Download or read book Inference with the Whittle Likelihood written by Richard E. Chandler and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theoretical properties of the Whittle likelihood have been studied extensively for many different types of process. In applications however, the utility of the approach is limited by the fact that the asymptotic sampling distribution of the estimator typically depends on third-order and fourth-order properties of the process that may be difficult to obtain. In this article, we show how the methodology can be embedded in the standard framework of estimating functions, which allows the asymptotic distribution to be estimated empirically without calculating higher-order spectra. We also demonstrate that some aspects of the inference, such as the calculation of confidence regions for the entire parameter vector, can be inaccurate but that a small adjustment, designed for application in situations where a mis-specified likelihood is used for inference, can lead to marked improvements.
Download or read book Optimal Statistical Inference in Financial Engineering written by Masanobu Taniguchi and published by CRC Press. This book was released on 2007-11-26 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: Until now, few systematic studies of optimal statistical inference for stochastic processes had existed in the financial engineering literature, even though this idea is fundamental to the field. Balancing statistical theory with data analysis, Optimal Statistical Inference in Financial Engineering examines how stochastic models can effectively des
Download or read book Fundamentals of Nonparametric Bayesian Inference written by Subhashis Ghosal and published by Cambridge University Press. This book was released on 2017-06-26 with total page 671 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explosive growth in computing power has made Bayesian methods for infinite-dimensional models - Bayesian nonparametrics - a nearly universal framework for inference, finding practical use in numerous subject areas. Written by leading researchers, this authoritative text draws on theoretical advances of the past twenty years to synthesize all aspects of Bayesian nonparametrics, from prior construction to computation and large sample behavior of posteriors. Because understanding the behavior of posteriors is critical to selecting priors that work, the large sample theory is developed systematically, illustrated by various examples of model and prior combinations. Precise sufficient conditions are given, with complete proofs, that ensure desirable posterior properties and behavior. Each chapter ends with historical notes and numerous exercises to deepen and consolidate the reader's understanding, making the book valuable for both graduate students and researchers in statistics and machine learning, as well as in application areas such as econometrics and biostatistics.
Download or read book Likelihood Inference for Discriminating Between Long Memory and Change Point Models written by Chun Yip Yau and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop a likelihood ratio (LR) test procedure for discriminating between a short-memory time series with a change-point (CP) and a long-memory (LM) time series. Under the null hypothesis, the time series consists of two segments of short-memory time series with different means and possibly different covariance functions. The location of the shift in the mean is unknown. Under the alternative, the time series has no shift in mean but rather is LM. The LR statistic is defined as the normalized log-ratio of the Whittle likelihood between the CP model and the LM model, which is asymptotically normally distributed under the null. The LR test provides a parametric alternative to the CUSUM test proposed by Berkes et al. (2006). Moreover, the LR test is more general than the CUSUM test in the sense that it is applicable to changes in other marginal or dependence features other than a change-in-mean. We show its good performance in simulations and apply it to two data examples.
Download or read book Maximum Likelihood Estimation and Inference written by Russell B. Millar and published by John Wiley & Sons. This book was released on 2011-07-26 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book takes a fresh look at the popular and well-established method of maximum likelihood for statistical estimation and inference. It begins with an intuitive introduction to the concepts and background of likelihood, and moves through to the latest developments in maximum likelihood methodology, including general latent variable models and new material for the practical implementation of integrated likelihood using the free ADMB software. Fundamental issues of statistical inference are also examined, with a presentation of some of the philosophical debates underlying the choice of statistical paradigm. Key features: Provides an accessible introduction to pragmatic maximum likelihood modelling. Covers more advanced topics, including general forms of latent variable models (including non-linear and non-normal mixed-effects and state-space models) and the use of maximum likelihood variants, such as estimating equations, conditional likelihood, restricted likelihood and integrated likelihood. Adopts a practical approach, with a focus on providing the relevant tools required by researchers and practitioners who collect and analyze real data. Presents numerous examples and case studies across a wide range of applications including medicine, biology and ecology. Features applications from a range of disciplines, with implementation in R, SAS and/or ADMB. Provides all program code and software extensions on a supporting website. Confines supporting theory to the final chapters to maintain a readable and pragmatic focus of the preceding chapters. This book is not just an accessible and practical text about maximum likelihood, it is a comprehensive guide to modern maximum likelihood estimation and inference. It will be of interest to readers of all levels, from novice to expert. It will be of great benefit to researchers, and to students of statistics from senior undergraduate to graduate level. For use as a course text, exercises are provided at the end of each chapter.
