The main subject of this book is the estimation and forecasting of continuous time processes. It leads to a development of the theory of linear processes in function spaces. Mathematical tools are presented, as well as autoregressive processes in Hilbert and Banach spaces and general linear processes and statistical prediction. Implementation and numerical applications are also covered. The book assumes knowledge of classical probability theory and statistics.

Linear Processes in Function Spaces: Theory and Applications (Lecture Notes in Statistics, 149)

Science & Math

Bosq, Denis

Mathematics

Springer

This book offers a predominantly theoretical coverage of statistical prediction, with some potential applications discussed, when data and/ or parameters belong to a large or infinite dimensional space. It develops the theory of statistical prediction, non-parametric estimation by adaptive projection – with applications to tests of fit and prediction, and theory of linear processes in function spaces with applications to prediction of continuous time processes. 
This work is in the Wiley-Dunod Series co-published between Dunod (www.dunod.com) and John Wiley and Sons, Ltd.

Inference and Prediction in Large Dimensions (Wiley Series in Probability and Statistics)

Blanke, Delphine

Wiley-Interscience

This text is an Elementary Introduction to Stochastic Processes in discrete and continuous time with an initiation of the statistical inference. The material is standard and classical for a first course in Stochastic Processes at the senior/graduate level (lessons 1-12). To provide students with a view of statistics of stochastic processes, three lessons (13-15) were added. These lessons can be either optional or serve as an introduction to statistical inference with dependent observations. Several points of this text need to be elaborated, (1) The pedagogy is somewhat obvious. Since this text is designed for a one semester course, each lesson can be covered in one week or so. Having in mind a mixed audience of students from different departments (Math ematics, Statistics, Economics, Engineering, etc.) we have presented the material in each lesson in the most simple way, with emphasis on moti vation of concepts, aspects of applications and computational procedures. Basically, we try to explain to beginners questions such as "What is the topic in this lesson?" "Why this topic?", "How to study this topic math ematically?". The exercises at the end of each lesson will deepen the stu dents' understanding of the material, and test their ability to carry out basic computations. Exercises with an asterisk are optional (difficult) and might not be suitable for homework, but should provide food for thought.

A Course in Stochastic Processes: Stochastic Models and Statistical Inference (Theory and Decision Library B, 34)

Business & Money

Hung T. Nguyêñ

Education & Reference

Generally, books on mathematical statistics are restricted to the case of independent identically distributed random variables. In this book however, both this case AND the case of dependent variables, i.e. statistics for discrete and continuous time processes, are studied. This second case is very important for today’s practitioners. Mathematical Statistics and Stochastic Processes is based on decision theory and asymptotic statistics and contains up-to-date information on the relevant topics of theory of probability, estimation, confidence intervals, non-parametric statistics and robustness, second-order processes in discrete and continuous time and diffusion processes, statistics for discrete and continuous time processes, statistical prediction, and complements in probability. This book is aimed at students studying courses on probability with an emphasis on measure theory and for all practitioners who apply and use statistics and probability on a daily basis.

Mathematical Statistics and Stochastic Processes (Applied Stochastic Methods)

Wiley-ISTE

This text is an Elementary Introduction to Stochastic Processes in discrete and continuous time with an initiation of the statistical inference. The material is standard and classical for a first course in Stochastic Processes at the senior/graduate level (lessons 1-12). To provide students with a view of statistics of stochastic processes, three lessons (13-15) were added. These lessons can be either optional or serve as an introduction to statistical inference with dependent observations. Several points of this text need to be elaborated, (1) The pedagogy is somewhat obvious. Since this text is designed for a one semester course, each lesson can be covered in one week or so. Having in mind a mixed audience of students from different departments (Math­ ematics, Statistics, Economics, Engineering, etc.) we have presented the material in each lesson in the most simple way, with emphasis on moti­ vation of concepts, aspects of applications and computational procedures. Basically, we try to explain to beginners questions such as "What is the topic in this lesson?" "Why this topic?", "How to study this topic math­ ematically?". The exercises at the end of each lesson will deepen the stu­ dents' understanding of the material, and test their ability to carry out basic computations. Exercises with an asterisk are optional (difficult) and might not be suitable for homework, but should provide food for thought.

A Course in Stochastic Processes: Stochastic Models and Statistical Inference (Theory and Decision Library B)