Nonparametric estimation of univariate and mixing densities
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# Nonparametric estimation of univariate and mixing densities a Bayesian Least Squares approach by John I. Shih

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### Subjects:

• Bayesian statistical decision theory.

## Book details:

Edition Notes

The Physical Object ID Numbers Statement by John I. Shih. Pagination [10], 120 leaves, bound : Number of Pages 120 Open Library OL14213096M

This article reviews recent developments in nonparametric density estimation and includes topics that have been omitted from review articles and books on the subject. The early density estimation methods, such as the histogram, kernel estimators, and orthogonal series estimators are still very popular, and recent research on them is described. Chapter 3 Kernel density estimation II. As it happens in the univariate case, any random vector $$\mathbf{X}$$ supported in $$\mathbb{R}^p$$ is completely characterized by its cdf. However, cdfs are even harder to visualize and interpret when $$p>1$$, as the accumulation of probability happens simultaneously in several a consequence, densities become highly valuable tools for. Multivariate kernel density estimation. Kernel density estimation can be extended to estimate multivariate densities $$f$$ in $$\mathbb{R}^p$$ based on the same principle: perform an average of densities “centered” at the data points. For a sample $$\mathbf{X}_1,\ldots,\mathbf{X}_n$$ in $$\mathbb{R}^p$$, the kde of $$f$$ evaluated at $$\mathbf{x}\in\mathbb{R}^p$$ is defined as. A multivariate mixture model is determined by three elements: the number of components, the mixing proportions, and the component distributions. Assuming that the number of components is given and that each mixture component has independent marginal distributions, we propose a nonparametric method to estimate the component distributions.