Download or read book Asymptotic Properties of Quasi maximum Likelihood Estimators and Test Statistics written by Thomas E. MaCurdy and published by . This book was released on 1981 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: We examine the implications of arbitrage in a market with many assets. The absence of arbitrage opportunities implies that the linear functionals that give the mean and cost of a portfolio are continuous; hence there exist unique portfolios that represent these functionals. The mean variance efficient set is a cone generated by these portfolios. Ross [16, 18J showed that if there is a factor structure, then the distance between the vector or mean returns and the space spanned by the factor loadings is bounded as the number of assets increases. We show that if the covariance matrix of asset returns has only K unbounded eigenvalues, then the corresponding K eigenvectors converge and play the role of factor loadings in Ross' result. Hence only a principal components analysis is needed to test the arbitrage pricing theory. Our eigenvalue conditional can hold even though conventional measures of the approximation error in a K factor model are unbounded. We also resolve the question of when a market with many assets permits so much diversification that risk-free investment opportunities are available.
Download or read book Asymptotic Properties of Induced Maximum Likelihood Estimates of Nonlinear Models for Item Response Variables The Finite Generic Item Pool Case written by Douglas H. Jones and published by . This book was released on 1985 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: The progress of modern mental test theory depends very much on the techniques of maximum likelihood estimation, and many popular applications make use of likelihoods induced by logistic item response models. While, in reality, item responses are nonreplicate within a single examinee and the logistic models are only ideal, practitioners make inferences using the asymptotic distribution of the maximum likelihood estimator derived as if item responses were replicated and satisfied their ideal model. This article proposes a sample space acknowledging these two realities and derives the asymptotic distribution of the induced maximum likelihood estimator. This article assumes that items, while sampled from an infinite set of items, have but a finite domain of alternate response functions: this situation is the case of the finite-generic-item-pool. Using the proposed sample space, the article applies the statistical functional approach of von Mises to derive the influence curve of the maximum likelihood estimator; to discuss related robustness properties; and to derive new classes of resistent estimators. The aim is revealing the value of these methods for uncovering the relative merits of different item response functions. Proofs and mathematical derivations are minimized to increase the accessability of this complex subject. (Author).
Download or read book Asymptotic Properties of Maximum Likelihood Estimators in the General Sampling Framework and Some Results in Non normal Linear Regression written by Robert Ernest Tarone and published by . This book was released on 1974 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Properties of Econometric Estimators written by Jeffrey M. Wooldridge and published by . This book was released on 1986 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quasi Likelihood And Its Application written by Christopher C. Heyde and published by Springer Science & Business Media. This book was released on 2008-01-08 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first account in book form of all the essential features of the quasi-likelihood methodology, stressing its value as a general purpose inferential tool. The treatment is rather informal, emphasizing essential principles rather than detailed proofs, and readers are assumed to have a firm grounding in probability and statistics at the graduate level. Many examples of the use of the methods in both classical statistical and stochastic process contexts are provided.
Download or read book Asymptotic Properties of maximum Likelihood estimators based on conditional specification written by Pranab Kumar Sen and published by . This book was released on 1978 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Properties of Some Estimators in Moving Average Models written by Stanford University. Department of Statistics and published by . This book was released on 1975 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author considers estimation procedures for the moving average model of order q. Walker's method uses k sample autocovariances (k> or = q). Assume that k depends on T in such a way that k nears infinity as T nears infinity. The estimates are consistent, asymptotically normal and asymptotically efficient if k = k (T) dominates log T and is dominated by (T sub 1/2). The approach in proving these theorems involves obtaining an explicit form for the components of the inverse of a symmetric matrix with equal elements along its five central diagonals, and zeroes elsewhere. The asymptotic normality follows from a central limit theorem for normalized sums of random variables that are dependent of order k, where k tends to infinity with T. An alternative form of the estimator facilitates the calculations and the analysis of the role of k, without changing the asymptotic properties.
Download or read book Asymptotic Properties and Computation of Maximum Likelihood Estimates in the Mixed Model of the Analysis of Variance written by Stanford University. Department of Statistics and published by . This book was released on 1973 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem considered is the estimation of the parameters in the mixed model of the analysis of variance, assuming normality of the random effects and errors. Both asymptotic properties of such estimates as the size of the design increases and numerical procedures for their calculation are discussed. Estimation is carried out by the method of maximum likelihood. It is shown that there is a sequence of roots of the likelihood equations which is consistent, asymptotically normal and asymptotically efficient in the sense of attaining the Cramer-Rao lower bound for the covariance matrix as the size of the design increases. This is accomplished using a Taylor series expansion of the log-likelihood. (Modified author abstract).
