Fisher and Inference for Scores

This paper examines the work of Fisher and Bartlett on discriminant analysis, ordinal response regression and correspondence analysis. Placing these methods with canonical correlation analysis in the context of the singular value decomposition of particular matrices, we use explicit models and vector space notation to unify these methods, understand Fisher's approach, understand Bartlett's criticisms of Fisher and relate both to modern thinking. We consider in particular the formulation of certain hypotheses and Fisher's arguments to obtain approximate distributions for tests of these hypotheses (without assuming multivariate normality) and put these in modern notation. Using perturbation techniques pioneered by G.S. Watson, we give an asymptotic justification for Fisher's test for assigned scores and thereby resolve a long standing conflict between Fisher and Bartlett.     

Understanding the Fisher equation

It is argued that univariate long memory estimates based on ex post data tend to underestimate the persistence of ex ante variables (and, hence, that of the ex post variables themselves) because of the presence of unanticipated shocks whose short‐run volatility masks the degree of long‐range dependence in the data. Empirical estimates of long‐range dependence in the Fisher equation are shown to manifest this problem and lead to an apparent imbalance in the memory characteristics of the variables in the Fisher equation. Evidence in support of this typical underestimation is provided by results obtained with inflation forecast survey data and by direct calculation of the finite sample biases. To address the problem of bias, the paper introduces a bivariate exact Whittle (BEW) estimator that explicitly allows for the presence of short memory noise in the data. The new procedure enhances the empirical capacity to separate low‐frequency behaviour from high‐frequency fluctuations, and it produces estimates of long‐range dependence that are much less biased when there is noise contaminated data. Empirical estimates from the BEW method suggest that the three Fisher variables are integrated of the same order, with memory parameter in the range (0.75, 1). Since the integration orders are balanced, the ex ante real rate has the same degree of persistence as expected inflation, thereby furnishing evidence against the existence of a (fractional) cointegrating relation among the Fisher variables and, correspondingly, showing little support for a long‐run form of Fisher hypothesis. Copyright © 2004 John Wiley & Sons, Ltd.     

Health, Government, and Irving Fisher

A bstract    This paper provides a few historical notes on government involvement in health, followed by a summary of the theoretical arguments that economists offer in its support. Irving Fisher's views and recommendations about health are examined in the light of today's perceptions concerning health, health economics, and health policy. The wide variety of roles that the U.S. and other governments currently play in health is reviewed, and the ability of economics to explain these roles is assessed. The consequences of government involvement for the health of populations, for expenditures on health care, and for political and social stability are examined. The paper concludes with an overview of new worldwide trends in health policy and some probable explanations for these trends.     

Fisher information in record data

We present some general results on Fisher information (FI) contained in upper (or lower) record values and associated record times generated from a sequence of i.i.d. continuous variables. For the record data obtained from a random sample of fixed size, we establish an interesting relationship between its FI content and the FI in the data consisting of sequential maxima. We also consider the record data from an inverse sampling plan (Samaniego and Whitaker, 1986). We apply the general results to evaluate the FI in upper as well as lower records data from the exponential distribution for both sampling plans. Further, we discuss the implication of our results to statistical inference from these record data. Received: December 2001 Acknowledgements. This research was supported by Fondo Nacional de Desarrollo Cientifico y Tecnologico (FONDECYT) grants 7990089 and 1010222 of Chile. We would like to thank the Department of Statistics at the University of Concepción for its hospitality during the stay of H. N. Nagaraja in Chile in March of 2000, when the initial work was done. We are grateful to the two referees for various comments that let to improvements in the paper.     

基于费舍尔模型的物流服务与成本分析

基于费舍尔模型的理论,通过对产品进行分类,对不同种类的产品提供的物流服务与成本进行研究,以期以适当的成本和服务来提高企业的产品竞争力.     

基于费舍尔模型的物流服务与成本分析

基于费舍尔模型的理论,通过对产品进行分类,对不同种类的产品提供的物流服务与成本进行研究,以期以适当的成本和服务来提高企业的产品竞争力。     

Around the world with Irving Fisher

This paper aims to show why Irving Fisher's own data on interest rates and inflation in New York, London, Paris, Berlin, Calcutta, and Tokyo during 1825–1927 suggested to him that nominal interest rates adjusted neither quickly nor fully to changes in inflation, not even in the long run. In Fisher's data, interest rates evolve less rapidly than inflation and change less than inflation over time. Even so, the “Fisher effect” is commonly defined as a point-for-point effect of inflation on nominal interest rates rather than what Fisher actually found: a persistent negative effect of increased inflation on real interest rates.     

