Librería Portfolio

Features

States concepts in a precise manner
Emphasizes practical value throughout the text
Provides a main body section which uses math stat sparingly, as well as an ´extras´ section for those who feel comfortable with analysis using math stat
Summary

Statistical Regression and Classification: From Linear Models to Machine Learning takes an innovative look at the traditional statistical regression course, presenting a contemporary treatment in line with today´s applications and users. The text takes a modern look at regression:

* A thorough treatment of classical linear and generalized linear models, supplemented with introductory material on machine learning methods.

* Since classification is the focus of many contemporary applications, the book covers this topic in detail, especially the multiclass case.

* In view of the voluminous nature of many modern datasets, there is a chapter on Big Data.

* Has special Mathematical and Computational Complements sections at ends of chapters, and exercises are partitioned into Data, Math and Complements problems.

* Instructors can tailor coverage for specific audiences such as majors in Statistics, Computer Science, or Economics.

* More than 75 examples using real data.

The book treats classical regression methods in an innovative, contemporary manner. Though some statistical learning methods are introduced, the primary methodology used is linear and generalized linear parametric models, covering both the Description and Prediction goals of regression methods. The author is just as interested in Description applications of regression, such as measuring the gender wage gap in Silicon Valley, as in forecasting tomorrow´s demand for bike rentals. An entire chapter is devoted to measuring such effects, including discussion of Simpson´s Paradox, multiple inference, and causation issues. Similarly, there is an entire chapter of parametric model fit, making use of both residual analysis and assessment via nonparametric analysis.



Table of Contents

Preface


Chapter One

Setting the Stage


Example: Predicting Bike-Sharing Activity

Example of the Prediction Goal: Body Fat

Example of the Description Goal: Who Clicks Web Ads?

Optimal Prediction

A Note About E(), Samples and Populations

Example: Do Baseball Players Gain Weight As They Age?
Prediction vs Description
A First Estimator
A Possibly Better Estimator, Using a Linear Model

Parametric vs Nonparametric Models

Example: Click-Through Rate

Several Predictor Variables
Multipredictor Linear Models
Estimation of Coefficients
The Description Goal
Nonparametric Regression Estimation: k-NN
Looking at Nearby Points
Measures of Nearness
The k-NN Method, and Tuning Parameters
Nearest-Neighbor Analysis in the regtools
Package
Example: Baseball Player Data

After Fitting a Model, How Do We Use It for Prediction?
Parametric Settings
Nonparametric Settings
The Generic predict() Function

Overfitting, and the Variance-Bias Tradeoff
Intuition
Example: Student Evaluations of Instructors

Cross-Validation
Linear Model Case
The Code
Applying the Code
k-NN Case
Choosing the Partition Sizes


Important Note on Tuning Parameters


Rough Rule of Thumb


Example: Bike-Sharing Data
Linear Modeling of _(t)
Nonparametric Analysis


Interaction Terms, Including Quadratics
Example: Salaries of Female Programmers and Engineers

Saving Your Work
Higher-Order Polynomial Models


Classification Techniques

It´s a Regression Problem!

Example: Bike-Sharing Data


Crucial Advice: Don´t Automate, Participate!


Mathematical Complements
Indicator Random Variables
Mean Squared Error of an Estimator
_(t) Minimizes Mean Squared Prediction Error
_(t) Minimizes the Misclassification Rate
Kernel-Based Nonparametric Estimation of Regression
Functions
General Nonparametric Regression
Some Properties of Conditional Expectation
Conditional Expectation As a Random Variable
The Law of Total Expectation
Law of Total Variance
Tower Property
Geometric View

Computational Complements
CRAN Packages
The Function tapply() and Its Cousins
The Innards of the k-NN Code
Function Dispatch


Centering and Scaling

Further Exploration: Data, Code and Math Problems



Chapter Two

Linear Regression Models



Notation

The ´Error Term´


Random- vs Fixed-X Cases

Least-Squares Estimation
Motivation
Matrix Formulations
() in Matrix Terms
Using Matrix Operations to Minimize ()
Models Without an Intercept Term


A Closer Look at lm() Output
Statistical Inference

Assumptions
Classical
Motivation: the Multivariate Normal Distribution Family


Unbiasedness and Consistency
b_ Is Unbiased
Bias As an Issue/Nonissue
b_ Is Statistically Consistent


Inference under Homoscedasticity
Review: Classical Inference on a Single Mean
Back to Reality
The Concept of a Standard Error
Extension to the Regression Case
Example: Bike-Sharing Data

Collective Predictive Strength of the X(j)
Basic Properties
Definition of R
Bias Issues
Adjusted-R
The Leaving-One-Out Method´
Extensions of LOOM
LOOM for k-NN
Other Measures


The Practical Value of p-Values Small OR Large
Misleadingly Small p-Values
Example: Forest Cover Data
Example: Click Through Data
Misleadingly LARGE p-Values
The Verdict

Missing Values

Mathematical Complements
Covariance Matrices
The Multivariate Normal Distribution Family
The Central Limit Theorem
Details on Models Without a Constant Term
Unbiasedness of the Least-Squares Estimator
Consistency of the Least-Squares Estimator
Biased Nature of S

The Geometry of Conditional Expectation
Random Variables As Inner Product Spaces
Projections
Conditional Expectations As Projections
Predicted Values and Error Terms Are Uncorrelated
Classical \Exact´ Inference
Asymptotic (p + )-Variate Normality of b_


Computational Complements
Details of the Computation of ()
R Functions Relating to the Multivariate Normal Distribution
Family
Example: Simulation Computation of a Bivariate
Normal Quantity
More Details of ´lm´ Objects

Further Exploration: Data, Code and Math Problems



Chapter Three

Homoscedasticity and Other Assumptions in Practice

Normality Assumption


Independence Assumption Don´t Overlook It
Estimation of a Single Mean
Inference on Linear Regression Coefficients
What Can Be Done?
Example: MovieLens Data

Dropping the Homoscedasticity Assumption
Robustness of the Homoscedasticity Assumption
Weighted Least Squares
A Procedure for Valid Inference
The Methodology
Example: Female Wages
Simulation Test
Variance-Stabilizing Transformations
The Verdict


Further Reading


Computational Complements
The R merge() Function


Mathematical Complements
The Delta Method
Dis