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E-raamat: Computational Statistics Handbook with MATLAB

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(Bureau of Labor Statistics, Washington, D.C., USA), (Strayer University, Fredericksburg, Virginia, USA)
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A Strong Practical Focus on Applications and AlgorithmsComputational Statistics Handbook with MATLAB®, Third Edition covers todays most commonly used techniques in computational statistics while maintaining the same philosophy and writing style of the bestselling previous editions. The text keeps theoretical concepts to a minimum, emphasizing the implementation of the methods.

New to the Third EditionThis third edition is updated with the latest version of MATLAB and the corresponding version of the Statistics and Machine Learning Toolbox. It also incorporates new sections on the nearest neighbor classifier, support vector machines, model checking and regularization, partial least squares regression, and multivariate adaptive regression splines.

Web ResourceThe authors include algorithmic descriptions of the procedures as well as examples that illustrate the use of algorithms in data analysis. The MATLAB code, examples, and data sets are available online.

Arvustused

Praise for Previous Editions:" useful as a reference where one can look to get a concise description of a statistical methodology and MATLAB code that can be used to implement it the book is excellent." Michael J. Evans, Mathematical Reviews, 2009e

"My own brief assessment of the book leaves me impressed with the number of subjects covered the book can be a valuable reference to practicing statisticians (or statistical researchers) using MATLAB as their computing engines." Biometrics, March 2009

" this book is perfectly appropriate as a textbook for an introductory course on computational statistics. It covers many useful topics, which in combination with the well-documented code, make the underlying concepts easy to grasp by the students. a very nice book to be used in an undergraduate- or masters-level computational statistics course. It would also prove useful to researchers in other fields that want to learn and implement quickly some advanced statistical techniques." Journal of Statistical Software, July 2004, Vol. 11

"I am pleased to see the publication of a comprehensive book related to computational statistics and MATLAB. this book is ambitious and well written. As a long-time user of MATLAB, I find this book useful as a reference, and thus recommend it highly to statisticians who use MATLAB. The book also would be very useful to engineers and scientists who are well trained in statistics." Journal of the American Statistical Association, June 2004, Vol. 99, No. 466

