On the asymptotic behaviour of the Stringer bound1

The Stringer bound is a widely used nonparametric 100(1 -α)% upper confidence bound for the fraction of errors in an accounting population. This bound has been found in practice to be rather conservative, but no rigorous mathematical proof of the correctness of the Stringer bound as an upper confidence bound is known and also no counterexamples are available. In a pioneering paper Bickel (1992) has given some fixed sample support to the bound's conservatism together with an asymptotic expansion in probability of the Stringer bound, which has led to his claim of the asymptotic conservatism of the Stringer bound. In the present paper we obtain expansions of arbitrary order of the coefficients in the Stringer bound. As a consequence we obtain Bickel's asymptotic expansion with probability 1 and we show that the asymptotic conservatism holds for confidence levels 1 -α, with α∈ (0,1/2]. It means that in general also in a finite sampling situation the Stringer bound does not necessarily have the right confidence level. Based on our expansions we propose a modified Stringer bound which has asymptotically precisely the right nominal confidence level. Finally, we discuss other consequences of the expansions of the Stringer bound such as a central limit theorem, a law of the iterated logarithm and the functional versions of them.     

基于经济责任审计的我国党政领导干部责任履行情况研究

选择可以量化的反映审计投入力度的审计查出金额、被审计人员数量、省级审计人员数量和审计报告量实证分析我国党政领导干部经济、社会责任目标的实现程度,研究发现:经常性考核党政领导干部的指标反映程度强于非经常性指标;真实性、合法性责任反映程度强于效益性责任的履行;各类支出项目的减少反映程度明显高于收入的增加;审计出金额、省级审计人员量和审计报告量的作用明显强于被审计人员数量的作用。     

Robust testing procedures of process locations

In many manufacturing and service industries, the quality department of the organization works continuously to ensure that the mean or location of the process is close to the target value. In order to understand the process, it is necessary to provide numerical statements of the processes that are being investigated. That is why the researcher needs to check the validity of the hypotheses that are concerned with some physical phenomena. It is usually assumed that the collected data behave well. However, sometimes the data may contain outliers. The presence of one or more outliers might seriously distort the statistical inference. Since the sample mean is very sensitive to outliers, this research will use the smooth adaptive (SA) estimator to estimate the population mean. The SA estimator will be used to construct testing procedures, called smooth adaptive test (SA test), for testing various null hypotheses. A Monte Carlo study is used to simulate the values of the probability of a Type I error and the power of the SA test. This is accomplished by constructing confidence intervals of the process mean by using the SA estimator and bootstrap methods. The SA test will be compared with other tests such as the normal test, t test and a nonparametric statistical method, namely, the Wilcoxon signed-rank test. Also, the cases with and without outliers will be considered. For the right-skewed distributions, the SA test is the best choice. When the population is a right-skewed distribution with one outlier, the SA test controls the probability of a Type I error better than other tests and is recommended.     

风险测量VAR及其原理

用公式可表示为:Prob(△P>VAR}=1-a(其中Prob表示:资产价值损失小于可能损失上限的概率;△P表示:某一金融资产在一定持有期△t的价值失额;VAR表示:给定置信水平a下的在险价值,即可能的损失上限;a表示:给定的置信水平。)     

Enforcement Actions and Auditor Changes

In this paper, we examine whether the uncovering of erroneous financial statements by German enforcement agencies is related to subsequent auditor changes. We argue that enforcement actions are likely to reveal information about the client or its auditor, which might affect auditor choice by initiating an update of mutual expectations. Our empirical findings indicate that firms with erroneous financial statements indeed have an increased probability of subsequent auditor changes. Firms also tend to change from a non-Big4 auditor to a Big4 auditor in this situation, suggesting that clients increasingly seek the reputation and services of Big4 auditors. Big4 auditors in turn do not appear to refrain from taking over error-firms as new clients in the German setting, which is characterized by limited auditor liability. Additionally, auditor changes are more likely to occur before the public announcement of an error, indicating that firms take action as soon as the uncovering of an accounting error becomes sufficiently certain.     

