Download or read book Disturbances in the linear model estimation and hypothesis testing written by C. Dubbelman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. 1. The general linear model All econometric research is based on a set of numerical data relating to certain economic quantities, and makes infer ences from the data about the ways in which these quanti ties are related (Malinvaud 1970, p. 3). The linear relation is frequently encountered in applied econometrics. Let y and x denote two economic quantities, then the linear relation between y and x is formalized by: where {31 and {32 are constants. When {31 and {32 are known numbers, the value of y can be calculated for every given value of x. Here y is the dependent variable and x is the explanatory variable. In practical situations {31 and {32 are unknown. We assume that a set of n observations on y and x is available. When plotting the ob served pairs (x l' YI)' (x ' Y2)' . . . , (x , Y n) into a diagram with x 2 n measured along the horizontal axis and y along the vertical axis it rarely occurs that all points lie on a straight line. Generally, no b 1 and b exist such that Yi = b + b x for i = 1,2, . . . ,n. Unless 2 l 2 i the diagram clearly suggests another type of relation, for instance quadratic or exponential, it is customary to adopt linearity in order to keep the analysis as simple as possible.
Download or read book Disturbances in the Linear Model Estimation and Hypothesis Testing written by Cornelis Dubbelman and published by . This book was released on 1978 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Parameter Estimation and Hypothesis Testing in Linear Models written by Karl-Rudolf Koch and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: A treatment of estimating unknown parameters, testing hypotheses and estimating confidence intervals in linear models. Readers will find here presentations of the Gauss-Markoff model, the analysis of variance, the multivariate model, the model with unknown variance and covariance components and the regression model as well as the mixed model for estimating random parameters. A chapter on the robust estimation of parameters and several examples have been added to this second edition. The necessary theorems of vector and matrix algebra and the probability distributions of test statistics are derived so as to make this book self-contained. Geodesy students as well as those in the natural sciences and engineering will find the emphasis on the geodetic application of statistical models extremely useful.
Download or read book Disturbances in the Linear Model written by C. Dubbelman and published by Springer. This book was released on 1978 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. 1. The general linear model All econometric research is based on a set of numerical data relating to certain economic quantities, and makes infer ences from the data about the ways in which these quanti ties are related (Malinvaud 1970, p. 3). The linear relation is frequently encountered in applied econometrics. Let y and x denote two economic quantities, then the linear relation between y and x is formalized by: where {31 and {32 are constants. When {31 and {32 are known numbers, the value of y can be calculated for every given value of x. Here y is the dependent variable and x is the explanatory variable. In practical situations {31 and {32 are unknown. We assume that a set of n observations on y and x is available. When plotting the ob served pairs (x l' YI)' (x ' Y2)' . . . , (x , Y n) into a diagram with x 2 n measured along the horizontal axis and y along the vertical axis it rarely occurs that all points lie on a straight line. Generally, no b 1 and b exist such that Yi = b + b x for i = 1,2, . . . ,n. Unless 2 l 2 i the diagram clearly suggests another type of relation, for instance quadratic or exponential, it is customary to adopt linearity in order to keep the analysis as simple as possible.
Download or read book Specification Analysis in the Linear Model written by Maxwell L. King and published by Routledge. This book was released on 2018-03-05 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1987. This collection of original papers deals with various issues of specification in the context of the linear statistical model. The volume honours the early econometric work of Donald Cochrane, late Dean of Economics and Politics at Monash University in Australia. The chapters focus on problems associated with autocorrelation of the error term in the linear regression model and include appraisals of early work on this topic by Cochrane and Orcutt. The book includes an extensive survey of autocorrelation tests; some exact finite-sample tests; and some issues in preliminary test estimation. A wide range of other specification issues is discussed, including the implications of random regressors for Bayesian prediction; modelling with joint conditional probability functions; and results from duality theory. There is a major survey chapter dealing with specification tests for non-nested models, and some of the applications discussed by the contributors deal with the British National Accounts and with Australian financial and housing markets.
