Methods and Theory for Nonparametric Inference In High-dimensional Settings

Released on by Yunhua Xiang
preview-18

  • Methods and Theory for Nonparametric Inference In High-dimensional Settings Book Detail

  • Author : Yunhua Xiang
  • Release Date : 2021
  • Publisher :
  • Genre :
  • Pages : 136
  • ISBN 13 :
  • File Size : 58,58 MB
DOWNLOAD BOOK

Methods and Theory for Nonparametric Inference In High-dimensional Settings by Yunhua Xiang PDF Summary

Book Description: This dissertation addresses nonparametric estimation and inference problems of graphical modeling, linear association assessment, and matrix completion. First, we introduce a flexible framework for nonparametric graphical modeling. We propose three nonparametric measures of conditional dependence, which have theoretically optimal estimators that allow incorporation of flexible machine learning techniques and yield wald-type confidence intervals. In the second project, we propose a nonparametric parameter to measure the linear association between the outcome and explanatory variables. This parameter is always explicitly defined even when the true relationship is nonlinear and is equivalent with the regression coefficient under a linear model space. Thus, its estimator can be a more robust alternative to the standard model-based techniques to estimate the coefficients of a linear model. In the final project, we theoretically show that nuclear-norm penalization used for recovering low-rank matrices, remains effective even when the underlying matrices are generated by a low-dimensional non-linear manifold. The convergence rate can be expressed as a function of the size of the matrix, as well as the smoothness and dimension of the manifold, which is minimax optimal (up to a log term).

Disclaimer: www.yourbookbest.com does not own Methods and Theory for Nonparametric Inference In High-dimensional Settings books pdf, neither created or scanned. We just provide the link that is already available on the internet, public domain and in Google Drive. If any way it violates the law or has any issues, then kindly mail us via contact us page to request the removal of the link.

Statistics for High-Dimensional Data

Statistics for High-Dimensional Data

File Size : 63,63 MB
Total View : 3314 Views
DOWNLOAD

Modern statistics deals with large and complex data sets, and consequently with models containing a large number of parameters. This book presents a detailed ac

Nonparametric Learning in High Dimensions

Nonparametric Learning in High Dimensions

File Size : 95,95 MB
Total View : 7157 Views
DOWNLOAD

Abstract: "This thesis develops flexible and principled nonparametric learning algorithms to explore, understand, and predict high dimensional and complex datas

High-Dimensional Statistics

High-Dimensional Statistics

File Size : 2,2 MB
Total View : 2565 Views
DOWNLOAD

A coherent introductory text from a groundbreaking researcher, focusing on clarity and motivation to build intuition and understanding.