Format: Hardback, 552 pages, height x width: 235x155 mm, 55 Illustrations, color; 26 Illustrations, black and white; XXXIV, 552 p. 81 illus., 55 illus. in color
Pub. Date: 27-Jun-2023
ISBN-13: 9789819908028
This book compiles theoretical developments on statistical inference for time series and related models in honor of Masanobu Taniguchi's 70th birthday. It covers models such as long-range dependence models, nonlinear conditionally heteroscedastic time series, locally stationary processes, integer-valued time series, Levy Processes, complex-valued time series, categorical time series, exclusive topic models, and copula models. Many cutting-edge methods such as empirical likelihood methods, quantile regression, portmanteau tests, rank-based inference, change-point detection, testing for the goodness-of-fit, higher-order asymptotic expansion, minimum contrast estimation, optimal transportation, and topological methods are proposed, considered, or applied to complex data based on the statistical inference for stochastic processes.
The performances of these methods are illustrated by a variety of data analyses. This collection of original papers provides the reader with comprehensive and state-of-the-art theoretical works on time series and related models. It contains deep and profound treatments of the asymptotic theory of statistical inference. In addition, many specialized methodologies based on the asymptotic theory are presented in a simple way for a wide variety of statistical models. This Festschrift finds its core audiences in statistics, signal processing, and econometrics.
Chapter
1. Frequency domain empirical likelihood method for infinite
variance models.
Chapter
2. Diagnostic testing for time series.
Chapter
3.
Statistical Inference for Glaucoma Detection.
Chapter
4. On Hysteretic
Vector Autoregressive Model with Applications.
Chapter
5. Probabilistic
Forecasting for Daily Electricity Loads and Quantiles for Curve-to-Curve
Regression.
Chapter
6. Exact topological inference on resting-state brain
networks.
Chapter
7. An Introduction to Geostatistics.
Chapter
8. Relevant
change points in high dimensional time series.
Chapter
9. Adaptiveness of
the empirical distribution of residuals in semi-parametric conditional
location scale models.
Chapter
10. Standard testing procedures for white
noise and heteroskedasticity.
Chapter
11. Estimation of Trigonometric
Moments for Circular Binary Series.
Chapter
12. Time series analysis with
unsupervised learning.
Chapter
13. Recovering the market volatility shocks
in high-dimensional time series.
Chapter
14. Asymptotic properties of mildly
explosive processes with locally stationary disturbance.
Chapter
15.
Multi-Asset Empirical Martingale Price Estimators for Financial Derivatives.-
Chapter
16. Consistent Order Selection for ARFIMA Processes.
Chapter
17.
Recursive asymmetric kernel density estimation for nonnegative data.
Chapter
18. Fitting an error distribution in some heteroscedastic time series
models.
Chapter
19. Symbolic Interval-Valued Data Analysis for Time Series
Based on Auto-Interval-Regressive Models.
Chapter
20. ROBUST LINEAR
INTERPOLATION AND EXTRAPOLATION OF STATIONARY TIME SERIES.
Chapter
21. Non
Gaussian models for fMRI data.
Chapter
22. Robust inference for ordinal
response models.
Chapter
23. Change point problems for diffusion processes
and time series models.
Chapter
24. Empirical likelihood approach for time
series.
Chapter
25. Exploring the Dependence Structure Between Oscillatory
Activities in Multivariate Time Series.
Chapter
26. Projection-based
nonparametric goodness-of-fit testing with functional data.
Format: Hardback, 192 pages, height x width: 235x155 mm, 7 Illustrations, black and white; VIII, 192 p. 7 illus.
Series: Progress in Probability 80
Pub. Date: 07-Jun-2023
ISBN-13: 9783031269783
This volume collects selected papers from the Ninth High Dimensional Probability Conference, held virtually from June 15-19, 2020. These papers cover a wide range of topics and demonstrate how high-dimensional probability remains an active area of research with applications across many mathematical disciplines. Chapters are organized around four general topics: inequalities and convexity; limit theorems; stochastic processes; and high-dimensional statistics. High Dimensional Probability IX will be a valuable resource for researchers in this area.