Confidence bounds for the mean in nonparametric multisample problems

In auditing practice it often occurs that a statement regarding the accounting error in a population consisting of several subpopulations has to be made. As the relative proportion of errors can differ dramatically across these subpopulations, it is desirable to take independent fixed-size dollar-unit samples from each of them, as this often leads to lower variability compared with dollar-unit sampling from the whole population. It also occurs that the results of the separate investigations of, e.g. different branches of one company need to be combined to make a statement on the bookkeeping quality in general.
The problem of estimating the total accounting error is thus related to the problem of estimating linear combinations of the mean values corresponding to several families of identically distributed independent random variables.
In this article, we propose several confidence upper bounds for such linear combinations based on Hoeffding-type inequalities and show how they can be applied to the actual auditing problems. Simulation results comparing these modifications to the Hoeffding-based bounds for the one-sample case are also provided. It must be emphasized that the technique that we propose in this paper is fully justified from a mathematical point of view.
Although the simulations show the proposed bounds to be highly conservative, they still present great interest, since we are not aware of any other method for estimation of the total accounting error in the multisample setting. Moreover, it is shown that significant improvements are hardly possible given the present conditions.     

Audit Quality and Banks' Assessment of Disclosed Accounting Information

The objective of this paper is to investigate whether banks view the information on the off-balance sheet liabilities (specifically, operating leases) disclosed in the notes to the financial statements as more reliable when it is audited by brand name auditors (i.e. a Big 4 audit firm). To the extent that banks assess a higher likelihood that the financial statements could have material misstatements if it is not audited by a Big 4 audit firm, they should charge a higher interest rate on private loans. Our findings suggest that the impact of operating leases on the interest rate is higher if the firm is audited by non-Big 4 audit firms.     

Finite-sample exact tests for linear regressions with bounded dependent variables

We introduce tests for finite-sample linear regressions with heteroskedastic errors. The tests are exact, i.e., they have guaranteed type I error probabilities when bounds are known on the range of the dependent variable, without any assumptions about the noise structure. We provide upper bounds on probability of type II errors, and apply the tests to empirical data.     

基于管理舞弊控制的审计质量研究

财务报表是由管理层负责编制的,即使由注册会计师依据一般公认审计准则进行了审计,财务报表所揭露的信息终究是财务性、历史性的,公开时点远在企业经济行为之后。尽管如此,注册会计师审计仍然被视为公司管理舞弊控制的重要防线。在管理舞弊控制方面,审计师有自己的职业优势,也存在着职业劣势。从理论上讲,高质量审计应该能够在管理舞弊控制方面有着良好表现,控制管理舞弊应该能够提高审计质量,能否以实证研究的方式为理论提供数据支持呢?本文的实证结论与相关学者的研究结论都表明,如果不改善中国内地独立审计制度安排,理论上的高质量审计在中国内地是难以发挥其高质量审计功能的。     

Accurate test limits under nonnormal measurement error

When screening a production process for nonconforming items the objective is to improve the average outgoing quality level. Due to measurement errors specification limits cannot be checked directly and hence test limits are required, which meet some given requirement, here given by a prescribed bound on the consumer loss. Classical test limits are based on normality, both for the product characteristic and for the measurement error. In practice, often nonnormality occurs for the product characteristic as well as for the measurement error. Recently, nonnormality of the product characteristic has been investigated. In this paper attention is focussed on the measurement error. Firstly, it is shown that nonnormality can lead to serious failure of the test limit. New test limits are therefore derived, which have the desired robustness property: a small loss under normality and a large gain in case of nonnormality when compared to the normal test limit. Monte Carlo results illustrate that the asymptotic theory is in agreement with moderate sample behaviour.     