Download or read book Some Asymptotic Properties of Quasi Likelihood Estimators for Semimartingales written by Michael Sørensen and published by . This book was released on 1988 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Higher Order Asymptotic Theory for Time Series Analysis written by Masanobu Taniguchi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: The initial basis of this book was a series of my research papers, that I listed in References. I have many people to thank for the book's existence. Regarding higher order asymptotic efficiency I thank Professors Kei Takeuchi and M. Akahira for their many comments. I used their concept of efficiency for time series analysis. During the summer of 1983, I had an opportunity to visit The Australian National University, and could elucidate the third-order asymptotics of some estimators. I express my sincere thanks to Professor E.J. Hannan for his warmest encouragement and kindness. Multivariate time series analysis seems an important topic. In 1986 I visited Center for Mul tivariate Analysis, University of Pittsburgh. I received a lot of impact from multivariate analysis, and applied many multivariate methods to the higher order asymptotic theory of vector time series. I am very grateful to the late Professor P.R. Krishnaiah for his cooperation and kindness. In Japan my research was mainly performed in Hiroshima University. There is a research group of statisticians who are interested in the asymptotic expansions in statistics. Throughout this book I often used the asymptotic expansion techniques. I thank all the members of this group, especially Professors Y. Fujikoshi and K. Maekawa foItheir helpful discussion. When I was a student of Osaka University I learned multivariate analysis and time series analysis from Professors Masashi Okamoto and T. Nagai, respectively. It is a pleasure to thank them for giving me much of research background.
Download or read book Research Reports written by and published by . This book was released on 1988 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Asymptotic Properties of the Maximum Likelihood Estimates of the General Growth Curve Model written by S. R. Chakravorti and published by . This book was released on 1973 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Some Asymptotic Properties of Maximum Likelihood Estimates and Related Bayes Estimates written by Lucien Marie Le Cam and published by . This book was released on 1953 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Properties of Conditional Maximum Likelihood Estimators written by Erling Bernhard Andersen and published by . This book was released on 1968 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Properties of the Restricted Maximum Likelihood Estimators written by and published by . This book was released on 2009 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimal Asymptotic Properties of Maximum Likelihood Estimators of Parameters of Some Econometric Models written by Mary Kathleen Vickers and published by . This book was released on 1977 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Four theorems are proven, which simplify the application to econometric models of Weiss's theorem on asymptotic properties of maximum likelihood estimators in nonstandard cases. The theorems require, roughly: the uniform convergence in any compact sets of the unknown parameters of the expection of the Hessian matrix of the log likelihood function; and the uniform convergence to 0 in the same sense of the variance of the same quantities. The fourth theorem allows one to conclude that the optimal properties hold on an image set of the parameters when the map satisfies certain smoothness conditions, and the first three theorems are satisfied for the original parameter set. These four theorems are applied to autoregressive models, nonlinear models, systems of equations, and probit and logit models to infer optimal asymptotic properties. (Author).
Download or read book Pseudo variance Quasi maximum Likelihood Estimation of Semiparametric Time Series Models written by Mirko Armillotta and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a novel estimation approach for a general class of semi-parametric time series models where the conditional expectation is modeled through a parametric function. The proposed class of estimators is based on a Gaussian quasi-likelihood function and it relies on the specification of a parametric pseudo-variance that can contain parametric restrictions with respect to the conditional expectation. The specification of the pseudo-variance and the parametric restrictions follow naturally in observation-driven models with bounds in the support of the observable process, such as count processes and double-bounded time series. We derive the asymptotic properties of the estimators and a validity test for the parameter restrictions. We show that the results remain valid irrespective of the correct specification of the pseudo-variance. The key advantage of the restricted estimators is that they can achieve higher efficiency compared to alternative quasi-likelihood methods that are available in the literature. Furthermore, the testing approach can be used to build specification tests for parametric time series models. We illustrate the practical use of the methodology in a simulation study and two empirical applications featuring integer-valued autoregressive processes, where assumptions on the dispersion of the thinning operator are formally tested, and autoregressions for double-bounded data with application to a realized correlation time series.
