A General Model for Repeated Audit Controls Using Monotone Subsampling

Abstract

In categorical repeated audit controls, fallible auditors classify sample elements in order to estimate the population fraction of elements in certain categories. To take possible misclassifications into account, subsequent checks are performed with a decreasing number of observations. In this paper a model is presented for a general repeated audit control system, where k subsequent auditors classify elements into r categories. Two different subsampling procedures will be discussed, named “stratified” and “random” sampling. Although these two sampling methods lead to different probability distributions, it is shown that the likelihood inferences are identical. The MLE are derived and the situations with undefined MLE are examined in detail; it is shown that an unbiased MLE can be obtained by stratified sampling. Three different methods for constructing confidence upper limits are discussed; the Bayesian upper limit seems to be the most satisfactory. Our theoretical results are applied to two cases with r = 2 and k = 2 or 3, respectively.     

False discovery rates for large-scale model checking under certain dependence

In many scientific fields, it is interesting and important to determine whether an observed data stream comes from a prespecified model or not, particularly when the number of data streams is of large scale, where multiple hypotheses testing is necessary. In this article, we consider large-scale model checking under certain dependence among different data streams observed at the same time. We propose a false discovery rate (FDR) control procedure to check those unusual data streams. Specifically, we derive an approximation of false discovery and construct a point estimate of FDR. Theoretical results show that, under some mild assumptions, our proposed estimate of FDR is simultaneously conservatively consistent with the true FDR, and hence it is an asymptotically strong control procedure. Simulation comparisons with some competing procedures show that our proposed FDR procedure behaves better in general settings. Application of our proposed FDR procedure is illustrated by the StarPlus fMRI data.     

腐败现象的经济伦理学分析初探

腐败在任何制度条件下都有可能产生,但其严重程度及普遍程度却不尽相同,其中的差异反映了特定制度对制度内个人行为的约束有效性之间的差异.本文主要从利己与利他、公共权力的客观存在以及制度对政府公职人员的监督与激励的有效性等角度,剖析了腐败产生的深层原因,并从制度建设角度,提出了抑制腐败的对策和建议.     

Moran's I statistic-based nonparametric test with spatio-temporal observations

Moran's I statistic [Moran, (1950), ‘Notes on Continuous Stochastic Phenomena’, Biometrika, 37, 17–23] has been widely used to evaluate spatial autocorrelation. This paper is concerned with Moran's I-induced testing procedure in residual analysis. We begin with exploring the Moran's I statistic in both its original and extended forms analytically and numerically. We demonstrate that the magnitude of the statistic in general depends not only on the underlying correlation but also on certain heterogeneity in the individual observations. One should exercise caution when interpreting the outcome on correlation by the Moran's I-induced procedure. On the other hand, the effect on the Moran's I due to heterogeneity in the observations enables a regression model checking procedure with the residuals. This novel application of Moran's I is justified by simulation and illustrated by an analysis of wildfire records from Alberta, Canada.     

Nonlinear regression models with general distortion measurement errors

This paper considers nonlinear regression models when neither the response variable nor the covariates can be directly observed, but are measured with both multiplicative and additive distortion measurement errors. We propose conditional variance and conditional mean calibration estimation methods for the unobserved variables, then a nonlinear least squares estimator is proposed. For the hypothesis testing of parameter, a restricted estimator under the null hypothesis and a test statistic are proposed. The asymptotic properties for the estimator and test statistic are established. Lastly, a residual-based empirical process test statistic marked by proper functions of the regressors is proposed for the model checking problem. We further suggest a bootstrap procedure to calculate critical values. Simulation studies demonstrate the performance of the proposed procedure and a real example is analysed to illustrate its practical usage.     

圆弧齿轮投影板CAD系统及反滚检验

介绍了圆弧齿轮投影板ＣＡＤ系统的模块化结构,并举例说明了此系统的设计情况,以及在反滚检验中的应用。     

Inference on semiparametric transformation model with general interval-censored failure time data

Failure time data occur in many areas and in various censoring forms and many models have been proposed for their regression analysis such as the proportional hazards model and the proportional odds model. Another choice that has been discussed in the literature is a general class of semiparmetric transformation models, which include the two models above and many others as special cases. In this paper, we consider this class of models when one faces a general type of censored data, case K informatively interval-censored data, for which there does not seem to exist an established inference procedure. For the problem, we present a two-step estimation procedure that is quite flexible and can be easily implemented, and the consistency and asymptotic normality of the proposed estimators of regression parameters are established. In addition, an extensive simulation study is conducted and suggests that the proposed procedure works well for practical situations. An application is also provided.     

Checking Normality and Homoscedasticity in the General Linear Model Using Diagnostic Plots

Inference for the general linear model makes several assumptions, including independence of errors, normality, and homogeneity of variance. Departure from the latter two of these assumptions may indicate the need for data transformation or removal of outlying observations. Informal procedures such as diagnostic plots of residuals are frequently used to assess the validity of these assumptions or to identify possible outliers. A simulation-based approach is proposed, which facilitates the interpretation of various diagnostic plots by adding simultaneous tolerance bounds. Several tests exist for normality or homoscedasticity in simple random samples. These tests are often applied to residuals from a linear model fit. The resulting procedures are approximate in that correlation among residuals is ignored. The simulation-based approach accounts for the correlation structure of residuals in the linear model and allows simultaneously checking for possible outliers, non normality, and heteroscedasticity, and it does not rely on formal testing.

[Supplementary materials are available for this article. Go to the publisher's online edition of Communications in Statistics—Simulation and Computation® for the following three supplemental resource: a word file containing figures illustrating the mode of operation for the bisectional algorithm, QQ-plots, and a residual plot for the mussels data.]     

Multivariate Stochastic Volatility: A Review

The literature on multivariate stochastic volatility (MSV) models has developed significantly over the last few years. This paper reviews the substantial literature on specification, estimation, and evaluation of MSV models. A wide range of MSV models is presented according to various categories, namely, (i) asymmetric models, (ii) factor models, (iii) time-varying correlation models, and (iv) alternative MSV specifications, including models based on the matrix exponential transformation, the Cholesky decomposition, and the Wishart autoregressive process. Alternative methods of estimation, including quasi-maximum likelihood, simulated maximum likelihood, and Markov chain Monte Carlo methods, are discussed and compared. Various methods of diagnostic checking and model comparison are also reviewed.     

Lack of fit tests based on sums of ordered residuals for linear models

Christensen & Lin ( 2015 ) suggested two lack of fit tests to assess the adequacy of a linear model based on partial sums of residuals. In particular, their tests evaluated the adequacy of the mean function. Their tests relied on asymptotic results without requiring small sample normality. We propose four new tests, find their asymptotic distributions, and propose an alternative simulation method for defining tests that is remarkably robust to the distribution of the errors. To assess their strengths and weaknesses, the Christensen & Lin ( 2015 ) tests and the new tests were compared in different scenarios by simulation. In particular, the new tests include two based on partial sums of absolute residuals. Previous partial sums of residuals tests have used signed residuals whose values when summed can cancel each other out. The use of absolute residuals requires small sample normality, but allows detection of lack of fit that was previously not possible with partial sums of residuals.