Format: Hardback, 317 pages, height x width: 235x155 mm, 202 Illustrations, color; 2 Illustrations, black and white; V, 317 p. 204 illus., 202 illus. in color.,
Pub. Date: 10-Jul-2023
ISBN-13: 9783031278921
This book helps a practitioner develop an intuitive understanding of the Fourier transform and its application to data analysis. The authors start with the Fourier series and progress step-by-step from CTFT, DTFT, discrete Fourier transform (DFT) to the Fast Fourier Transform (FFT). Each equation is accompanied by a detailed explanation and graphs. The book also covers the application of the Fourier transform to random signals and how to assess their spectral distribution. Spectrum analysis using both the Parseval's and the Wiener-Khintchine-Einstein theorems of power estimation are discussed. Periodogram and Autopower, the two most common methods of doing non-parametric spectral analysis, are discussed and guidelines are given for creating low-variance, low-bias spectrum using windows and ACF truncation. The book includes numerous examples, detailed explanations and plots, making difficult concepts clear and easy to grasp.
Introduction.- Trigonometric Representation of CT Periodic Signals.-
Complex Representation of CT Periodic Signals.- Discrete-Time Signals and
Fourier Series Representation.- Fourier Transform of aperiodic and periodic
signals.- DT Fourier Transform of Aperiodic and Periodic Signals.- Discrete
Fourier Transform.- Leakage Mitigation with Windows.- Fourier Analysis of
Random Signals.- Power Spectrum of Random Signals.- Conclusion.
Format: Hardback, height x width: 235x155 mm, Approx. 290 p.
Series: University Texts in the Mathematical Sciences
Pub. Date: 11-Jul-2023
ISBN-13: 9789819905645
Targeted to graduate students of mathematics, this book discusses major topics like the Lie group in the study of smooth manifolds. It is said that mathematics can be learned by solving problems and not only by just reading it. To serve this purpose, this book contains a sufficient number of examples and exercises after each section in every chapter. Some of the exercises are routine ones for the general understanding of topics. The book also contains hints to difficult exercises. Answers to all exercises are given at the end of each section. It also provides proofs of all theorems in a lucid manner. The only pre-requisites are good working knowledge of point-set topology and linear algebra.
Preface1 Calculus on Rn ..........................5
1.1 Smooth Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 5
1.2 Tangent Vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 15
1.3 Germ of a Function . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 19
1.4 Inverse Function Theorem . . . . . . . . . . . . . . . . . . . . . . . .
. . . 23
1.5 Implicit Function Theorem . . . . . . . . . . . . . . . . . . . . . . . .
. . . 36
2 Manifold Theory 47
2.1 Topological Manifold . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 47
2.2 Smooth Germs on a topological manifold . . . . . . . . . . . . . . . . .
. . 55
2.3 Smooth Manifold . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 64
2.4 Stereographic Projection . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 75
iii
iv CONTENTS
2.5 Orientable Surface . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 79
2.6 Product Manifold . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 82
2.7 Smooth Function on Smooth Manifold . . . . . . . . . . . . . . . . . . .
. 84
2.8 Differential Curve, Tangent Vector . . . . . . . . . . . . . . . . . . .
. . . 91
2.9 Inverse Function Theorem for Smooth Manifold . . . . . . . . . . . . . .
. 97
2.10 Vector Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 102
2.11 Integral Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 109
2.12 Differential of a Mapping . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 117
2.13 Submanifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 137
2.14 f-related vector fields . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 144
2.15 One Parameter Group of Transformations on a Manifold . . . . . . . . . .
149
Format: Paperback / softback, height x width: 235x155 mm, Approx. 300 p
Series: UNITEXT 151
Pub. Date: 30-Jun-2023
ISBN-13: 9783031272196
This book is based on a course for first-semester science students, held by the second author at the University of Zurich several times. Its goal is threefold: to have students learn a minimal working knowledge of linear algebra, acquire some computational skills, and familiarize them with mathematical language to make mathematical literature more accessible. Therefore, we give precise definitions, introduce helpful notations, and state any results carefully worded. We provide no proofs of these results but typically illustrate them with numerous examples. Additionally, for better understanding, we often give supporting arguments for why they are valid.