Download or read book Inference in General Statistical Models written by M. Bhupathi Naidu and published by LAP Lambert Academic Publishing. This book was released on 2013 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, an attempt has been made by proposing some new inferential procedures for linear regression models with different autoregressive schemes for disturbances. These estimation procedures have used iterative methods based on studentized residuals. It proposes some new inferential methods for linear statistical models with first, second and fourth order autoregressive disturbances. A new estimated iterative restricted GLS estimator has been derived for linear regression model with first order autoregressive disturbances. Later it has been applied for testing the general linear hypothesis. The linear statistical models have been specified with AR (1), AR (2) and AR (4) disturbances. The EGLS methods of estimation have been developed with particular AR (2) and AR (4) disturbances by using Iterative procedures. Here, Studentized residuals have been used in the place of OLS residuals. The parametric tests for particular second order and fourth order autocorrelations also have been discussed in this book
Download or read book The Linear Regression Model Under Test written by W. Kraemer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph grew out of joint work with various dedicated colleagues and students at the Vienna Institute for Advanced Studies. We would probably never have begun without the impetus of Johann Maurer, who for some time was the spiritus rector behind the Institute's macromodel of the Austrian economy. Manfred Deistler provided sustained stimulation for our research through many discussions in his econometric research seminar. Similar credits are due to Adrian Pagan, Roberto Mariano and Garry Phillips, the econometrics guest professors at the Institute in the 1982 - 1984 period, who through their lectures and advice have contributed greatly to our effort. Hans SchneeweiB offered helpful comments on an earlier version of the manuscript, and Benedikt Poetscher was always willing to lend a helping . hand when we had trouble with the mathematics of the tests. Needless to say that any errors are our own. Much of the programming for the tests and for the Monte Carlo experiments was done by Petr Havlik, Karl Kontrus and Raimund Alt. Without their assistance, our research project would have been impossible. Petr Havlik and Karl Kontrus in addition. read and criticized portions of the manuscript, and were of great help in reducing our error rate. Many of the more theoretical results in this monograph would never have come to light without the mathematical expertise of Werner Ploberger, who provided most of the statistical background of the chapter on testing for structural change . .
Download or read book Estimation and Hypothesis Testing in Singular Equation Systems with Autoregressive Disturbances written by Ernst R. Berndt and published by . This book was released on 1974 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multiple Hypotheses Testing in the Linear Regression Model with Applications to Economics and Finance written by Raimund Alt and published by Cuvillier Verlag. This book was released on 2005 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Linear Models with Correlated Disturbances written by Paul Knottnerus and published by Springer. This book was released on 1991 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: In each chapter of this volume some specific topics in the econometric analysis of time series data are studied. All topics have in common the statistical inference in linear models with correlated disturbances. The main aim of the study is to give a survey of new and old estimation techniques for regression models with disturbances that follow an autoregressive-moving average process. In the final chapter also several test strategies for discriminating between various types of autocorrelation are discussed. In nearly all chapters it is demonstrated how useful the simple geometric interpretation of the well-known ordinary least squares (OLS) method is. By applying these geometric concepts to linear spaces spanned by scalar stochastic variables, it emerges that well-known as well as new results can be derived in a simple geometric manner, sometimes without the limiting restrictions of the usual derivations, e. g. , the conditional normal distribution, the Kalman filter equations and the Cramer-Rao inequality. The outline of the book is as follows. In Chapter 2 attention is paid to a generalization of the well-known first order autocorrelation transformation of a linear regression model with disturbances that follow a first order Markov scheme. Firstly, the appropriate lower triangular transformation matrix is derived for the case that the disturbances follow a moving average process of order q (MA(q». It turns out that the calculations can be carried out either analytically or in a recursive manner.
Download or read book The Implementation and Constructive Use of Misspecification Tests in Econometrics written by L. G. Godfrey and published by Manchester University Press. This book was released on 1992 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of papers co-authored by members of the Department of Economics and Related Studies and the Institute for Research in the Social Sciences at the University of York, which deals with methods for calculating asymptotically valid tests for use with samples of the size available in empirical economics. The papers also address the scope for using test statistics to determine the nature of specification errors and for providing suitable corrections to estimates or parameters.