Maxima voor de eenzijdige overschrijdingskans en voor de grootte van de gemiddelde overschrijding bij discontinue en continue, eentoppige verdelingen

The well-known inequality of Bienaymé-Tschébyschef (for short B-T), generalized by Camp and Meidell (for short C-M) for continuous, unimodal distributions gives specific limits for total probabilities outside the ± to limits.
In many cases however, especially in the field of industrial applications we are interested only in the probability of one tail of the distribution, which of course must be smaller than the limits given by the B-T and C-M formula.
For these cases the maximum probability of surpassing the to limit on one side equals under B-T conditions and under C-M conditions instead of the two-sided values of 1/t² and 47/9 · 1/t² respectively (cf e.g. Uspensky: "Introduction to mathematical probability", 1937, p. 198) These results set upper limits for the value of

Alternatively we may also set an upper limit for the integral

which measures in terms of σ the average amount by which the limit + tσ is exceeded. This problem is also discussed and under C-M conditions an upper limit

is derived.
Some practical applications of these results are considered.     

Efficient semiparametric estimation for endogenously stratified regression via smoothed likelihood

This paper presents efficient semiparametric estimators for endogenously stratified regression with two strata, in the case where the error distribution is unknown and the regressors are independent of the error term. The method is based on the use of a kernel-smoothed likelihood function which provides an explicit solution for the maximization problem for the unknown density function without losing information in the asymptotic limit. We consider both standard stratified sampling and variable probability sampling, and allow for the population shares of the strata to be either unknown or known a priori.     

低质量审计是审计师个人特质导致的特例吗？——基于“污点”签字注册会计师的研究

在签字注册会计师层面研究低质量审计的发生原因时发现:审计失败被发现前,与同所未受罚签字注册会计师相比,受到证监会处罚的签字注册会计师的审计质量持续较低;部分受罚签字注册会计师因事务所合并而被动进入质量控制较好的环境中,其审计质量较合并前有显著改善。这说明在相同质量控制体系下,低质量审计是由审计师个人特质导致的特例;而良好的质量控制有助于抑制"污点"签字注册会计师个人特质对审计质量的不利影响。     

我国政府开展绩效审计的困境与出路——基于制度安排的分析

制约我国政府开展绩效审计的因素较多。从产生绩效审计交易成本的原因看,开展绩效审计面临的困境主要为定位不清、职责认定不清、对被审计单位了解不清三个方面。博弈模型能够推导出节约交易成本的绩效审计模式,该模式要求被审计单位出具绩效水平评价报告,而由审计人员对绩效水平评价报告的真实性进行复核,然后提出审计意见,这就为突破现有绩效审计困境提供了新的思路。     

Swedish auditors' view of auditing: Doing things right versus doing the right things

Abstract

This paper aims to describe and analyse the thought patterns of Swedish auditors with regard to the way in which they audit information provided by listed companies, and possible changes in their duties. Eighty-two auditors were interviewed using the repertory grid technique and open-ended interview questions. To check the stability in the thought patterns of the respondents, six retests were made and, to validate the findings, an expert panel and two reference groups consisting of auditors and other representatives of the accounting and auditing professions were consulted. Distinct patterns emerged in the mean grid of the thought patterns of all the respondents. One dimension was related to the time perspective, past versus future, and another to auditing practice. Auditors devote a relatively long time and considerable effort to objects that can be satisfactorily verified, but not to objects that they perceive as being of primary importance to investors and other stakeholders. This inconsistency in the thought patterns of the auditors is similar to the gap between auditing in practice and stakeholders' expectations of auditing, which is a phenomenon frequently found in previous research. Moreover, the auditors were very reluctant to make statements about any information except that elicited according to current practice. In addition to this traditional view, the auditors appear to be more concerned about their own situation than that of the parties they are meant to be protecting. Doing things right seems to be more important than doing the right things. That the auditors spend much time on objects that they themselves do not consider to be of primary importance for the investors and other stakeholders, and their unwillingness to change current practice is of great concern in Sweden, where there is a strong belief in self-regulation of the auditing profession.     

