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Full-Text Articles in Probability
Advances In Semi-Nonparametric Density Estimation And Shrinkage Regression, Hossein Zareamoghaddam
Advances In Semi-Nonparametric Density Estimation And Shrinkage Regression, Hossein Zareamoghaddam
Electronic Thesis and Dissertation Repository
This thesis advocates the use of shrinkage and penalty techniques for estimating the parameters of a regression model that comprises both parametric and nonparametric components and develops semi-nonparametric density estimation methodologies that are applicable in a regression context.
First, a moment-based approach whereby a univariate or bivariate density function is approximated by means of a suitable initial density function that is adjusted by a linear combination of orthogonal polynomials is introduced. Such adjustments are shown to be mathematically equivalent to making use of standard polynomials in one or two variables. Once extended to apply to density estimation, in which case …
Offline And Online Density Estimation For Large High-Dimensional Data, Aref Majdara
Offline And Online Density Estimation For Large High-Dimensional Data, Aref Majdara
Dissertations, Master's Theses and Master's Reports
Density estimation has wide applications in machine learning and data analysis techniques including clustering, classification, multimodality analysis, bump hunting and anomaly detection. In high-dimensional space, sparsity of data in local neighborhood makes many of parametric and nonparametric density estimation methods mostly inefficient.
This work presents development of computationally efficient algorithms for high-dimensional density estimation, based on Bayesian sequential partitioning (BSP). Copula transform is used to separate the estimation of marginal and joint densities, with the purpose of reducing the computational complexity and estimation error. Using this separation, a parallel implementation of the density estimation algorithm on a 4-core CPU is …