Estimation of Stochastic Processes with Missing Observations

Estimation of Stochastic Processes with Missing Observations PDF

Author: Mikhail Moklyachuk

Publisher:

Published: 2019

Total Pages: 0

ISBN-13: 9781536158908

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We propose results of the investigation of the problem of mean square optimal estimation of linear functionals constructed from unobserved values of stationary stochastic processes. Estimates are based on observations of the processes with additive stationary noise process. The aim of the book is to develop methods for finding the optimal estimates of the functionals in the case where some observations are missing. Formulas for computing values of the mean-square errors and the spectral characteristics of the optimal linear estimates of functionals are derived in the case of spectral certainty, where the spectral densities of the processes are exactly known. The minimax robust method of estimation is applied in the case of spectral uncertainty, where the spectral densities of the processes are not known exactly while some classes of admissible spectral densities are given. The formulas that determine the least favourable spectral densities and the minimax spectral characteristics of the optimal estimates of functionals are proposed for some special classes of admissible densities.

Estimation of Stochastic Processes with Stationary Increments and Cointegrated Sequences

Estimation of Stochastic Processes with Stationary Increments and Cointegrated Sequences PDF

Author: Maksym Luz

Publisher: John Wiley & Sons

Published: 2019-12-12

Total Pages: 308

ISBN-13: 1786305038

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Estimation of Stochastic Processes is intended for researchers in the field of econometrics, financial mathematics, statistics or signal processing. This book gives a deep understanding of spectral theory and estimation techniques for stochastic processes with stationary increments. It focuses on the estimation of functionals of unobserved values for stochastic processes with stationary increments, including ARIMA processes, seasonal time series and a class of cointegrated sequences. Furthermore, this book presents solutions to extrapolation (forecast), interpolation (missed values estimation) and filtering (smoothing) problems based on observations with and without noise, in discrete and continuous time domains. Extending the classical approach applied when the spectral densities of the processes are known, the minimax method of estimation is developed for a case where the spectral information is incomplete and the relations that determine the least favorable spectral densities for the optimal estimations are found.

Non-Stationary Stochastic Processes Estimation

Non-Stationary Stochastic Processes Estimation PDF

Author: Maksym Luz

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2024-05-20

Total Pages: 310

ISBN-13: 3111325628

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The problem of forecasting future values of economic and physical processes, the problem of restoring lost information, cleaning signals or other data observations from noise, is magnified in an information-laden word. Methods of stochastic processes estimation depend on two main factors. The first factor is construction of a model of the process being investigated. The second factor is the available information about the structure of the process under consideration. In this book, we propose results of the investigation of the problem of mean square optimal estimation (extrapolation, interpolation, and filtering) of linear functionals depending on unobserved values of stochastic sequences and processes with periodically stationary and long memory multiplicative seasonal increments. Formulas for calculating the mean square errors and the spectral characteristics of the optimal estimates of the functionals are derived in the case of spectral certainty, where spectral structure of the considered sequences and processes are exactly known. In the case where spectral densities of the sequences and processes are not known exactly while some sets of admissible spectral densities are given, we apply the minimax-robust method of estimation.

Missing Data and Small-Area Estimation

Missing Data and Small-Area Estimation PDF

Author: Nicholas T. Longford

Publisher: Springer Science & Business Media

Published: 2005-08-05

Total Pages: 384

ISBN-13: 9781852337605

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This book evolved from lectures, courses and workshops on missing data and small-area estimation that I presented during my tenure as the ?rst C- pion Fellow (2000–2002). For the Fellowship I proposed these two topics as areas in which the academic statistics could contribute to the development of government statistics, in exchange for access to the operational details and background that would inform the direction and sharpen the focus of a- demic research. After a few years of involvement, I have come to realise that the separation of ‘academic’ and ‘industrial’ statistics is not well suited to either party, and their integration is the key to progress in both branches. Most of the work on this monograph was done while I was a visiting l- turer at Massey University, Palmerston North, New Zealand. The hospitality and stimulating academic environment of their Institute of Information S- ence and Technology is gratefully acknowledged. I could not name all those who commented on my lecture notes and on the presentations themselves; apart from them, I want to thank the organisers and silent attendees of all the events, and, with a modicum of reluctance, the ‘grey ?gures’ who kept inquiring whether I was any nearer the completion of whatever stage I had been foolish enough to attach a date.

