Functions of measurements under general laws of error

Abstract

The first object of this paper is to extend somewhat a theorem of MISES ¹ (1) Fundamentalsätze der Wahrscheinlichkeitsrechnung, (2) Grundlagen der Wahr. Mathematische Zeitschrift (1919) vol. 4, pp. 1–97; vol. 5, pp. 52–99. , who by the use of the STIELTJES integral ² Bliss, Integrals of Lebesgue, Bulletin of the American Mathematical Society, vol. 24 (1917), pp. 1–47. Bliss, A necessary and sufficient condition for the existence of a Stieltjes integral, Proceedings of the National Academy of Sciences vol 3 (1917), pp. 633–637. HILDEBRANDT, On Integrals related to and Extensions of the Lebesgue Integrals, Bulletin of the American Mathematical Society, vol. 24 (1917), pp. 113–144; Ibid., pp. 177–202. CARMICHEAL, Conditions necessary and sufficient for the existence of the STIELTJE'S Integral, Proceedings of the National Academy of Sciences, vol. 5 (1919), pp. 551–555. treats as a single subject continuous (geometric) and discontinuous (arithmetic) probability. Laplace ³ Oeuvres complete de LAPLACE, 3rd Ed., vol. 7, p. 266. , indeed, used a probability function which was in general continuous but had finite jumps, but he left no systematic treatment of the whole field of probability under such general conditions.     

On the reduction of frequency curves

1. When a frequency distribution is given, it is often important to know whether the corresponding frequency curve is Gauss' normal curve, and if not, whether it can be reduced to one by an adequate change of variable, i.e. by changing bhe method of measuring the attribute. In this note I will give a simple method by which an arbitrary frequency curve may be reduced.     

关于贸易收汇和贸易出口真实性与一致性的研究

贸易收支是异常资金流入与流出的重要渠道之一,异常资金流动会导致贸易收汇和贸易出口所对应的资金流与货物流之间的匹配出现偏差。本研究探索了有关贸易收汇和贸易出口真实性与一致性非现场监测的非参数分析方法,并利用此方法对江苏省2007年贸易收汇和贸易出口之间真实性和一致性的情况进行了实证分析。     

On the Gram series on Pearson's system of frequency functions

Abstract

Among the manifold frequency curves that may conceivably arise when it is assumed that, instead of the variate χ itself, a function of the latter, u = ψ(χ), is normally distributed, the logarithmic normal curve occupies a unique position for two reasons: it can be theoretically deduced from a slightly modified elementary error hypothesis and it is applicable in practice to different cases.     

Toehold strategies,takeover laws and rival bidders

Prior to the announcement of a tender offer, the bidding firm is legally allowed to acquire shares in the open market, subject to some limitations. These pre-announcement purchases are known as toeholds. This paper presents a simple model that describes the bidder's optimal toehold acquisition strategy, within an environment that closely parallels the present legal institutions. The model shows that toeholds and bids interact in a complex manner even without the presence of asymmetric information. By examining a simple environment the paper provides a useful alternative hypothesis for tests of other, presumably more complex, models. One of the main implications of our model is that if no competing bidders are expected, no toeholds should be purchased. The paper also demonstrates that the correct specification of an empirical model can be critical. For example, under some parameter values toehold purchases may exhibit a negative cross-sectional correlation with the pre-announcement run up in the stock price. This occurs even though prices are strictly increasing the size of the toehold. Several implications concerning various aspects of merger legislation are considered. For example, we demonstrate that a rule similar to a “fair price” provision has the desirable property that a second bidder arrives and wins if and only if he places a higher value on the target than the initial bidder.     

出口骗税税收行政法律的界定——兼评一起出口退税主体是否合格案

退税主体是否合格直接关系到纳税人能否享受出口退税政策,《出口骗税税收行政法律的界定——兼评一起出口退税主体是否合格案》一文作者,以实践中一起借“壳”出口退税典型案件切入,通过对比分析征纳双方就退税主体问题的不同理解,提示我们关注案件背后隐藏的利益分割与税收风险。不仅如此,对于由本案引发的在税收行政执法中如何界定“假报出口”及“其他欺骗手段”问题,值得立法者高度重视。     

Stochastic volatility,power laws and long memory

Benoit B Mandelbrot comments on the paper by Blake LeBaron, on page 621 of this issue, by tracing the merits and pitfalls of power-law scaling models from antiquity to the present.     

