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SUMMARY: Multivariate versions of variable bandwidth kernel density estimators can be used to combat the eeects of the curse of dimensionality. They are also more exible than the xed bandwidth estimator to model complex (multimodal) densities. In this work, two variable bandwidth estimators are discussed: the balloon estimator which varies the smoothing(More)
Modern data analysis requires a number of tools to undercover hidden structure. For initial exploration of data, animated scatter diagrams and nonparametric density estimation in many forms and varieties are the techniques of choice. This article focuses on the application of histograms and nonparametric kernel methods to explore data. The details of(More)
In this paper, theoretical and practical aspects of the sample-point adaptive positive kernel density estimator are examined. A closed-form expression for the mean integrated squared error is obtained through the device of preprocessing the data by binning. With this expression, the exact behavior of the optimally adaptive smoothing parameter function is(More)
In recent years, the focus of study in smoothing parameter selection for kernel density estimation has been on the univariate case, while multivariate kernel density estimation has been largely neglected. In part, this may be due to the perception that calibrating multivariate densities is substantially more diicult. In this paper, we explicitly derive and(More)
The need for improvements over the xed kernel density estimator in certain situations has been discussed extensively in the literature, particularly in the application of density estimation to mode hunting. Problem densities often exhibit skewness or multimodality with diierences in scale for each mode. By varying the bandwidth in some fashion, it is(More)
OBJECTIVE Cerebral cavernous malformations (CCMs) are focal dysmorphic blood vessel anomalies predisposing individuals to hemorrhagic stroke and epilepsy. CCMs are sporadic or inherited as autosomal dominant disease with three known genes. The hypothesis that genetic heterogeneity would account for the remarkable variability in CCM manifestations was(More)
Functional analysis of variance (ANOVA) models partition a functional response according to the main effects and interactions of various factors. This article develops a general framework for functional ANOVA modeling from a Bayesian viewpoint, assigning Gaussian process prior distributions to each batch of functional effects. We discuss the choices to be(More)