慈铭“抄底”扩张

2008年下半年，慈铭体检集团总裁韩小红频繁往来于京广两地——两桩并购案让她忙得不可开交。继11月下旬低调完成对北京“佰众体检”的收购后，12月8日，慈铭体检集团又将广东“我佳体检”收归旗下。     

Fisher information under Gaussian quadrature models

This paper develops formulae to compute the Fisher information matrix for the regression parameters of generalized linear models with Gaussian random effects. The Fisher information matrix relies on the estimation of the response variance under the model assumptions. We propose two approaches to estimate the response variance: the first is based on an analytic formula (or a Taylor expansion for cases where we cannot obtain the closed form), and the second is an empirical approximation using the model estimates via the expectation–maximization process. Further, simulations under several response distributions and a real data application involving a factorial experiment are presented and discussed. In terms of standard errors and coverage probabilities for model parameters, the proposed methods turn out to behave more reliably than does the ‘disparity rule’ or direct extraction of results from the generalized linear model fitted in the last expectation–maximization iteration.     

Fisher, Keynes, and the Corridor of Stability

A bstract .   This chapter draws on the debt-deflation process of Fisher (1933 ) as well as on Keynes (1936 , chapter 19) and Tobin (1975 , 1980 ) to explore the concept of a corridor of stability, where an economy will be self-adjusting only for demand shocks small enough to leave it within that corridor.     

Panel cointegration tests of the Fisher effect

Most empirical evidence suggests that the Fisher effect, stating that inflation and nominal interest rates should cointegrate with a unit slope on inflation, does not hold, a finding at odds with many theoretical models. This paper argues that these results can be attributed in part to the low power of univariate tests, and that the use of panel data can generate more powerful tests. For this purpose, we propose two new panel cointegration tests that can be applied under very general conditions, and that are shown by simulation to be more powerful than other existing tests. These tests are applied to a panel of quarterly data covering 20 OECD countries between 1980 and 2004. The evidence suggest that the Fisher effect cannot be rejected once the panel evidence on cointegration has been taken into account. Copyright © 2007 John Wiley & Sons, Ltd.     

On the Fisher information in record values

In this article, we establish some general results concerning the comparison of the amount of the Fisher information contained in n record values with the Fisher information contained in n iid observations from the original distribution. Some common distributions are classified according to this criterion. We also propose some methods of estimation based on record values. The results may be of interest in some life testing problems. Received: September 1999     

Estimation of Fisher information using model selection

In the paper the problem of estimation of Fisher information I _f for a univariate density supported on [0, 1] is discussed. A starting point is an observation that when the density belongs to an exponential family of a known dimension, an explicit formula for I _f there allows for its simple estimation. In a general case, for a given random sample, a dimension of an exponential family which approximates it best is sought and then estimator of I _f is constructed for the chosen family. As a measure of quality of fit a modified Bayes Information Criterion is used. The estimator, which is an instance of Post Model Selection Estimation method is proved to be consistent and asymptotically normal when the density belongs to the exponential family. Its consistency is also proved under misspecification when the number of exponential models under consideration increases in a suitable way. Moreover we provide evidence that in most of considered parametric cases the small sample performance of proposed estimator is superior to that of kernel estimators.     

Fisher ideal output,input, and productivity indexes revisited

A productivity index for a firm is generally defined as an output index divided by an input index. The first part of the paper uses the test or axiomatic approach to index number theory in order to determine the appropriate functional form for the output and input indexes. It is found that the Fisher ideal index satisfies 21 reasonable tests and is uniquely characterized by a subset of these tests. In the remainder of the paper, the economic approach to productivity indexes introduced by Caves, Christensen, and Diewert is adopted and, again, a strong justification for the Fisher productivity index is provided.The editor of this paper was N.R. Adam.This research was supported by a Strategic Grant from the Social Science and Humanities Research Council of Canada. The author is indebted to Shelley Hey for typing assistance.     

Irving Fisher (1867–1947)

A bstract .   This essay is reprinted from Eatwell, J., M. Milgate and P. Newman (eds.) The New Palgrave: A Dictionary of Economics . 1987, 2: 369–376. United Kingdom, London and Basingstoke: The Macmillan Press Limited; New York, N.Y. The Stockton Press and Japan, Maruzen Company Limited. The essay is reproduced with the kind permission of Palgrave Macmillan.     

On the asymptotic Fisher information in order statistics

Metrika - We extend the result of Efron and Johnstone (1990), who expressed the Fisher information in terms of the hazard function, to express the Fisher information in order statistics as an...     

Irving Fisher and the Contribution of Improved Longevity to Living Standards

A bstract    It is not widely recognized that conventional measures of national income and output exclude the value of improvements in the health status of the population. The present study discusses the theory of the measurement of national income, proposes a new concept called "health income" that can be used to incorporate improvements in health status, and applies the theory to data for the United States over the 20^th century. It concludes that accounting for improvements in the health status would, over the twentieth century in the United States, make a substantial difference to our measures of economic welfare.