On the role of the estimation error in prediction of expected shortfall

In the estimation of risk measures such as Value at Risk and Expected shortfall relatively short estimation windows are typically used rendering the estimation error a possibly non-negligible component. In this paper we build upon previous results for the Value at Risk and discuss how the estimation error comes into play for the Expected Shortfall. We identify two important aspects where it may be of importance. On the one hand there is in the evaluation of predictors of the measure. On the other there is in the interpretation and communication of it. We illustrate magnitudes numerically and emphasize the practical importance of the latter aspect in an empirical application with stock market index data.     

Enforceability and the effectiveness of laws and regulations

A major threat to the development of financial markets in emerging markets is “tunneling.” In China, this took on the form of controlling shareholders diverting assets from listed firms or coercing firms to serve as guarantors on questionable loans. A new set of rules enacted in 2005 prohibited asset diversion for “non-operational” purposes. Firms complying with these rules have experienced a reduction in related party transactions, an increase in investment, and better performance. In contrast, another set of contemporary rules, which aimed to standardize the practice of firms providing loan guarantees, has had very little impact. We attribute the contrasting design, implementation, and effectiveness of these two sets of rules to the difference in enforcement costs of the two types of tunneling activities. Relative to loan guarantees, it is much easier for a third party to determine (ex ante) whether a particular form of diversion destroys firm value, and to verify (ex post) that the losses to the firm resulted from the diversion. Our results highlight the importance of enforceability—laws and regulations that can be enforced at lower costs are more likely to succeed, especially in countries with underdeveloped formal institutions.     

On discontinuous frequency functions of two variables

The theory of discontinuous frequency functions of one variable has been well elaborated, especially due to the important researches of Professor Steffensen ¹ See f. i. Steffensen: Matematisk Iagtagelseslære, p. 32 f. while the theory of discontinuous frequency functions of two and more variables has been almost neglected, in spite of the fact that all statisticians agree as to the importance of this topic.     

Study on the effect of sample size on type I error,in the first,second and first-two digits excessmad tests

The first-two digits ExcessMAD test was created in 2016, allowing to evaluate whether a certain data set conforms to Benford’s Law (BL). The purpose of this study is to explore some questions that remained open: develop the exact and approximate mathematical formulation of the first and second digit ExcessMAD test and study the type I error of these tests when applied to different sample sizes conforming to BL and to the uniform distribution, due to its wide use in accounting data. The importance of this study is to make available to accountants, auditors and researchers the first and second digit ExcessMAD tests, which will make it possible to conduct further investigations involving BL, especially for smaller samples. In addition, the relevance of the type I error analysis stems from the reduction of unnecessary additional studies for the investigation of non-conformity, in the case of the erroneous rejection of the null hypothesis stated as conforming to BL. The application of the second digit ExcessMAD test in the uniform distribution reveals that the close proximity between the uniform and BL distributions can lead to misinterpretations. Based on the exact and approximate mathematical formulations of the three ExcessMAD tests and the use of the Monte Carlo simulation technique, samples were generated in accordance with the BL and uniform distributions, with sizes between 100 and 3,500 elements, which allowed the study of type I error and the comparison of the tests applied to those distributions. This paper seeks to cover three gaps in the literature on ExcessMAD tests. In the previous studies, the following approaches were not found: the exact and approximate mathematical formulation of the first and second digit ExcessMAD tests; the analysis of type I error in these tests and the comparison of such results in the BL and Uniform distributions.     

The effect of state antitakeover laws on the firm's bondholders

We examine how state antitakeover laws affect bondholders and the cost of debt, and report four findings. First, bonds issued by firms incorporated in takeover-friendly states have significantly higher at-issue yield spreads than bonds issued by firms in states with restrictive antitakeover laws. Second, firms in takeover friendly states have significantly higher leverage than their counterparts in restrictive law states. Third, bond issues are associated with negative average stock price reactions among firms in takeover-friendly states, but positive stock price reactions among firms in restrictive law states. Fourth, existing bond values increase, on average, upon the introduction of Business Combination antitakeover law. These results indicate that state antitakeover laws tend to decrease bond yields and increase bond values, which is the opposite of their effect on equity values. This, in turn, implies that state laws help mitigate the agency cost of debt by shielding bondholders from expropriation in takeovers. Overall, the empirical evidence suggests that the effect of antitakeover provisions on firm value must take into account the impacts of both bondholders and stockholders.     

