Copyright Year 2020
ISBN 9781032337722
Published June 13, 2022 by Chapman & Hall
324 Pages 6 B/W Illustrations
Leibniz Algebras: Structure and Classification is designed to introduce the reader to the theory of Leibniz algebras.
Leibniz algebra is the generalization of Lie algebras. These algebras preserve a unique property of Lie algebras that the right multiplication operators are derivations. They first appeared in papers of A.M Blokh in the 1960s, under the name D-algebras, emphasizing their close relationship with derivations. The theory of D-algebras did not get as thorough an examination as it deserved immediately after its introduction. Later, the same algebras were introduced in 1993 by Jean-Louis Loday , who called them Leibniz algebras due to the identity they satisfy. The main motivation for the introduction of Leibniz algebras was to study the periodicity phenomena in algebraic K-theory.
Nowadays, the theory of Leibniz algebras is one of the more actively developing areas of modern algebra. Along with (co)homological, structural and classification results on Leibniz algebras, some papers with various applications of the Leibniz algebras also appear now. However, the focus of this book is mainly on the classification problems of Leibniz algebras. Particularly, the authors propose a method of classification of a subclass of Leibniz algebras based on algebraic invariants. The method is applicable in the Lie algebras case as well.
Provides a systematic exposition of the theory of Leibniz algebras and recent results on Leibniz algebras
Suitable for final year bachelor's students, master's students and PhD students going into research in the structural theory of finite-dimensional algebras, particularly, Lie and Leibniz algebras
Covers important and more general parts of the structural theory of Leibniz algebras that are not addressed in other texts
Chapter 1: Introduction
Chapter 2: Structure of Leibniz Algebra
Chapter 3: Classification Problems in Low Dimensions
Chapter 4: On some Classes of Leibniz Algebra
Chapter 5: Isomorphism Criteria for Filiform Leibniz Algebra
Chapter 6: Classification of Filiform Leibniz Algebra in Low Dimensions
Copyright Year 2020
ISBN 9780367494247
Published August 1, 2022 by Chapman & Hall
340 Pages
Praise for the first edition:
[This book] reflects the extensive experience and significant contributions of the author to non-linear and non-Gaussian modeling. c [It] is a valuable book, especially with its broad and accessible introduction of models in the state-space framework.
?Statistics in Medicine
What distinguishes this book from comparable introductory texts is the use of state-space modeling. Along with this come a number of valuable tools for recursive filtering and smoothing, including the Kalman filter, as well as non-Gaussian and sequential Monte Carlo filters.
?MAA Reviews
Introduction to Time Series Modeling with Applications in R, Second Edition covers numerous stationary and nonstationary time series models and tools for estimating and utilizing them. The goal of this book is to enable readers to build their own models to understand, predict and master time series. The second edition makes it possible for readers to reproduce examples in this book by using the freely available R package TSSS to perform computations for their own real-world time series problems.
This book employs the state-space model as a generic tool for time series modeling and presents the Kalman filter, the non-Gaussian filter and the particle filter as convenient tools for recursive estimation for state-space models. Further, it also takes a unified approach based on the entropy maximization principle and employs various methods of parameter estimation and model selection, including the least squares method, the maximum likelihood method, recursive estimation for state-space models and model selection by AIC.
Along with the standard stationary time series models, such as the AR and ARMA models, the book also introduces nonstationary time series models such as the locally stationary AR model, the trend model, the seasonal adjustment model, the time-varying coefficient AR model and nonlinear non-Gaussian state-space models.
Genshiro Kitagawa is a project professor at the University of Tokyo, the former Director-General of the Institute of Statistical Mathematics, and the former President of the Research Organization of Information and Systems.
1 Introduction and Preparatory Analysis
1.1 Time Series Data
1.2 Classi?cation of Time Series
1.3 Objectives of Time Series Analysis
1.4 Pre-processing of Time Series
1.4.1 Transformation of variables
1.4.2 Differencing
1.4.3 Month-to-month basis and year-over-year
1.4.4 Moving average
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Copyright Year 2021
ISBN 9780367715366
September 26, 2022 Forthcoming by Chapman & Hall
360 Pages 45 B/W Illustrations
Survival data analysis is a very broad field of statistics, encompassing a large variety of methods used in a wide range of applications, and in particular in medical research. During the last twenty years, several extensions of "classical" survival models have been developed to address particular situations often encountered in practice. This book aims to gather in a single reference the most commonly used extensions, such as frailty models (in case of unobserved heterogeneity or clustered data), cure models (when a fraction of the population will not experience the event of interest), competing risk models (in case of different types of event), and joint survival models for a time-to-event endpoint and a longitudinal outcome.
