nutrients.     

A simple test of the homogeneity of risk difference in sparse data: an application to a multicenter study

In this paper, we focus discussion on testing the homogeneity of risk difference for sparse data, in which we have few patients in each stratum, but a moderate or large number of strata. When the number of patients per treatment within strata is small (2 to 5 patients), none of test procedures proposed previously for testing the homogeneity of risk difference for sparse data can really perform well. On the basis of bootstrap methods, we develop a simple test procedure that can improve the power of the previous test procedures. Using Monte Carlo simulations, we demonstrate that the test procedure developed here can perform reasonable well with respect to Type I error even when the number of patients per stratum for each treatment is as small as two patients. We evaluate and study the power of the proposed test procedure in a variety of situations. We also include a comparison of the performance between the test statistics proposed elsewhere and the test procedure developed here. Finally, we briefly discuss the limitation of using the proposed test procedure. We use the data comparing two chemotherapy treatments in patients with multiple myeloma to illustrate the use of the proposed test procedure.     

Background choice as an anti-predator strategy: the roles of background matching and visual complexity in the habitat choice of the least killifish

Because background matching improves concealment, prey animals have traditionally been expected to prefer parts of the habitat that match their visual appearance. However, empirical support for this is scarce. Moreover, this idea has recently been challenged by an alternative hypothesis: visual complexity of the background impedes prey detection, and hence prey could instead prefer complex parts of the habitat. We used the least killifish to test, with and without predation threat, for the importance of the visual similarity between the fish and the background, and the level of visual complexity of the background. We observed their choice between backgrounds patterned with elements based on the longitudinal black stripe of the fish. Predation risk was important under some circumstances, and induced a preference for a background of matching horizontal stripes compared with mismatching vertical stripes. Interestingly, females under predation threat showed a preference for a complex background of randomly oriented and overlapping stripes compared with matching stripes, whereas males did not discriminate between these two. Additionally, males showed a preference for matching stripes compared with complex shapes, whereas females did not discriminate between these backgrounds. We conclude that matching is important in the choice for safe habitat, but some aspects of visual complexity may override or act together with background matching.     

Shoal and prey patch choice by co-occurring fishes and prawns: inter-taxa use of socially transmitted cues

Animals can use socially transmitted information to learn about the distribution and quality of resources without incurring the costs associated with having to search for and sample them first hand. Recently, it has been shown that the use of chemical social information specific to patterns of diet and habitat use is an important mechanism underpinning recognition and social organization in shoaling fishes. In this study we revealed that the use of resource-specific chemical information is not limited to conspecifics, or even members of the same taxon. In a series of laboratory experiments, we showed that threespine sticklebacks (Gasterosteus aculeatus) could recognize similar patterns of habitat use in common prawns (Leander serratus), preferentially orientating towards groups of prawns exposed to the same habitats as themselves, and even selecting foraging patches located close to them. Prawns were seen to use habitat-specific cues generated by conspecifics, but not by sticklebacks, suggesting that the benefits of forming these heterospecific social association patterns may be unequal for prawns and fishes. Our findings suggest that some species might use co-occurring, unrelated species as information centres in order to orient and locate resources within their surroundings.     

River phytoplankton prediction model by Artificial Neural Network: Model performance and selection of input variables to predict time-series phytoplankton proliferations in a regulated river system

In this study, a comparison between statistical regression model and Artificial Neural Network (ANN) is given on the effectiveness of ecological model of phytoplankton dynamics in a regulated river. From the results of the study, the effectiveness of ANN over statistical method was proposed. Also feasible direction of increasing ANN models' performance was provided. A hypertrophic river data was used to develop prediction models (chlorophyll a (chl. a) 41.7 ± 56.8 μg L^− 1; n = 406). Higher time-series predictability was found from the ANN model. Failure of statistical methods would be due to the complex nature of ecological data in the regulated river ecosystems. Reduction of ANN model size by decreasing the number of input variables according to the sensitivity analysis did not have effectiveness with respect to the predictability on testing data set (RMSE of the ANN with all 27 variables, 25.7; 47.9 from using 2 highly sensitive variables; 42.9 from using 5 sensitive variables; 33.1 from using 15 variables). Even though the ANN model presented high performance in prediction accuracy, more efficient methods of selecting feasible input information are strongly requested for the prediction of freshwater ecological dynamics.     

The uropod as a proxy for total length distribution in Antarctic krill: an assessment of different models

The properties of the regression of standard length on the length of the exopodit of the uropod of Euphausia superba as a method to estimate the distribution of the standard length from penguin stomach contents samples are explored. The distance between the estimated and observed distributions was measured with the Kolmogorov–Smirnov statistic. Sample variability was determined using resampling techniques. The ability of linear functions (Models I and II), allometric and non-parametric methods to recover the observed distributions was evaluated within samples and exchanging parameters between samples. Linear and allometric models proved inadequate to recover the distribution, while the differences obtained with non-parametric methods fall within the bounds of sample variability, suggesting that a linear equation does not capture the relation between total and exopodit length. The use of a non-parametric regression is recommended to increase the sample size when estimating the distributions of prey lengths in the stomach contents of Antarctic penguins.