Download or read book Sample Size Choice written by Robert E. Odeh and published by CRC Press. This book was released on 2020-08-12 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guide to testing statistical hypotheses for readers familiar with the Neyman-Pearson theory of hypothesis testing including the notion of power, the general linear hypothesis (multiple regression) problem, and the special case of analysis of variance. The second edition (date of first not mentione
Download or read book Conflict Among Testing Procedures in a Linear Regression Model written by Daniel F. Kohler and published by . This book was released on 1981 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: Savin and Berndt and Savin have shown that an inequality relation exists between different test statistics used for testing hypotheses of the form r-R Beta = 0. They found that the value of the likelihood ratio test statistic (LR = 21og lambda), the Wald test statistic (W), and the Lagrange multiplier test statistic (LM) are always such that (1) W greater than or = LR greater than or = LM. This result has been generalized by Breusch who showed that the only necessary assumption for this inequality to hold is, that the disturbances follow a distribution which allows maximum-likelihood estimation. However, neither Breusch nor any of the authors before him were able to conclude anything about the power of the different tests. In this paper it will be shown that for finite but large samples a similar inequality relation to (1) exists between the powers of the three tests. The Wald test is uniformly more powerful than either of the other two tests, and the likelihood ratio test is more powerful than the Lagrange multiplier test for very large samples and for moderate-to-large differences between the null hypothesis and the true value of the tested parameters. The assumption of a scalar covariance matrix is made to simplify the exposition. The results can probably be generalized to hold for any disturbance vector which allows maximum-likelihood estimation.
Download or read book Applied Econometrics with R written by Christian Kleiber and published by Springer Science & Business Media. This book was released on 2008-12-10 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: R is a language and environment for data analysis and graphics. It may be considered an implementation of S, an award-winning language initially - veloped at Bell Laboratories since the late 1970s. The R project was initiated by Robert Gentleman and Ross Ihaka at the University of Auckland, New Zealand, in the early 1990s, and has been developed by an international team since mid-1997. Historically, econometricians have favored other computing environments, some of which have fallen by the wayside, and also a variety of packages with canned routines. We believe that R has great potential in econometrics, both for research and for teaching. There are at least three reasons for this: (1) R is mostly platform independent and runs on Microsoft Windows, the Mac family of operating systems, and various ?avors of Unix/Linux, and also on some more exotic platforms. (2) R is free software that can be downloaded and installed at no cost from a family of mirror sites around the globe, the Comprehensive R Archive Network (CRAN); hence students can easily install it on their own machines. (3) R is open-source software, so that the full source code is available and can be inspected to understand what it really does, learn from it, and modify and extend it. We also like to think that platform independence and the open-source philosophy make R an ideal environment for reproducible econometric research.
Download or read book The Linear Model and Hypothesis written by George Seber and published by Springer. This book was released on 2015-10-08 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a concise and integrated overview of hypothesis testing in four important subject areas, namely linear and nonlinear models, multivariate analysis, and large sample theory. The approach used is a geometrical one based on the concept of projections and their associated idempotent matrices, thus largely avoiding the need to involvematrix ranks. It is shown that all the hypotheses encountered are either linear or asymptotically linear, and that all the underlying models used are either exactly or asymptotically linear normal models. This equivalence can be used, for example, to extend the concept of orthogonality to other models in the analysis of variance, and to show that the asymptotic equivalence of the likelihood ratio, Wald, and Score (Lagrange Multiplier) hypothesis tests generally applies.
Download or read book Specification Analysis in the Linear Model written by Maxwell L. King and published by Routledge. This book was released on 2018-03-05 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1987. This collection of original papers deals with various issues of specification in the context of the linear statistical model. The volume honours the early econometric work of Donald Cochrane, late Dean of Economics and Politics at Monash University in Australia. The chapters focus on problems associated with autocorrelation of the error term in the linear regression model and include appraisals of early work on this topic by Cochrane and Orcutt. The book includes an extensive survey of autocorrelation tests; some exact finite-sample tests; and some issues in preliminary test estimation. A wide range of other specification issues is discussed, including the implications of random regressors for Bayesian prediction; modelling with joint conditional probability functions; and results from duality theory. There is a major survey chapter dealing with specification tests for non-nested models, and some of the applications discussed by the contributors deal with the British National Accounts and with Australian financial and housing markets.
Download or read book Inference in Linear Models With Auto Correlated Disturbances written by M. V. Chalapathi Rao and published by LAP Lambert Academic Publishing. This book was released on 2014-01 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the Present Book Chapter-I is an introductory one. It contains the general introduction about the problem of autocorrelation . Chapter-II presents statistical inferential problems in linear models. It explains the specification of classical linear regression model together with its estimation. Chapter-III describes the review about inferential methods in linear models under the problem of autocorrelation. Chapter-IV proposes some alternative inferential methods for linear model with autocorrelated disturbances. It uses the various types of residuals such as ordinary least squares, studentized and predicted residuals to develop alternative iterative estimation methods and tests for the autocorrelation. Chapter-V depicts the conclusions. Several selected references for the present book are given under the title 'BIBLIOGRAPHY'