Presents state-of-the art approaches for different advanced survival models including frailty models, cure models, competing risk models and joint models for a longitudinal and a survival outcome
Uses consistent notation throughout the book for the different techniques presented
Explains in which situation each of these models should be used, and how they are linked to specific research questions
Focuses on the understanding of the models, their implementation, and their interpretation, with an appropriate level of methodological development for masters students and applied statisticians
Provides references to existing R packages and SAS procedure or macros, and illustrates the use of the main ones on real datasets
This book is primarily aimed at applied statisticians and graduate students of statistics and biostatistics. It can also serve as an introductory reference for methodological researchers interested in the main extensions of classical survival analysis.
1. Introduction
2. Classical Survival Analysis
3. Frailty Models
4. Cure Models
5. Competing Risks
6. Joint Modeling
Copyright Year 2021
ISBN 9780367749125
September 26, 2022 Forthcoming by Chapman & Hall
444 Pages 63 B/W Illustrations
Probability and Statistical Inference: From Basic Principles to Advanced Models covers aspects of probability, distribution theory, and inference that are fundamental to a proper understanding of data analysis and statistical modelling. It presents these topics in an accessible manner without sacrificing mathematical rigour, bridging the gap between the many excellent introductory books and the more advanced, graduate-level texts. The book introduces and explores techniques that are relevant to modern practitioners, while being respectful to the history of statistical inference. It seeks to provide a thorough grounding in both the theory and application of statistics, with even the more abstract parts placed in the context of a practical setting.
?Complete introduction to mathematical probability, random variables, and distribution theory.
?Concise but broad account of statistical modelling, covering topics such as generalised linear models, survival analysis, time series, and random processes.
?Extensive discussion of the key concepts in classical statistics (point estimation, interval estimation, hypothesis testing) and the main techniques in likelihood-based inference.
?Detailed introduction to Bayesian statistics and associated topics.
?Practical illustration of some of the main computational methods used in modern statistical inference (simulation, boostrap, MCMC).
This book is for students who have already completed a first course in probability and statistics, and now wish to deepen and broaden their understanding of the subject. It can serve as a foundation for advanced undergraduate or postgraduate courses. Our aim is to challenge and excite the more mathematically able students, while providing explanations of statistical concepts that are more detailed and approachable than those in advanced texts. This book is also useful for data scientists, researchers, and other applied practitioners who want to understand the theory behind the statistical methods used in their fields.
1. Introduction
2. Probability
3. Random Variables and Univariate Distributions
4. Multivariate Distributions
5. Conditional Distributions
6. Statistical Models
7. Sample Moments and Quantiles
8. Estimation, Testing, and Prediction
9. Likelihood-based Inference
10. Inferential Theory
11. Bayesian Inference
12. Simulation Methods
Copyright Year 2023
ISBN 9781032381008
December 22, 2022 Forthcoming by Chapman & Hall
154 Pages 90 B/W Illustrations
Every physicist, engineer, and certainly a mathematician, would undoubtedly agree that vector algebra is a part of basic mathematical instruments packed in their toolbox.
Classic Vector Algebra should be viewed as a prerequisite, an introduction, for other mathematical courses dealing with vectors, following typical form and appropriate rigor of more advanced mathematics texts.
Vector algebra discussed in this book briefly addresses vectors in general 3-dimensional Euclidian space, and then, in more detail, vectors in Cartesian 3 space. These vectors are easier to visualize, their operational techniques are relatively simple, but they are necessary for the study of Vector Analysis. In addition, this could also serve as a good intuition build up for more abstract structures of -dimensional vector spaces.
Definition, theorem, proof, corollary, example, etc. is not useless formalism, even in an introductory treatise -- it is the way mathematical thinking has to be structured. In other words, "introduction" and "rigor" should not exclude one another.
