Some aspects of density estimation by the kernel method
Başlık:
Some aspects of density estimation by the kernel method
Yazar:
Bowman, Adrian William, author.
ISBN:
9780438053489
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (128 pages)
Genel Not:
Source: Dissertation Abstracts International, Volume: 76-08C.
Advisors: D. M. Titterington.
Özet:
This thesis is concerned with the nonparametric estimation of probability density functions. Chapter 1 provides a brief introduction by contrasting the parametric and nonparametric approaches to statistical analysis. Some examples of applications of nonparametric density estimation are also given. In Chapter 2, three methods of density estimation are introduced, related and compared. These are the fixed kernel, variable kernel and nearest neighbour procedures. Common to all methods is the problem of choosing a parameter controlling the smoothness of the estimator. Approaches to this problem are reviewed, some new suggestions made and a simulation study carried out to evaluate performance. Particular attention is paid to a new variable kernel method based on a transformation to Normality. This technique combines the benefit of variable kernels with a simple method of choice of smoothing parameter. The consistency of some of the estimators is also discussed. Chapter 3 is concerned with the application of density estimates to goodness-of-fit testing for Normality. Several test statistics, based on distance measures between density functions, are proposed. Simulations on power against various alternatives are used to evaluate their practical effectiveness and the theoretical problem of establishing the asymptotic distributions of the test statistics is also discussed. Chapter 4 deals principally with location parameter estimation and relates the technique of M-estimation, which is designed to be robust against outliers, to estimation of the mode of a distribution by the maximising value of a density estimate. The two approaches are compared and contrasted, with numerical evidence given for Normal and non-Normal distributions. The methods of maximum likelihood and minimum distance estimation are also formulated in a density estimation framework. Chapter 5 deals with nonparametric estimation of the cell probabilities in a discrete distribution. The kernel approach is outlined and suggested methods of choice of smoothing parameter are reviewed. Kernels appropriate to ordered categorical data are discussed, with particular interest in the identification of assumptions implicit in their use and of the types of distribution for which they are most appropriate. The consistency of the estimators based on the possible choices of smoothing parameter and of kernel function are investigated and small sample comparisons made in terms of mean square error. Some of these methods are also applied to estimation of an index of species diversity in an ecological community.
Notlar:
School code: 0547
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Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
---|---|---|---|
XX(684462.1) | 684462-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
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