DENSITY ESTIMATION FOR STATISTICS AND DATA ANALYSIS

Published in Monographs on STATISTICS and Applied Probability, London: Chapman and Hall, ESTIMATION FOR STATISTICS AND SilvermanSchool of Mathematics University of Bath, UKTable of ContentsINTRODUCTIONWhat is DENSITY ESTIMATION ? DENSITY estimates in the exploration and presentation of dataFurther readingSURVEY OF EXISTING METHODSI ntroductionHistogramsThe naive estimatorThe kernel estimatorThe nearest neighbour methodThe variable kernel methodOrthogonal series estimatorsMaximum penalized likelihood estimatorsGeneral weight function estimatorsBounded domains and directional dataDiscussion and bibliography1. What is DENSITY ESTIMATION ?Theprobability DENSITY functionis a fundamental concept in STATISTICS . Consider any random quantityXthat has probabilitydensity functionf. Specifying the functionfgives a natural description of the distribution ofX, and allows probabilitiesassociated withXto be found from the relationSuppose, now, that we have a set of observed data points assumed to be a sample from an unknown probability DENSITY , as discussed in this book, is the construction of an estimate of the DENSITY function from the observed two main aims of the book are to explain how to

the sudden infant death cases might be a mixture of the control density with a smaller proportion of a contaminating densityof higher mean. Thus it appeared that in a minority (perhaps a quarter to a third) of the sudden deaths, the degranulated mast cell count was exceptionally high. In this example the conclusions could only be regarded as a ...

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