The material in this book is not difficult nor easy. The text is a serious exposition of a part of mathematics students need to master in order to be proficient in their field. In addition to the detailed outline of the theory, the book contains literally hundreds of corresponding examples/exercises.
1. Introduction
2. Vector Space ? Definitions, Notation and Examples
3. Three ? dimensional Vector Space V
3.1 Definition and Basic Features of V
3.2 Multiplication of a Vector by a Scalar
3.3 Collinear and Coplanar Vectors
3.4 Addition of Vectors
3.5 Basis of a Vector Space
4. Vectors in R^3 Space
4.1 {i,j,k} - basis of R^3 Space
4.2 Multiplication by a Scalar and Addition of Vectors in R^3 Space
4.3 Scalar (dot) Product of Vectors
4.4 Cross (vector) Product of Vectors
4.5 Mixed Product of Vectors
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Copyright Year 2023
ISBN 9781032007458
November 17, 2022 Forthcoming by Chapman & Hall
240 Pages 27 B/W Illustrations
Designed for a one-semester advanced undergraduate or graduate statistical theory course, Statistical Theory: A Concise Introduction, Second Edition clearly explains the underlying ideas, mathematics, and principles of major statistical concepts, including parameter estimation, confidence intervals, hypothesis testing, asymptotic analysis, Bayesian inference, linear models, nonparametric statistics, and elements of decision theory. It introduces these topics on a clear intuitive level using illustrative examples in addition to the formal definitions, theorems, and proofs.
Based on the authorsf lecture notes, the book is self-contained, which maintains a proper balance between the clarity and rigor of exposition. In a few cases, the authors present a "sketched" version of a proof, explaining its main ideas rather than giving detailed technical mathematical and probabilistic arguments.
Second edition has been updated with a new chapter on Nonparametric Estimation; a significant update to the chapter on Statistical Decision Theory; and other updates throughout
No requirement for heavy calculus, and simple questions throughout the text help students check their understanding of the material
Each chapter also includes a set of exercises that range in level of difficulty
Self-contained, and can be used by the students to understand the theory
Chapters and sections marked by asterisks contain more advanced topics and may be omitted
Special chapters on linear models and nonparametric statistics show how the main theoretical concepts can be applied to well-known and frequently used statistical tools
The primary audience for the book is students who want to understand the theoretical basis of mathematical statistics; either advanced undergraduate or graduate students. It will also be an excellent reference for researchers from statistics and other quantitative disciplines.
1. Introduction. 1.1. Preamble. 1.2. Likelihood. 1.3. Sufficiency. 1.4. Minimal sufficiency. 1.5. Completeness. 1.6. Exponential family of distributions. 1.7. Exercises. 2. Point Estimation. 2.1. Introduction. 2.2. Maximum likelihood estimation. 2.3. Method of moments. 2.4. Method of least squares. 2.5. M-estimators. 2.6. Goodness-of-estimation. Mean squared error. 2.7. Unbiased estimation. 2.8. Exercises. 3. Confidence Intervals, Bounds, and Regions. 3.1. Introduction. 3.2. Quoting the estimation error. 3.3. Confidence intervals. 3.4. Confidence bounds. 3.5. Confidence regions. 3.6. Exercises. 4. Hypothesis testing. 4.1. Introduction. 4.2. Simple hypotheses. 4.3. Composite hypotheses. 4.4. Duality between hypothesis testing and confidence intervals (regions). 4.5. Sequential testing. 4.6. Multiple testing. 4.7. Exercises. 5. Asymptotic Analysis. 5.1. Introduction. 5.2. Convergence and consistency in MSE. 5.3. Convergence and consistency in probability. 5.4. Convergence in distribution. 5.5. The central limit theorem. 5.6. Asymptotically normal consistency. 5.7. Asymptotic confidence intervals. 5.8. Asymptotic properties of MLEs, Wald confidence intervals, and tests. 5.9. Multiparameter case. 5.10. Asymptotic properties of M-estimators. 5.11. Score (Rao) asymptotic tests, and confidence regions. 5.12. Asymptotic distribution of the GLRT, Wilksf theorem. 5.13. Exercises. 6. Bayesian Inference. 6.1. Introduction. 6.2. Choice of priors. 6.3. Point estimation. 6.4. Interval estimation. Credible sets.
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