Empirical likelihood inference with applications to some econometric models

In this paper we analyse the higher order asymptotic properties of the empirical likelihood ratio test, by means of the dual likelihood theory. It is shown that when the econometric model is just identified, these tests are accurate to an order o(1/n), and this accuracy can always be improved to an order O(1/n^2) by means of a scale correction, as in standard parametric theory. To show this, we first develop a valid Edgeworth expansion for the empirical likelihood ratio under a local alternative in terms of an "induced" local alternative. As a by-product of the expansion, we find an explicit expression for the Bartlett correction in terms of cumulants of dual likelihood derivatives which is slightly different from the standard adjustment reported in the literature on Bartlett corrections of the empirical likelihood ratio. We then highlight the connection between the empirical likelihood method and the bootstrap by obtaining a valid Edgeworth expansion for a bootstrap based empirical likelihood ratio test. The theory is then applied to some standard econometric models and illustrated by means of some Monte Carlo simulations.

Applications of differential geometry to statistics

Chapters 1 and 2 are both surveys of the current work in applying geometry to statistics. Chapter 1 is a broad outline of all the work done so far, while Chapter 2 studies, in particular, the work of Amari and that of Lauritzen. In Chapters 3 and 4 we study some open problems which have been raised by Lauritzen's work. In particular we look in detail at some of the differential geometric theory behind Lauritzen's defmition of a Statistical manifold. The following chapters follow a different line of research. We look at a new non symmetric differential geometric structure which we call a preferred point manifold. We show how this structure encompasses the work of Amari and Lauritzen, and how it points the way to many generalizations of their results. In Chapter 5 we define this new structure, and compare it to the Statistical manifold theory. Chapter 6 develops some examples of the new geometry in a statistical context. Chapter 7 starts the development of the pure theory of these preferred point manifolds. In Chapter 8 we outline possible paths of research in which the new geometry may be applied to statistical theory. We include, in an appendix, a copy of a joint paper which looks at some direct applications of differential geometry to a statistical problem, in this case it is the problem of the behaviour of the Wald test with nonlinear restriction functions

Glosarium Matematika

273 p.; 24 cm

Assessing the evolving nature of European stock markets convergence using dynamic cointegration analysis

This thesis assesses the long-run convergence process among five major European financial markets over a period of four decades. Equity price indexes are examined first within the framework of a static cointegration analysis; the Johansen-Juselius approach is then supplemented by a dynamic rolling cointegration technique which takes into account the extent of time-varying integration from a complementary perspective. The results show that the degree of convergence among European stock markets has been increasing during the recent two decades

Differential geometric MCMC methods and applications

This thesis presents novel Markov chain Monte Carlo methodology that exploits the natural representation of a statistical model as a Riemannian manifold. The methods developed provide generalisations of the Metropolis-adjusted Langevin algorithm and the Hybrid Monte Carlo algorithm for Bayesian statistical inference, and resolve many shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlation structure. The performance of these Riemannian manifold Markov chain Monte Carlo algorithms is rigorously assessed by performing Bayesian inference on logistic regression models, log-Gaussian Cox point process models, stochastic volatility models, and both parameter and model level inference of dynamical systems described by nonlinear differential equations

Modelling macroeconomic adjustment with growth in developing economies : the case of India

The aim of this research is to understand the current economic scene and the stabilisation policies in historical perspective, and to survey and develop models for analysing issues of macroeconomic adjustment with growth. The topics have been chosen for their continued relevance in the current policy debates. The standard open economy model on which the Bretton Woods macroeconomics is based takes into account neither the endogeneity and decomposition of aggregate government expenditure or investment nor the price formation process in a developing economy. Further, with the opening up of the Indian economy since 1991, macroeconomic policy analysis needs to be examined in a different analytical framework from the essentially closed economy framework that has hitherto characterised policy discussions in India.T he present study investigates the appropriateness of the Fund-Bank approach to macroeconomic adjustment; modifies and analyses the respective effects of the model in light of the structural constraints in the form of low capital formation in the Indian economy after having disaggregated government expenditure into government consumption and investment expenditures. This thesis models trade, inflation and the determinants of long-run growth considering the role of endogenous growth and the demand factors in growth. The modelling procedure follows the VAR-based time series literature as against the traditional Cowles Commission approach to structural macroeconometric modelling. It estimates a macroeconomic model that incorporates the paradigm underlying the IMF's policy recommendations to developing countries, using Indian time series data from 1950-51 to 1995-96. It discusses structural sensitivities, dynamics and deterministic optimal control. This study investigates the effectiveness of three sets of key macroeconomic policy instruments which are typical in financial liberalisation process - namely, a tight credit policy, a depreciation of domestic currency and, a hike in regulated interest rates. Finally this study solves a multi-target and multi-instrument optimal control problem and finds that the two-target two-instrument problem of a standard policy package is not growth inducive and must target output growth in order to make the adjustment program as growth-oriented. This research has focused on explicitly recognising and analysing the operation of a credit or lending channel in the transmission of monetary policy

Maximum likelihood estimation for stochastic processes - a martingale approach

This thesis is primarily concerned with the investigation of asymptotic properties of the maximum likelihood estimate (MLE) of parameters of a stochastic process. These asymptotic properties are related to martingale limit theory by recognizing the (known) fact that, under certain regularity conditions, the derivative of the logarithm of the likelihood function is a martingale. To this end, part of the thesis is devoted to using or developing martingale limit theory to provide conditions for the consistency and/or asymptotic normality of the MLE. Thus, Chapter 1 is concerned with the martingale limit theory, while the remaining chapters look at its application to three broad types of stochastic processes. Chapter 2 extends the classical development of asymptotic theory of MLE’s (a la Cramer [1]) to stochastic processes which, basically, behave in a non-explosive way and for which non-random norming sequences can be used. In this chapter we also introduce a generalization of Fisher's measure of information to the stochastic process situation. Chapter 3 deals with the theory for general processes and develops the notion of "conditional" exponential families of processes, as well as establishing the importance of using random norming sequences. In Chapter 4 we consider the asymptotic theory of maximum likelihood estimation for continuous time processes and establish results which are analogous to those for discrete time processes. In each of these chapters many applications are considered in an attempt to show how known and new results fit into the general framework of estimation for stochastic processes. In Appendix B, a report on the use of the empirical characteristic function in inference is included in order to indicate how one might deal with situations where the likelihood is intractable