Preface to the Third Edition xix
Preface to the Second Edition xxi
Preface to the First Edition xxv
Chapter 1 Introduction
1.1 What Is Computational Statistics?
1(2)
1.2 An Overview of the Book
3(3)
Philosophy
3(1)
What Is Covered
4(1)
A Word About Notation
5(1)
1.3 MATLAB® Code
6(3)
Computational Statistics Toolbox
8(1)
Internet Resources
8(1)
1.4 Further Reading
9(2)
Chapter 2 Probability Concepts
2.1 Introduction
11(1)
2.2 Probability
12(5)
Background
12(2)
Probability
14(2)
Axioms of Probability
16(1)
2.3 Conditional Probability and Independence
17(4)
Conditional Probability
17(1)
Independence
18(1)
Bayes' Theorem
19(2)
2.4 Expectation
21(3)
Mean and Variance
21(2)
Skewness
23(1)
Kurtosis
23(1)
2.5 Common Distributions
24(24)
Binomial
24(2)
Poisson
26(3)
Uniform
29(1)
Normal
30(4)
Exponential
34(2)
Gamma
36(1)
Chi-Square
37(1)
Weibull
38(2)
Beta
40(2)
Student's t Distribution
42(1)
Multivariate Normal
43(4)
Multivariate t Distribution
47(1)
2.6 MATLAB® Code
48(1)
2.7 Further Reading
49(2)
Exercises
51(4)
Chapter 3 Sampling Concepts
3.1 Introduction
55(1)
3.2 Sampling Terminology and Concepts
55(8)
Sample Mean and Sample Variance
57(1)
Sample Moments
58(2)
Covariance
60(3)
3.3 Sampling Distributions
63(2)
3.4 Parameter Estimation
65(8)
Bias
66(1)
Mean Squared Error
66(1)
Relative Efficiency
67(1)
Standard Error
67(1)
Maximum Likelihood Estimation
68(3)
Method of Moments
71(2)
3.5 Empirical Distribution Function
73(5)
Quantiles
74(4)
3.6 MATLAB® Code
78(1)
3.7 Further Reading
79(1)
Exercises
80(3)
Chapter 4 Generating Random Variables
4.1 Introduction
83(1)
4.2 General Techniques for Generating Random Variables
83(11)
Uniform Random Numbers
83(3)
Inverse Transform Method
86(4)
Acceptance-Rejection Method
90(4)
4.3 Generating Continuous Random Variables
94(12)
Normal Distribution
94(1)
Exponential Distribution
94(2)
Gamma
96(1)
Chi-Square
97(2)
Beta
99(2)
Multivariate Normal
101(2)
Multivariate Student's t Distribution
103(2)
Generating Variates on a Sphere
105(1)
4.4 Generating Discrete Random Variables
106(6)
Binomial
106(2)
Poisson
108(2)
Discrete Uniform
110(2)
4.5 MATLAB® Code
112(2)
4.6 Further Reading
114(1)
Exercises
115(2)
Chapter 5 Exploratory Data Analysis
5.1 Introduction
117(2)
5.2 Exploring Univariate Data
119(24)
Histograms
119(3)
Stem-and-Leaf
122(2)
Quantile-Based Plots - Continuous Distributions
124(8)
Quantile Plots - Discrete Distributions
132(6)
Box Plots
138(5)
5.3 Exploring Bivariate and Trivariate Data
143(13)
Scatterplots
145(2)
Surface Plots
147(1)
Contour Plots
148(1)
Bivariate Histogram
149(6)
3D Scatterplot
155(1)
5.4 Exploring Multi-Dimensional Data
156(22)
Scatterplot Matrix
157(2)
Slices and Isosurfaces
159(5)
Glyphs
164(3)
Andrews Curves
167(5)
Parallel Coordinates
172(6)
5.5 MATLAB® Code
178(2)
5.6 Further Reading
180(2)
Exercises
182(3)
Chapter 6 Finding Structure
6.1 Introduction
185(1)
6.2 Projecting Data
186(2)
6.3 Principal Component Analysis
188(4)
6.4 Projection Pursuit EDA
192(10)
Projection Pursuit Index
195(1)
Finding the Structure
196(1)
Structure Removal
197(5)
6.5 Independent Component Analysis
202(7)
6.6 Grand Tour
209(4)
6.7 Nonlinear Dimensionality Reduction
213(9)
Multidimensional Scaling
214(3)
Isometric Feature Mapping (ISOMAP)
217(5)
6.8 MATLAB° Code
222(2)
6.9 Further Reading
224(3)
Exercises
227(2)
Chapter 7 Monte Carlo Methods for Inferential Statistics
7.1 Introduction
229(1)
7.2 Classical Inferential Statistics
230(11)
Hypothesis Testing
230(9)
Confidence Intervals
239(2)
7.3 Monte Carlo Methods for Inferential Statistics
241(11)
Basic Monte Carlo Procedure
242(1)
Monte Carlo Hypothesis Testing