Download or read book Empirical Likelihood and Quantile Methods for Time Series written by Yan Liu and published by Springer. This book was released on 2018-12-05 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Probability via Expectation written by Peter Whittle and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a complete revision of the earlier work Probability which ap peared in 1970. While revised so radically and incorporating so much new material as to amount to a new text, it preserves both the aim and the approach of the original. That aim was stated as the provision of a 'first text in probability, de manding a reasonable but not extensive knowledge of mathematics, and taking the reader to what one might describe as a good intermediate level'. In doing so it attempted to break away from stereotyped applications, and consider applications of a more novel and significant character. The particular novelty of the approach was that expectation was taken as the prime concept, and the concept of expectation axiomatized rather than that of a probability measure. In the preface to the original text of 1970 (reproduced below, together with that to the Russian edition of 1982) I listed what I saw as the advantages of the approach in as unlaboured a fashion as I could. I also took the view that the text rather than the author should persuade, and left the text to speak for itself. It has, indeed, stimulated a steady interest, to the point that Springer-Verlag has now commissioned this complete reworking.
Download or read book In All Likelihood written by Yudi Pawitan and published by Oxford University Press, USA. This book was released on 2013-01-17 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces likelihood as a unifying concept in statistical modelling and inference. The complete range of concepts and applications are covered, from very simple to very complex studies. It relies on realistic examples, and presents the main results using heuristic rather than formal mathematical arguments.
Download or read book Selected Proceedings of the Symposium on Inference for Stochastic Processes written by Ishwar V. Basawa and published by IMS. This book was released on 2001 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Characterizing Interdependencies of Multiple Time Series written by Yuzo Hosoya and published by Springer. This book was released on 2017-10-26 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces academic researchers and professionals to the basic concepts and methods for characterizing interdependencies of multiple time series in the frequency domain. Detecting causal directions between a pair of time series and the extent of their effects, as well as testing the non existence of a feedback relation between them, have constituted major focal points in multiple time series analysis since Granger introduced the celebrated definition of causality in view of prediction improvement. Causality analysis has since been widely applied in many disciplines. Although most analyses are conducted from the perspective of the time domain, a frequency domain method introduced in this book sheds new light on another aspect that disentangles the interdependencies between multiple time series in terms of long-term or short-term effects, quantitatively characterizing them. The frequency domain method includes the Granger noncausality test as a special case. Chapters 2 and 3 of the book introduce an improved version of the basic concepts for measuring the one-way effect, reciprocity, and association of multiple time series, which were originally proposed by Hosoya. Then the statistical inferences of these measures are presented, with a focus on the stationary multivariate autoregressive moving-average processes, which include the estimation and test of causality change. Empirical analyses are provided to illustrate what alternative aspects are detected and how the methods introduced here can be conveniently applied. Most of the materials in Chapters 4 and 5 are based on the authors' latest research work. Subsidiary items are collected in the Appendix.
