Parameter Estimation in Mathematical Models for Spectroscopic Observations PDF Download

Author: Radmila Pribić
Publisher:
ISBN:
Category :
Languages : en
Pages : 156

View

Book Description

Author: Adriaan van den Bos
Publisher: John Wiley & Sons
ISBN: 9780470173855
Category : Technology & Engineering
Languages : en
Pages : 296

View

Book Description
The subject of this book is estimating parameters of expectation models of statistical observations. The book describes the most important aspects of the subject for applied scientists and engineers. This group of users is often not aware of estimators other than least squares. Therefore one purpose of this book is to show that statistical parameter estimation has much more to offer than least squares estimation alone. In the approach of this book, knowledge of the distribution of the observations is involved in the choice of estimators. A further advantage of the chosen approach is that it unifies the underlying theory and reduces it to a relatively small collection of coherent, generally applicable principles and notions.

Author: K. Dzhaparidze
Publisher: Springer Science & Business Media
ISBN: 1461248426
Category : Mathematics
Languages : en
Pages : 331

View

Book Description
. . ) (under the assumption that the spectral density exists). For this reason, a vast amount of periodical and monographic literature is devoted to the nonparametric statistical problem of estimating the function tJ( T) and especially that of leA) (see, for example, the books [4,21,22,26,56,77,137,139,140,]). However, the empirical value t;; of the spectral density I obtained by applying a certain statistical procedure to the observed values of the variables Xl' . . . , X , usually depends in n a complicated manner on the cyclic frequency). . This fact often presents difficulties in applying the obtained estimate t;; of the function I to the solution of specific problems rela ted to the process X . Theref ore, in practice, the t obtained values of the estimator t;; (or an estimator of the covariance function tJ~( T» are almost always "smoothed," i. e. , are approximated by values of a certain sufficiently simple function 1 = 1

Author: Edward A. Ingham
Publisher:
ISBN: 9781423578406
Category : Parameter estimation
Languages : en
Pages : 212

View

Book Description
The approach of modeling measured signals as superimposed exponentials in white Gaussian noise is popular and effective. However, estimating the parameters of the assumed model is challenging, especially when the data record length is short, the signal strength is low, or the parameters are closely spaced. In this dissertation, we first review the most effective parameter estimation scheme for the superimposed exponential model: maximum likelihood. We then provide a historical review of the linear prediction approach to parameter estimation for the same model. After identifying the improvements made to linear prediction and demonstrating their weaknesses, we introduce a completely tractable and statistically sound modification to linear prediction that we call iterative generalized least squares. It is shown, that our algorithm works to minimize the exact maximum likelihood cost function for the superimposed exponential problem and is therefore, equivalent to the previously developed maximum likelihood approach. However, our algorithm is indeed linear prediction, and thus revives a methodology previously categorized as inferior to maximum likelihood. With our modification, the insight provided by linear prediction can be carried to actual applications. We demonstrate this by developing an effective algorithm for deep level transient spectroscopy analysis. The signal of deep level transient spectroscopy is not a straight forward superposition of exponentials. However, with our methodology, an estimator, based on the exact maximum likelihood cost function for the actual signal, is quickly derived. At the end of the dissertation, we verify that our estimator extends the current capabilities of deep level transient spectroscopy analysis.

Author: Murray Rosenblatt
Publisher: IMS
ISBN: 9780940600225
Category : Curve fitting
Languages : en
Pages : 202

View

Book Description

Author: Steven M. Kay
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 574

View

Book Description

Author: Maksym Luz
Publisher: John Wiley & Sons
ISBN: 1786305038
Category : Mathematics
Languages : en
Pages : 308

View

Book Description
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.

Author: Gustaaf van Tendeloo
Publisher: John Wiley & Sons
ISBN: 3527317066
Category : Technology & Engineering
Languages : en
Pages : 1484

View

Book Description
This completely revised successor to the Handbook of Microscopy supplies in-depth coverage of all imaging technologies from the optical to the electron and scanning techniques. Adopting a twofold approach, the book firstly presents the various technologies as such, before going on to cover the materials class by class, analyzing how the different imaging methods can be successfully applied. It covers the latest developments in techniques, such as in-situ TEM, 3D imaging in TEM and SEM, as well as a broad range of material types, including metals, alloys, ceramics, polymers, semiconductors, minerals, quasicrystals, amorphous solids, among others. The volumes are divided between methods and applications, making this both a reliable reference and handbook for chemists, physicists, biologists, materials scientists and engineers, as well as graduate students and their lecturers.

Author: Yan Liu
Publisher: Springer
ISBN: 9811001529
Category : Mathematics
Languages : en
Pages : 136

View

Book Description
This book integrates the fundamentals of asymptotic theory of statistical inference for time series under nonstandard settings, e.g., infinite variance processes, not only from the point of view of efficiency but also from that of robustness and optimality by minimizing prediction error. This is the first book to consider the generalized empirical likelihood applied to time series models in frequency domain and also the estimation motivated by minimizing quantile prediction error without assumption of true model. It provides the reader with a new horizon for understanding the prediction problem that occurs in time series modeling and a contemporary approach of hypothesis testing by the generalized empirical likelihood method. Nonparametric aspects of the methods proposed in this book also satisfactorily address economic and financial problems without imposing redundantly strong restrictions on the model, which has been true until now. Dealing with infinite variance processes makes analysis of economic and financial data more accurate under the existing results from the demonstrative research. The scope of applications, however, is expected to apply to much broader academic fields. The methods are also sufficiently flexible in that they represent an advanced and unified development of prediction form including multiple-point extrapolation, interpolation, and other incomplete past forecastings. Consequently, they lead readers to a good combination of efficient and robust estimate and test, and discriminate pivotal quantities contained in realistic time series models.

Author:
Publisher: Academic Press
ISBN: 0080956351
Category : Mathematics
Languages : en
Pages : 606

View

Book Description
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression. - Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering