N. L. Johnson
Bio: N. L. Johnson is an academic researcher. The author has contributed to research in topics: Statistical model & Statistical inference. The author has an hindex of 1, co-authored 1 publications receiving 1579 citations.
TL;DR: Rao's Linear Statistical Inference and Its Applications as discussed by the authors is one of the earliest works in statistical inference in the literature and has been translated into six major languages of the world.
Abstract: "C. R. Rao would be found in almost any statistician's list of five outstanding workers in the world of Mathematical Statistics today. His book represents a comprehensive account of the main body of results that comprise modern statistical theory." -W. G. Cochran "[C. R. Rao is] one of the pioneers who laid the foundations of statistics which grew from ad hoc origins into a firmly grounded mathematical science." -B. Efrom Translated into six major languages of the world, C. R. Rao's Linear Statistical Inference and Its Applications is one of the foremost works in statistical inference in the literature. Incorporating the important developments in the subject that have taken place in the last three decades, this paperback reprint of his classic work on statistical inference remains highly applicable to statistical analysis. Presenting the theory and techniques of statistical inference in a logically integrated and practical form, it covers: * The algebra of vectors and matrices * Probability theory, tools, and techniques * Continuous probability models * The theory of least squares and the analysis of variance * Criteria and methods of estimation * Large sample theory and methods * The theory of statistical inference * Multivariate normal distribution Written for the student and professional with a basic knowledge of statistics, this practical paperback edition gives this industry standard new life as a key resource for practicing statisticians and statisticians-in-training.
TL;DR: The Condensation algorithm uses “factored sampling”, previously applied to the interpretation of static images, in which the probability distribution of possible interpretations is represented by a randomly generated set.
Abstract: The problem of tracking curves in dense visual clutter is challenging. Kalman filtering is inadequate because it is based on Gaussian densities which, being unimo dal, cannot represent simultaneous alternative hypotheses. The Condensation algorithm uses “factored sampling”, previously applied to the interpretation of static images, in which the probability distribution of possible interpretations is represented by a randomly generated set. Condensation uses learned dynamical models, together with visual observations, to propagate the random set over time. The result is highly robust tracking of agile motion. Notwithstanding the use of stochastic methods, the algorithm runs in near real-time.
TL;DR: In this paper, the authors propose a model in which there is an equilibrium degree of disequilibrium: prices reflect the information of informed individuals (arbitrageurs) but only partially, so that those who expend resources to obtain information do receive compensation.
Abstract: If competitive equilibrium is defined as a situation in which prices are such that all arbitrage profits are eliminated, is it possible that a competitive economy always be in equilibrium? Clearly not, for then those who arbitrage make no (private) return from their (privately) costly activity. Hence the assumptions that all markets, including that for information, are always in equilibrium and always perfectly arbitraged are inconsistent when arbitrage is costly. We propose here a model in which there is an equilibrium degree of disequilibrium: prices reflect the information of informed individuals (arbitrageurs) but only partially, so that those who expend resources to obtain information do receive compensation. How informative the price system is depends on the number of individuals who are informed; but the number of individuals who are informed is itself an endogenous variable in the model. The model is the simplest one in which prices perform a well-articulated role in conveying information from the informed to the uninformed. When informed individuals observe information that the return to a security is going to be high, they bid its price up, and conversely when they observe information that the return is going to be low. Thus the price system makes publicly available the information obtained by informed individuals to the uninformed. In general, however, it does this imperfectly; this is perhaps lucky, for were it to do it perfectly , an equilibrium would not exist. In the introduction, we shall discuss the general methodology and present some conjectures concerning certain properties of the equilibrium. The remaining analytic sections of the paper are devoted to analyzing in detail an important example of our general model, in which our conjectures concerning the nature of the equilibrium can be shown to be correct. We conclude with a discussion of the implications of our approach and results, with particular emphasis on the relationship of our results to the literature on "efficient capital markets."
TL;DR: In this article, the authors propose simple and directional likelihood-ratio tests for discriminating and choosing between two competing models whether the models are nonnested, overlapping or nested and whether both, one, or neither is misspecified.
Abstract: In this paper, we propose a classical approach to model selection. Using the Kullback-Leibler Information measure, we propose simple and directional likelihood-ratio tests for discriminating and choosing between two competing models whether the models are nonnested, overlapping or nested and whether both, one, or neither is misspecified. As a prerequisite, we fully characterize the asymptotic distribution of the likelihood ratio statistic under the most general conditions.
TL;DR: In this paper, the EM algorithm converges to a local maximum or a stationary value of the (incomplete-data) likelihood function under conditions that are applicable to many practical situations.
Abstract: Two convergence aspects of the EM algorithm are studied: (i) does the EM algorithm find a local maximum or a stationary value of the (incomplete-data) likelihood function? (ii) does the sequence of parameter estimates generated by EM converge? Several convergence results are obtained under conditions that are applicable to many practical situations Two useful special cases are: (a) if the unobserved complete-data specification can be described by a curved exponential family with compact parameter space, all the limit points of any EM sequence are stationary points of the likelihood function; (b) if the likelihood function is unimodal and a certain differentiability condition is satisfied, then any EM sequence converges to the unique maximum likelihood estimate A list of key properties of the algorithm is included