243(5)
Monte Carlo Assessment of Hypothesis Testing
248(4)
7.4 Bootstrap Methods
252(12)
General Bootstrap Methodology
252(2)
Bootstrap Estimate of Standard Error
254(3)
Bootstrap Estimate of Bias
257(1)
Bootstrap Confidence Intervals
258(6)
7.5 MATLAB° Code
264(1)
7.6 Further Reading
265(1)
Exercises
266(3)
Chapter 8 Data Partitioning
8.1 Introduction
269(1)
8.2 Cross-Validation
270(7)
8.3 Jackknife
277(8)
8.4 Better Bootstrap Confidence Intervals
285(4)
8.5 Jackknife-After-Bootstrap
289(3)
8.6 MATLAB° Code
292(1)
8.7 Further Reading
293(1)
Exercises
293(4)
Chapter 9 Probability Density Estimation
9.1 Introduction
297(2)
9.2 Histograms
299(19)
1D Histograms
299(7)
Multivariate Histograms
306(1)
Frequency Polygons
307(5)
Averaged Shifted Histograms
312(6)
9.3 Kernel Density Estimation
318(7)
Univariate Kernel Estimators
318(5)
Multivariate Kernel Estimators
323(2)
9.4 Finite Mixtures
325(19)
Univariate Finite Mixtures
327(2)
Visualizing Finite Mixtures
329(2)
Multivariate Finite Mixtures
331(3)
EM Algorithm for Estimating the Parameters
334(5)
Adaptive Mixtures
339(5)
9.5 Generating Random Variables
344(8)
9.6 MATLAB® Code
352(1)
9.7 Further Reading
352(2)
Exercises
354(5)
Chapter 10 Supervised Learning
10.1 Introduction
359(2)
10.2 Bayes Decision Theory
361(15)
Estimating Class-Conditional Probabilities: Parametric Method
363(2)
Naive Bayes Classifiers
365(1)
Estimating Class-Conditional Probabilities: Nonparametric
365(2)
Bayes Decision Rule
367(5)
Likelihood Ratio Approach
372(4)
10.3 Evaluating the Classifier
376(11)
Independent Test Sample
376(2)
Cross-Validation
378(3)
Receiver Operating Characteristic (ROC) Curve
381(6)
10.4 Classification Trees
387(23)
Growing the Tree
390(4)
Pruning the Tree
394(4)
Choosing the Best Tree
398(9)
Other Tree Methods
407(3)
10.5 Combining Classifiers
410(9)
Bagging
410(3)
Boosting
413(3)
Arcing Classifiers
416(2)
Random Forests
418(1)
10.6 Nearest Neighbor Classifier
419(3)
10.7 Support Vector Machines
422(11)
Maximal Margin Classifier
422(4)
Support Vector Classifier
426(1)
Support Vector Machines
427(6)
10.8 MATLAB® Code
433(3)
10.9 Further Reading
436(1)
Exercises
437(4)
Chapter 11 Unsupervised Learning
11.1 Introduction
441(1)
11.2 Measures of Distance
442(2)
11.3 Hierarchical Clustering
444(8)
11.4 K-Means Clustering
452(3)
11.5 Model-Based Clustering
455(13)
Finite Mixture Models and the EM Algorithm
456(4)
Model-Based Agglomerative Clustering
460(3)
Bayesian Information Criterion
463(1)
Model-Based Clustering Procedure
463(5)
11.6 Assessing Cluster Results
468(7)
Mojena - Upper Tail Rule
468(1)
Silhouette Statistic
469(3)
Other Methods for Evaluating Clusters
472(3)
11.7 MATLAB® Code
475(2)
11.8 Further Reading
477(1)
Exercises
478(3)
Chapter 12 Parametric Models
12.1 Introduction
481(6)
12.2 Spline Regression Models
487(5)
12.3 Logistic Regression
492(6)
Creating the Model
492(4)
Interpreting the Model Parameters
496(2)
12.4 Generalized Linear Models
498(19)
Exponential Family Form
499(5)
Generalized Linear Model
504(5)
Model Checking
509(8)
12.5 Model Selection and Regularization
517(15)
Best Subset Selection
518(1)
Stepwise Regression
519(2)
Ridge Regression
521(6)
Lasso-Least Absolute Shrinkage and Selection Operator
527(2)
Elastic Net
529(3)
12.6 Partial Least Squares Regression
532(6)
Principal Component Regression
533(2)
Partial Least Squares Regression
535(3)
12.7 MATLAB® Code
538(2)
12.8 Further Reading
540(1)
Exercises
540(3)
Chapter 13 Nonparametric Models
13.1 Introduction
543(1)
13.2 Some Smoothing Methods
544(14)
Bin Smoothing
545(2)
Running Mean
547(1)
Running Line
548(1)