Part I Systems of linear equations.- 1 Introduction.- 2 Systems with two
equations and two unknowns.- 3 Gaussian elimination.- Part II Matrices and
related topics.- 4 Basic operations.- 5 Linear dependence, bases,
coordinates.- 6 Determinants.- Part III Complex numbers.- 7 Complex numbers:
definition and operations.- 8 The Fundamental Theorem of Algebra.- 9 Linear
systems with complex coefficients.- Part IV Vector spaces and linear maps.-
10 Vector spaces and their linear subspaces.- 11 Linear maps.- 12 Inner
products on K-vector spaces.- Part V Eigenvalues and eigenvectors.- 13
Eigenvalues and eigenvectors of C-linear maps.- 14 Eigenvalues and
eigenvectors of R-linear maps.- 15 Quadratic forms on Rn.- Part VI
Differential equations.- 16 Introduction.- 17 Linear ODEs with constant
coefficients of first order.- 18 Linear ODEs with constant coefficients of
higher order.- Appendix A Solutions.
Format: Paperback / softback, 360 pages, height x width: 235x155 mm, X, 360 p.,
Series: Lecture Notes in Mathematics 2327
Pub. Date: 11-Aug-2023
ISBN-13: 9783031262999
This book reflects general trends in the study of geometric aspects of functional analysis, understood in a broad sense. A classical theme in the local theory of Banach spaces is the study of probability measures in high dimension and the concentration of measure phenomenon. Here this phenomenon is approached from different angles, including through analysis on the Hamming cube, and via quantitative estimates in the Central Limit Theorem under thin-shell and related assumptions. Classical convexity theory plays a central role in this volume, as well as the study of geometric inequalities. These inequalities, which are somewhat in spirit of the Brunn-Minkowski inequality, in turn shed light on convexity and on the geometry of Euclidean space. Probability measures with convexity or curvature properties, such as log-concave distributions, occupy an equally central role and arise in the study of Gaussian measures and non-trivial properties of the heat flow in Euclidean spaces. Also discussed are interactions of this circle of ideas with linear programming and sampling algorithms, including the solution of a question in online learning algorithms using a classical convexity construction from the 19th century.
Preface by the EditorsExtended Foreword by V. Milman - "Asymptotic
Geometric Analysis: Achievements and Perspective"1. S. Arunschalam, O. Regev
And P. Yao - "On The Gaussian Surface Area Of Spectrahedra"2. S. Bobkov, G.
P. Chistyakov And F. Gotze - "Asymptotic Expansions And Two- Sided Bounds In
Randomized Central Limit Theorems"3. K. J. Boroczky And P. Kalantzopoulos -
"About The Case Of Equality In The Reverse Brascamp-Lieb Inequality".4. P.
Cattiaux And A. Guillin - "A Journey With The Integrated #2 Criterion And Its
Weak Forms".5. S. Chewi - "The Entropic Barrier Is N-Self-Concordant"
6. B.
Klartag And S. Sodin - "Local Tail Bounds For Polynomials On The Discrete
Cube".7. S. Mendelson And G. Paouris - "Stable Recovery And The Coordinate
Small-Ball Behaviour Of Random Vectors"8. D. Mikulincer And Y. Shenfeld - "On
The Lipschitz Properties Of Transportation Along Heat Flows".9. P. Nayar And
J. Rutkowski - "A Short Direct Proof Of The Ivanisvili-Volberg Inequality"10.
L. Rotem - "The Anisotropic Total Variation And Surface Area Measures".11. M.
Sellke - "Chasing Convex Bodies Optimally".12. M. Lotz And J. A. Tropp -
"Sharp Phase Transitions In Euclidean Integral Geometry".