Impact of anti-discrimination laws on credit scoring

The political desire for further integration within the European Union will have an increasing effect on the financial services industry, including banking and credit lending. Harmonisation can potentially have great benefit for consumers as the European banks compete for their business across the Union. Harmonisation, however, brings with it a set of decisions for both credit grantors and regulators. There are issues associated with information that can be used in risk assessment to ensure fair decisions in granting credit. In the past the rules have been developed under national legislation. EU directives seek to harmonise the national rules and provide a new guidance on variables that may be held. The major concern relates to the issue of discrimination. The aim of the law is to promote the principle of equal treatment, which can be interpreted in a number of ways. The legal interpretation of discrimination does not necessarily coincide with the economic standpoint. Furthermore, previous empirical research suggests that prohibition of variables may not only affect the ability to distinguish between good and bad risk, but may also be disadvantageous to the groups the legislation is supposed to protect. This paper explores these issues from both theoretical and practical points of view.     

审计质量法律确定的国际比较与可移植性

20世纪70年代以来法与金融学的兴起与发展,为研究审计质量与投资者保护提供了全新视角。以拉波塔等人(La Porta、Lopez-de- Silanes、Shleifer&Vishny,以下简称LLSV)为代表的学者从法律渊源出发,对世界各国的投资者保护水平进行比较,认为法律渊源的不同会导致各国投资者保护水平存在差异,执法水平也会影响到投资者权益的保护效果。     

Aggregate consumption spending,the stock market and asymmetric error correction

In this study, we show how changes in wealth resulting from unanticipated changes in the value of equity holdings begin a process whereby households alter consumption growth in order to close the gap between actual and target spending. Because of changing uncertainty or equity price volatility over the stock market cycle, we found the time path of this adjustment to exhibit near-random walk behaviour during stock market downturns. Conversely, during ‘boom’ periods, e.g. when the value of equities held by households was greater than the threshold, the growth in consumer spending was quick to eliminate the disparity between actual and target spending.     

Information dissemination,market efficiency and the frequency of transactions

Casual observers of the New York Stock Exchange are often dumbfounded by the frenetic behavior of its participants. If asked how such chaos generates accurate prices many academicians would reply that the ability to transact frequently is a virtue since it promotes prompt information dissemination and therefore market efficiency. However, in contrast to the NYSE where, during trading hours, trades may be consumated almost continuously, the Paris Stock Exchange trades each security only a handful of times a day. This continental contrast in market structure led us to reexamine the role of speed in markets. We have discovered that if sufficient uncertainty surrounds the dissemination of information, frequent transacting may be deleterious to market efficiency. In fact, in our paradigm we are able to show that our measure of market efficiency may be maximized when there is a unique, non-zero time interval between consecutive trades. The measure of efficiency used throughout the paper is minus the mean squared error. This measure was chosen to focus upon the information content of prices at times when they are posted (i.e., at times of tâtonnements). For this purpose we ignore costs of illiquidity and costs associated with obsolete information that would occur between tâtonnements. In this restricted sphere, maximazation of our efficiency measure is consistent with maximizing Social Pareto Optimality.     

在探索中寻找非审计服务规律

一、我们所开展的非审计业务 1.对投资创业园区的投资进行发展战略咨询及效益分析.其目的是研究投资园区投资发展的战略意义,分析投资后的经济效益与社会效益,以供当地政府相关主要部门领导投资决策作参考.业务内容主要分二块:一是从战略角度进行分析,以战略使命、成就与问题、发展战略三个具体内容进行分析;二是从效益角度进行分析,以经济效益、社会效益、及效益产生的时间分界点三个具体内容进行分析.操作方法是:搜集当地与周边地区的经济、投资等相关信息与数据,审核创业园区的财务资料,听取有关人员的介绍,获取创业园区投资相关文件、合同等,然后加以分析研究.     

我国会计制度与税收法规的协作研究——基于税会关系模式与二者差异的分析

本文对我国会计制度与税收法规的协作进行了研究 ,通过对会计制度与税收法规的基本关系、税会关系模式、会计制度与税收法规的目标差异以及业务处理差异等方面的分析 ,提出了我国会计制度与税收法规协作的可行思路     

The effect of state laws on capital structure

US manufacturing firms incorporated in states with stronger payout restrictions use less debt, while antitakeover statutes do not significantly reduce long-run leverage. Correcting for the endogenously determined choice of where to incorporate, we find that firms sort themselves according to state laws and capital structure needs. After accounting for self-selection, state antitakeover laws are positively associated with debt as a fraction of market value, possibly due to lower market values for these firms. Payout restrictions appear to reduce leverage for firms that have not reincorporated outside their home states. These constraints explain part of the negative relation between profitability and leverage.     

香港保险法律制度的研究与思考

在香港保险业的发展历程中,良好的法律环境起到了相当重要的重要。本文通过分析香港保险法律制度的沿革及特征分析,比较两地保险业监管的差异性,思考借鉴香港保险法律制度的一些经验做法,为我国保险业的发展营造良好的法律环境。