Statistical foundations of data science. (2020)

• Record Type: Book
• Further Information: Note: Jianqing Fan, Runze Li, Cun-Hui Zhang, Hui Zou.
• Authors: Fan, Jianqing; Li, Runze; Zhang, Cun-Hui; Zou, Hui
• Contents: I. Introduction Rise of Big Data and Dimensionality Biological Sciences Health Sciences Computer and Information Sciences Economics and Finance Business and Program Evaluation Earth Sciences and Astronomy Impact of Big Data Impact of Dimensionality Computation Noise Accumulation Spurious Correlation Statistical theory Aim of High-dimensional Statistical Learning What big data can do Scope of the book 2. Multiple and Nonparametric Regression Introduction Multiple Linear Regression The Gauss-Markov Theorem Statistical Tests Weighted Least-Squares Box-Cox Transformation Model Building and Basis Expansions Polynomial Regression Spline Regression Multiple Covariates Ridge Regression Bias-Variance Tradeo Penalized Least Squares Bayesian Interpretation Ridge Regression Solution Path Kernel Ridge Regression Regression in Reproducing Kernel Hilbert Space Leave-one-out and Generalized Cross-validation Exercises 3. Introduction to Penalized Least-Squares Classical Variable Selection Criteria Subset selection Relation with penalized regression Selection of regularization parameters Folded-concave Penalized Least Squares Orthonormal designs Penalty functions Thresholding by SCAD and MCP Risk properties Characterization of folded-concave PLS Lasso and L Regularization Nonnegative garrote Lasso Adaptive Lasso Elastic Net Dantzig selector SLOPE and Sorted Penalties Concentration inequalities and uniform convergence A brief history of model selection Bayesian Variable Selection Bayesian view of the PLS A Bayesian framework for selection Numerical Algorithms Quadratic programs Least angle regression_ Local quadratic approximations Local linear algorithm Penalized linear unbiased selection_ Cyclic coordinate descent algorithms Iterative shrinkage-thresholding algorithms Projected proximal gradient method ADMM Iterative Local Adaptive Majorization and Minimization Other Methods and Timeline Regularization parameters for PLS Degrees of freedom Extension of information criteria Application to PLS estimators Residual variance and refitted cross-validation Residual variance of Lasso Refitted cross-validation Extensions to Nonparametric Modeling Structured nonparametric models Group penalty Applications Bibliographical notes Exercises 4. Penalized Least Squares: Properties Performance Benchmarks Performance measures Impact of model uncertainty Bayes lower bounds for orthogonal design Minimax lower bounds for general design Performance goals, sparsity and sub-Gaussian noise Penalized L Selection Lasso and Dantzig Selector Selection consistency Prediction and coefficient estimation errors Model size and least squares after selection Properties of the Dantzig selector Regularity conditions on the design matrix Properties of Concave PLS Properties of penalty functions Local and oracle solutions Properties of local solutions Global and approximate global solutions Smaller and Sorted Penalties Sorted concave penalties and its local approximation Approximate PLS with smaller and sorted penalties Properties of LLA and LCA Bibliographical notes Exercises 5. Generalized Linear Models and Penalized Likelihood Generalized Linear Models Exponential family Elements of generalized linear models Maximum likelihood Computing MLE: Iteratively reweighed least squares Deviance and Analysis of Deviance Residuals Examples Bernoulli and binomial models Models for count responses Models for nonnegative continuous responses Normal error models Sparest solution in high confidence set A general setup Examples Properties Variable Selection via Penalized Likelihood Algorithms Local quadratic approximation Local linear approximation Coordinate descent Iterative Local Adaptive Majorization and Minimization Tuning parameter selection An Application Sampling Properties in low-dimension Notation and regularity conditions The oracle property Sampling Properties with Diverging Dimensions Asymptotic properties of GIC selectors Properties under Ultrahigh Dimensions The Lasso penalized estimator and its risk property Strong oracle property Numeric studies Risk properties Bibliographical notes Exercises 6. Penalized M-estimators Penalized quantile regression Quantile regression Variable selection in quantile regression A fast algorithm for penalized quantile regression Penalized composite quantile regression Variable selection in robust regression Robust regression Variable selection in Huber regression Rank regression and its variable selection Rank regression Penalized weighted rank regression Variable Selection for Survival Data Partial likelihood Variable selection via penalized partial likelihood and its properties Theory of folded-concave penalized M-estimator Conditions on penalty and restricted strong convexity Statistical accuracy of penalized M-estimator with folded concave penalties Computational accuracy Bibliographical notes Exercises 7. High Dimensional Inference Inference in linear regression Debias of regularized regression estimators Choices of weights Inference for the noise level Inference in generalized linear models Desparsified Lasso Decorrelated score estimator Test of linear hypotheses Numerical comparison An application Asymptotic efficiency Statistical efficiency and Fisher information Linear regression with random design Partial linear regression Gaussian graphical models Inference via penalized least squares Sample size in regression and graphical models General solutions_ Local semi-LD decomposition Data swap Gradient approximation Bibliographical notes Exercises 8. Feature Screening Correlation Screening Sure screening property Connection to multiple comparison Iterative SIS Generalized and Rank Correlation Screening Feature Screening for Parametric Models Generalized linear models A unified strategy for parametric feature screening Conditional sure independence screening <P
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2020
• Extent: 1 online resource, illustrations (black and white)
• Subjects: 519.5; Statistics
• Languages: English
• ISBNs: 9780429527616
• Related ISBNs: 9781466510852; 9780429542312; 9780429096280
• Notes: Note: Description based on CIP data; resource not viewed.
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