Download or read book Contributions to Inference Without Likelihoods written by J. Jesus and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is concerned with statistical inference in situations where one is unwilling or unable to formulate a likelihood function. The theory of estimating functions (EFs) provides an alternative inference framework in such settings. The research was motivated by problems arising in the application of a class of stochastic models for rainfall based on point processes. These models are often used by hydrologists to produce synthetic rainfall sequences for risk assessment purposes, notably in the UKCP09 climate change projections for the UK. In the absence of a likelihood function, the models are usually fitted by minimizing some measure of disagreement between theoretical properties and the observed counterparts. In general situations of this type, two" subjective" decisions are required: what properties to use, and how to weight their contribution to the objective function. The choice of weights can be formalised by defining a minimum variance criterion for the estimator. This is equivalent to the Generalized Method of Moments estimator which is widely used in econometrics. The first contribution of this thesis is to translate the problem to an EF framework which is much more familiar to statisticians. Simulations show that the theory has poor finite sample performance for point process rainfall models. This is associated with inaccurate estimation of the covariance matrix of observed properties. A two-stage approach is developed to overcome this problem. The second main contribution is to apply EF theory to the Whittle likelihood, which is based on the periodogram of the data. A problem here is that the covariance matrix of the estimators depends on fourth-order properties which are often intractable. An EF approach provides a feasible alternative in practical applications. After establishing the conditions under which EF theory can be applied to Whittle estimation, simulations are once again used to explore the finite sample performance.
Download or read book Research Papers in Statistical Inference for Time Series and Related Models written by Yan Liu and published by Springer Nature. This book was released on 2023-05-31 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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, Lévy 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.
Download or read book The Likelihood Principle written by James O. Berger and published by IMS. This book was released on 1988 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Bayesian Analysis written by Jayanta K. Ghosh and published by Springer Science & Business Media. This book was released on 2007-07-03 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a graduate-level textbook on Bayesian analysis blending modern Bayesian theory, methods, and applications. Starting from basic statistics, undergraduate calculus and linear algebra, ideas of both subjective and objective Bayesian analysis are developed to a level where real-life data can be analyzed using the current techniques of statistical computing. Advances in both low-dimensional and high-dimensional problems are covered, as well as important topics such as empirical Bayes and hierarchical Bayes methods and Markov chain Monte Carlo (MCMC) techniques. Many topics are at the cutting edge of statistical research. Solutions to common inference problems appear throughout the text along with discussion of what prior to choose. There is a discussion of elicitation of a subjective prior as well as the motivation, applicability, and limitations of objective priors. By way of important applications the book presents microarrays, nonparametric regression via wavelets as well as DMA mixtures of normals, and spatial analysis with illustrations using simulated and real data. Theoretical topics at the cutting edge include high-dimensional model selection and Intrinsic Bayes Factors, which the authors have successfully applied to geological mapping. The style is informal but clear. Asymptotics is used to supplement simulation or understand some aspects of the posterior.
Download or read book Testing Statistical Hypotheses written by Erich L. Lehmann and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 795 pages. Available in PDF, EPUB and Kindle. Book excerpt: The third edition of Testing Statistical Hypotheses updates and expands upon the classic graduate text, emphasizing optimality theory for hypothesis testing and confidence sets. The principal additions include a rigorous treatment of large sample optimality, together with the requisite tools. In addition, an introduction to the theory of resampling methods such as the bootstrap is developed. The sections on multiple testing and goodness of fit testing are expanded. The text is suitable for Ph.D. students in statistics and includes over 300 new problems out of a total of more than 760.
Download or read book Methods and Models in Statistics written by John A. Nelder and published by Imperial College Press. This book was released on 2004 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: John Nelder is one of today''s leading statisticians, having made an impact on many parts of the discipline. This book contains reviews of some of those areas, written by top researchers. It is accessible to non-specialists, and is noteworthy for its breadth of coverage.
Download or read book Time Series written by Raquel Prado and published by CRC Press. This book was released on 2021-07-27 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: • Expanded on aspects of core model theory and methodology. • Multiple new examples and exercises. • Detailed development of dynamic factor models. • Updated discussion and connections with recent and current research frontiers.