Estimation of Stochastic Processes with Stationary Increments and Cointegrated Sequences

Estimation of Stochastic Processes with Stationary Increments and Cointegrated Sequences PDF

Author: Maksym Luz

Publisher: John Wiley & Sons

Published: 2019-09-20

Total Pages: 314

ISBN-13: 1119663520

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Estimation of Stochastic Processes is intended for researchers in the field of econometrics, financial mathematics, statistics or signal processing. This book gives a deep understanding of spectral theory and estimation techniques for stochastic processes with stationary increments. It focuses on the estimation of functionals of unobserved values for stochastic processes with stationary increments, including ARIMA processes, seasonal time series and a class of cointegrated sequences. Furthermore, this book presents solutions to extrapolation (forecast), interpolation (missed values estimation) and filtering (smoothing) problems based on observations with and without noise, in discrete and continuous time domains. Extending the classical approach applied when the spectral densities of the processes are known, the minimax method of estimation is developed for a case where the spectral information is incomplete and the relations that determine the least favorable spectral densities for the optimal estimations are found.

Logistic Regression with Missing Values in the Covariates

Logistic Regression with Missing Values in the Covariates PDF

Author: Werner Vach

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 152

ISBN-13: 1461226503

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In many areas of science a basic task is to assess the influence of several factors on a quantity of interest. If this quantity is binary logistic, regression models provide a powerful tool for this purpose. This monograph presents an account of the use of logistic regression in the case where missing values in the variables prevent the use of standard techniques. Such situations occur frequently across a wide range of statistical applications. The emphasis of this book is on methods related to the classical maximum likelihood principle. The author reviews the essentials of logistic regression and discusses the variety of mechanisms which might cause missing values while the rest of the book covers the methods which may be used to deal with missing values and their effectiveness. Researchers across a range of disciplines and graduate students in statistics and biostatistics will find this a readable account of this.

Semiparametric Theory and Missing Data

Semiparametric Theory and Missing Data PDF

Author: Anastasios Tsiatis

Publisher: Springer Science & Business Media

Published: 2007-01-15

Total Pages: 392

ISBN-13: 0387373454

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This book summarizes current knowledge regarding the theory of estimation for semiparametric models with missing data, in an organized and comprehensive manner. It starts with the study of semiparametric methods when there are no missing data. The description of the theory of estimation for semiparametric models is both rigorous and intuitive, relying on geometric ideas to reinforce the intuition and understanding of the theory. These methods are then applied to problems with missing, censored, and coarsened data with the goal of deriving estimators that are as robust and efficient as possible.

Statistical Methods for Handling Incomplete Data

Statistical Methods for Handling Incomplete Data PDF

Author: Jae Kwang Kim

Publisher: CRC Press

Published: 2013-07-23

Total Pages: 221

ISBN-13: 1482205076

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Along with many examples, this text covers the most up-to-date statistical theories and computational methods for analyzing incomplete data. It presents a thorough treatment of statistical theories of likelihood-based inference with missing data. It also discusses numerous computational techniques and theories on imputation and extensively covers methods involving propensity score weighting, nonignorable missing data, longitudinal missing data, survey sampling, and statistical matching. Some of the research ideas introduced can be developed further for specific applications.

Modelling and Application of Stochastic Processes

Modelling and Application of Stochastic Processes PDF

Author: Uday B. Desai

Publisher: Springer Science & Business Media

Published: 1986-10-31

Total Pages: 310

ISBN-13: 9780898381771

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The subject of modelling and application of stochastic processes is too vast to be exhausted in a single volume. In this book, attention is focused on a small subset of this vast subject. The primary emphasis is on realization and approximation of stochastic systems. Recently there has been considerable interest in the stochastic realization problem, and hence, an attempt has been made here to collect in one place some of the more recent approaches and algorithms for solving the stochastic realiza tion problem. Various different approaches for realizing linear minimum-phase systems, linear nonminimum-phase systems, and bilinear systems are presented. These approaches range from time-domain methods to spectral-domain methods. An overview of the chapter contents briefly describes these approaches. Also, in most of these chapters special attention is given to the problem of developing numerically ef ficient algorithms for obtaining reduced-order (approximate) stochastic realizations. On the application side, chapters on use of Markov random fields for modelling and analyzing image signals, use of complementary models for the smoothing problem with missing data, and nonlinear estimation are included. Chapter 1 by Klein and Dickinson develops the nested orthogonal state space realization for ARMA processes. As suggested by the name, nested orthogonal realizations possess two key properties; (i) the state variables are orthogonal, and (ii) the system matrices for the (n + l)st order realization contain as their "upper" n-th order blocks the system matrices from the n-th order realization (nesting property).

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