论诉讼风险起点审计

风险导向审计能够揭示出重大错报从而防范会计报表风险,却不足以有效化解审计风险。文章采用演绎方法,分析基于重大错报的审计模式的缺陷,提出建立以诉讼风险为起点的新审计模式,并以此为基础将被审计单位的经营风险予以尽可能地揭示,从而有效化解会计师事务所的审计风险。     

Small Area Quantile Estimation

Sample surveys are widely used to obtain information about totals, means, medians and other parameters of finite populations. In many applications, similar information is desired for subpopulations such as individuals in specific geographic areas and socio‐demographic groups. When the surveys are conducted at national or similarly high levels, a probability sampling can result in just a few sampling units from many unplanned subpopulations at the design stage. Cost considerations may also lead to low sample sizes from individual small areas. Estimating the parameters of these subpopulations with satisfactory precision and evaluating their accuracy are serious challenges for statisticians. To overcome the difficulties, statisticians resort to pooling information across the small areas via suitable model assumptions, administrative archives and census data. In this paper, we develop an array of small area quantile estimators. The novelty is the introduction of a semiparametric density ratio model for the error distribution in the unit‐level nested error regression model. In contrast, the existing methods are usually most effective when the response values are jointly normal. We also propose a resampling procedure for estimating the mean square errors of these estimators. Simulation results indicate that the new methods have superior performance when the population distributions are skewed and remain competitive otherwise.     

Ein allgemeines Konstruktionsverfahren für Konfidenzbereiche

Summary A theorem ofTakács concerning interchangeable random variables is used to derive a simple method for the construction of confidence regions. Applying this method to a location parametera we get a.s. convergence of the confidence interval toa if the sample sizen increases while its probability is (n–1)/(n+1). Under certain conditions the interval contains always the maximum-likelihood estimate and another estimate which results from a least squares postulate. Lower bounds are given for the probability that our intervals become shorter than the intervals we would get relying on the central limit theorem. In order to avoid an assumption of finite support needed first to derive the a.s. convergence, we modify our method omitting extreme values.The modified intervals converge forn with probability 1 to the true parameter value under weaker conditions. A lower bound for the probability and-using a result due toRényi-theasymptotic probability of the modified interval is given. For the two kinds of intervals a formula concerning the velocity of their convergence to the length 0 is derived.Finally, the results are extended to a shift parameter in the two-sample case. Here we derive for equal sample sizes the exact probability of the modified interval and give upper and lower bounds fir its asymptotic probability. The method is practicable also if one sample size is an integer multiple of the other.     

顺从还是懈怠？中注协约谈与执业质量检查的叠加监管压力研究

基于压力理论和制度理论,以2014—2018年沪深A股非金融类上市公司为研究对象,探究中注协约谈与执业质量检查的叠加监管压力对审计质量的影响。实证结果表明,在中注协约谈与执业质量检查的叠加监管压力下,审计师显著提升了审计质量。进一步研究发现,行业叠加监管压力对审计质量的提升作用只在当面约谈、签字注册会计师同性别、签字注册会计师平均执业年限较长、签字注册会计师年平均客户数量较少时才明显;行业叠加监管压力与法律监管压力之间存在着替代作用;在面对行业叠加监管压力时,审计师也收取了一定的溢价。研究结论能够明晰审计师面临行业叠加监管压力时的行为表现,也对证券审计市场行业自律性监管具有借鉴意义。     

On estimation of some abbreviated social welfare measures

Point and interval estimations of two abbreviated social welfare functions are studied based on Schutz and Gini coefficients. The limit distributions of the estimators are derived in terms of sample L-moments and mean absolute deviation. A simulation study is performed to assess the bias in the estimators and the coverage probability of the confidence intervals. Unlike the previous studies our results do not require the grouping of population into a fixed number of quantiles. The proposed methods use distribution-free unbiased estimators and exact sample L-moment variances. An application is given that illustrates the benefits of the proposed methods.