Local Polynomial Regression - Loess
549(6)
Robust Loess
555(3)
13.3 Kernel Methods
558(7)
Nadaraya-Watson Estimator
561(1)
Local Linear Kernel Estimator
562(3)
13.4 Smoothing Splines
565(7)
Natural Cubic Splines
565(2)
Reinsch Method for Finding Smoothing Splines
567(2)
Values for a Cubic Smoothing Spline
569(1)
Weighted Smoothing Spline
570(2)
13.5 Nonparametric Regression - Other Details
572(9)
Choosing the Smoothing Parameter
572(5)
Estimation of the Residual Variance
577(1)
Variability of Smooths
577(4)
13.6 Regression Trees
581(10)
Growing a Regression Tree
583(2)
Pruning a Regression Tree
585(2)
Selecting a Tree
587(4)
13.7 Additive Models
591(6)
13.8 Multivariate Adaptive Regression Splines
597(8)
13.9 MATLAB® Code
605(3)
13.10 Further Reading
608(2)
Exercises
610(3)
Chapter 14 Markov Chain Monte Carlo Methods
14.1 Introduction
613(1)
14.2 Background
614(4)
Bayesian Inference
614(1)
Monte Carlo Integration
615(2)
Markov Chains
617(1)
Analyzing the Output
618(1)
14.3 Metropolis-Hastings Algorithms
618(12)
Metropolis-Hastings Sampler
619(2)
Metropolis Sampler
621(5)
Independence Sampler
626(1)
Autoregressive Generating Density
627(3)
14.4 The Gibbs Sampler
630(10)
14.5 Convergence Monitoring
640(7)
Gelman and Rubin Method
642(3)
Raftery and Lewis Method
645(2)
14.6 MATLAB® Code
647(1)
14.7 Further Reading
648(1)
Exercises
649(4)
Appendix A MATLAB® Basics
A.1 Desktop Environment
653(2)
A.2 Getting Help and Other Documentation
655(1)
A.3 Data Import and Export
656(3)
Data Import and Export in Base MATLAB
656(2)
Data Import and Export with the Statistics Toolbox
658(1)
A.4 Data in MATLAB®
659(6)
Data Objects in Base MATLAB
659(3)
Accessing Data Elements
662(3)
Object-Oriented Programming
665(1)
A.5 Workspace and Syntax
665(5)
File and Workspace Management
666(1)
Syntax in MATLAB
667(2)
Functions in MATLAB
669(1)
A.6 Basic Plot Functions
670(7)
Plotting 2D Data
670(3)
Plotting 3D Data
673(1)
Scatterplots
674(1)
Scatterplot Matrix
675(1)
GUIs for Graphics
675(2)
A.7 Summary and Further Reading
677(4)
Appendix B Projection Pursuit Indexes
B.1 Friedman-Tukey Index
681(1)
B.2 Entropy Index
682(1)
B.3 Moment Index
682(1)
B.4 Distances
683(2)
Appendix C Data Sets
C.1 Introduction
685(1)
C.2 Descriptions
685(10)
Appendix D Notation
D.1 Observed Data
695(1)
D.2 Greek Letters
696(1)
D.3 Functions and Distributions
696(1)
D.4 Matrix Notation
696(1)
D.5 Statistics
697(2)
References 699(22)
Subject Index 721
Wendy L. Martinez is a mathematical statistician with the U.S. Bureau of Labor Statistics. She is a fellow of the American Statistical Association, a co-author of several popular Chapman & Hall/CRC books, and a MATLAB® user for more than 20 years. Her research interests include text data mining, probability density estimation, signal processing, scientific visualization, and statistical pattern recognition. She earned an M.S. in aerospace engineering from George Washington University and a Ph.D. in computational sciences and informatics from George Mason University.

Angel R. Martinez is fully retired after a long career with the U.S. federal government and as an adjunct professor at Strayer University, where he taught undergraduate and graduate courses in statistics and mathematics. Before retiring from government service, he worked for the U.S. Navy as an operations research analyst and a computer scientist. He earned an M.S. in systems engineering from the Virginia Polytechnic Institute and State University and a Ph.D. in computational sciences and informatics from George Mason University.
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