César Sánchez-Sellero

Universal smoothing factor selection in density estimation: theory and practice

AbstractIn earlier work with Gabor Lugosi, we introduced a method to select a smoothing factor for kernel density estimation such that, forall densities in all dimensions, theL1 error of the corresponding kernel estimate is not larger than 3+∈ times the error of the estimate with the optimal smoothing factor plus a constant times

Accuracy of binned kernel functional approximations

\sqrt {\log n/n}

Density estimation using game theory

, wheren is the sample size, and the constant only depends on the complexity of the kernel used in the estimate. The result is nonasymptotic, that is, the bound is valid for eachn. The estimate uses ideas from the minimum distance estimation work of Yatracos. We present a practical implementation of this estimate, report on some comparative results, and highlight some key properties of the new method.

Local Differences in the Archbishopric of Santiago de Compostela (Galicia, Spain) in Relation to the Consanguinity Structure, 1900-1979

A plug-in type bandwidth selector is presented for density estimation with truncated and censored data. It is based on a representation of the MISE function obtained in the paper. Rate of convergence and limit distribution are derived for this selector. A bootstrap method is introduced to estimate the MISE whose minimizer is an alternative bandwidth selector. A simulation study was carried out to assess the behavior with small samples. This methodology is applied to a real-data problem consisting of reporting delay of AIDS cases. The almost sure representation of the product-limit estimator is a key tool in our proofs.

Testing the Predictor Effect on a Functional Response

Virtually all common bandwidth selection algorithms are based on a certain type of kernel functional estimator. Such estimators can be computationally very expensive, so in practice they are often replaced by fast binned approximations. This is especially worthwhile when the bandwidth selection method involves iteration. Results for the accuracy of these approximations are derived and then used to provide an understanding of the number of binning grid points required to achieve a given level of accuracy. Our results apply to both univariate and multivariate settings. Multivariate contexts are of particular interest since the cost due to having a higher number of grid points can be quite significant.

Predicting trace gas concentrations using quantile regression models

A new lack-of-fit test for quantile regression models, that is suitable even with high-dimensional covariates, is proposed. The test is based on the cumulative sum of residuals with respect to unidimensional linear projections of the covariates. To approximate the critical values of the test, a wild bootstrap mechanism convenient for quantile regression is used. An extensive simulation study was undertaken that shows the good performance of the new test, particularly when the dimension of the covariate is high. The test can also be applied and performs well under heteroscedastic regression models. The test is illustrated with real data about the economic growth of 161 countries.

Cytokine-based Predictive Models to Estimate the Probability of Chronic Periodontitis: Development of Diagnostic Nomograms

Abstract.In this note we show that the mathematical tools of cooperative game theory allow a successful approach to the statistical problem of estimating a density function. Specifically, any random sample of an absolutely continuous random variable determines a transferable utility game, the Shapley value of which proves to be an estimator of the density function of binned kernel and WARPing types, with good computational and statistical properties.

Projection-based nonparametric goodness-of-fit testing with functional covariates

The microgeographic variability of consanguinity in the Archbishopric of Santiago de Compostela (Galicia) between 1900 and 1979 was studied. This Archbishopric covers 106 local councils integrated by 964 parishes, of which 677 (70.23%) were analyzed. Of the 307,094 marriages counted within this period, 15,739 corresponded to weddings between biologically related couples. Within the Archbishopric, eight geographical regions were considered: six coastal regions (Golfo Artabro, Bergantiños, Fisterra, Xallas, Santiago Oeste, and Rías Baixas) and two inland regions (Santiago Este and Terra de Montes). In order to evaluate the differences and similarities among them, the frequencies of all types of marriages (consanguineous and nonconsanguineous) were considered. First, a hierarchical grouping of the regions based on their chi-squared distances was performed. Then, in order to analyze relationships that are exclusively due to the structure of consanguinity, a correspondence analysis was performed and only the frequency of the different types of consanguineous marriages was taken into account. The results from both statistical analyses indicate special features of the Xallas region, both in the level of inbreeding (8.75%, the highest in the Archbishopric) and in the structure of consanguinity, for which a high proportion of uncle-niece marriages was found (6.22% of all consanguineous marriages). In all cases the structure of consanguinity provides informative nuances on the differences and similarities among population groups.