Query: density estimation

title: Estimation of the concentration of low density lipoprotein cholesterol in plasma, without use of the preparative ultracentrifuge.
abstract: A method for estimating the cholesterol content of the serum low density lipoprotein fraction (Sf0 20) is presented. The method involves measurements of fasting plasma total cholesterol, triglyceride, and high density lipoprotein cholesterol concentrations, none of which requires the use of the preparative ultracentrifuge. Comparison of this suggested procedure with the more direct procedure, in which the ultracentrifuge is used, yielded correlation coefficients of .94 to .99, depending on the patient population compared.

title: On Estimation of a Probability Density Function and Mode
abstract: Given a sequence of independent identically distributed random variables with a common probability density function, the problem of the estimation of a probability density function and of determining the mode of a probability function are discussed. Only estimates which are consistent and asymptotically normal are constructed.

title: Density estimation for statistics and data analysis
abstract: Survey of Existing Methods. The Kernel Method for Univariate Data. The Kernel Method for Multivariate Data. Three Important Methods.  Estimation in Action.

title: Density Estimation for Statistics and Data Analysis

title: Body fat assessed from total body density and its estimation from skinfold thickness: measurements on 481 men and women aged from 16 to 72 years.
abstract: The fat content of the human body has physiological and medical importance. It may influence morbidity and mortality, it may aIter the effectiveness of drugs and anaesthetics, and it may affect the ability to withstand exposure to cold and starvation. Thus the measurement of the total body fat provides useful information. In many people, but by no means everyone, a moderately satisfactory estimate of the body fat content can be obtained from the height and weight. However, for more precise evaluation several methods are available which give a reasonably accurate measure of body fat both in normal subjects and in individuals with unusual body builds. Most of these methods are based on the assumption that the body can be considered to consist of two compartments of relatively constant composition but which are distinctly different; these compartments are: (I) the body fat, which includes the entire content of chemical fat or lipids in the body, and (2) the fat free mass (FFM) which includes all the rest of the body apart from fat. The body fat compartment is anhydrous, contains no potassium and has a fairly constant density of about 0.90 x 103 kg/m3. The fat free compartment on the other hand probably has a fairly constant density of about 1.10 x 103 kg/m3, a potassium content of about 68 mequiv./kg in males (about 10% less in females) and a water content of about 720 g/kg. Thus measurement of body density or of total body K or of total body water allows a calculation of the relative proportion of these two compartments in the body and therefore also of the total fat content. The accuracy of these measures, however, is limited by the variability of the composition and density of the fat free compartment in different individuals. In particular, individuals with a relatively high or

title: Density Estimation for Statistics and Data Analysis.
abstract: Suppose, now, that we have a set of observed data points assumed to be a sample from an unknown probability density function. Density estimation, as discussed in this book, is the construction of an estimate of the density function from the observed data. The two main aims of the book are to explain how to estimate a density from a given data set and to explore how density estimates can be used, both in their own right and as an ingredient of other statistical procedures.

title: Multivariate Density Estimation, Theory, Practice and Visualization
abstract: Representation and Geometry of Multivariate Data. Nonparametric Estimation Criteria.  Averaged Shifted Histograms. Kernel Density Estimators. The Curse of Dimensionality and Dimension Reduction. Nonparametric Regression and Additive Models. Special Topics.

title: Model Based Clustering, Discriminant Analysis, and Density Estimation
abstract: Cluster analysis is the automated search for groups of related observations in a dataset. Most clustering done in practice is based largely on heuristic but intuitively reasonable procedures, and most clustering methods available in commercial software are also of this type. However, there is little systematic guidance associated with these methods for solving important practical questions that arise in cluster analysis, such as how many clusters are there, which clustering method should be used, and how should outliers be handled. We review a general methodology for model based clustering that provides a principled statistical approach to these issues. We also show that this can be useful for other problems in multivariate analysis, such as discriminant analysis and multivariate density estimation. We give examples from medical diagnosis, minefield detection, cluster recovery from noisy data, and spatial density estimation. Finally, we mention limitations of the methodology and discuss recent developments in model based clustering for non Gaussian data, high dimensional datasets, large datasets, and Bayesian estimation.

title: The estimation of the gradient of a density function, with applications in pattern recognition
abstract: Nonparametric density gradient estimation using a generalized kernel approach is investigated. Conditions on the kernel functions are derived to guarantee asymptotic unbiasedness, consistency, and uniform consistency of the estimates. The results are generalized to obtain a simple mcan shift estimate that can be extended in a k nearest neighbor approach. Applications of gradient estimation to pattern recognition are presented using clustering and intrinsic dimensionality problems, with the ultimate goal of providing further understanding of these problems in terms of density gradients.

title: Bayesian Density Estimation and Inference Using Mixtures
abstract: We describe and illustrate Bayesian inference in models for density estimation using mixtures of Dirichlet processes. These models provide natural settings for density estimation and are exemplified by special cases where data are modeled as a sample from mixtures of normal distributions. Efficient simulation methods are used to approximate various prior, posterior, and predictive distributions. This allows for direct inference on a variety of practical issues, including problems of local versus global smoothing, uncertainty about density estimates, assessment of modality, and the inference on the numbers of components. Also, convergence results are established for a general class of normal mixture models.