A Cascaded Inference Model for Evaluation of the Internal Audit Report*

This paper provides a normative framework for how external auditors should evaluate internal audit (IA) work, with a view to assessing the risk of material misstatement. The central issue facing the external auditor when evaluating IA work is the reliability of IA work. Reliability assessments are structured using the cascaded inference framework from behavioral decision theory, in which attributes of source reliability are explicitly modeled and combined using Bayes' rule in order to determine the inferential value of IA work. Results suggest that the inferential value of an IA report is highly sensitive to internal auditor reporting bias, but relatively insensitive to reporting veracity. Veracity refers to internal auditors' propensity to report truthfully, whereas bias refers to the propensity to misreport findings. Results also indicate that this sensitivity to reporting bias is conditional on the level of internal auditor competence, thus suggesting significant interaction effects between the objectivity and competence factors. Collectively, these findings suggest that the impact of source reliability attributes may be more complex than portrayed in the auditing standards and that recognizing these subtleties may lead to greater efficiency and effectiveness.     

Nonparametric Predictive Inference for diagnostic accuracy

Measuring the accuracy of diagnostic tests is crucial in many application areas including medicine and health care. Good methods for determining diagnostic accuracy provide useful guidance on selection of patient treatment, and the ability to compare different diagnostic tests has a direct impact on quality of care. In this paper Nonparametric Predictive Inference (NPI) methods for accuracy of diagnostic tests with continuous test results are presented and discussed. For such tests, Receiver Operating Characteristic (ROC) curves have become popular tools for describing the performance of diagnostic tests. We present the NPI approach to ROC curves, and some important summaries of these curves. As NPI does not aim at inference for an entire population but instead explicitly considers a future observation, this provides an attractive alternative to standard methods. We show how NPI can be used to compare two continuous diagnostic tests.     

Inference Robustness vs. Criterion Robustness: An Example

The two distinct concepts of inference and criterion robustness are illustrated with a simple example based on the one-parameter exponential model. The study of inference and criterion robustness of point and interval estimators of the population mean under a more general exponential power model involves simple but fascinating distribution theory. This example could be usefully exploited in elementary mathematical statistics courses, where the topic of robustness is often neglected.     

We Must Preach what is Practiced

Much of what we teach in statistics is seldom used in practice. Much of what students need we do not teach.     

CONDITIONAL INFERENCE PROCEDURES FOR THE PARETO AND POWER FUNCTION DISTRIBUTIONS BASED ON TYPE-II RIGHT CENSORED SAMPLES

In this paper we consider conditional inference procedures for the Pareto and power function distributions. We develop procedures for obtaining confidence intervals for the location and scale parameters as well as upper and lower n probability tolerance intervals for a proportion g, given a Type-II right censored sample from the corresponding distribution. The intervals are exact, and are obtained by conditioning on the observed values of the ancillary statistics. Since, for each distribution, the procedures assume that a shape parameter x is known, a sensitivity analysis is also carried out to see how the procedures are affected by changes in x.     

Estimation for aggregate models: The aggregate Markov chain

An argument in favour of projecting the score function for models involving incomplete data is presented. Projection is then applied to the aggregate Markov-chain model resulting in weighted least-squares estimators. The limit theory and efficiency of these estimators are studied using martingale limit theory.     

A bayesian analysis of trend determination in economic time series

In this paper we provide a comprehensive Bayesian posterior analysis of trend determination in general autoregressive models. Multiple lag autoregressive models with fitted drifts and time trends as well as models that allow for certain types of structural change in the deterministic components are considered. We utilize a modified information matrix-based prior that accommodates stochastic nonstationarity, takes into account the interactions between long-run and short-run dynamics and controls the degree of stochastic nonstationarity permitted. We derive analytic posterior densities for all of the trend determining parameters via the Laplace approximation to multivariate integrals. We also address the sampling properties of our posteriors under alternative data generating processes by simulation methods. We apply our Bayesian techniques to the Nelson-Plosser macroeconomic data and various stock price and dividend data. Contrary to DeJong and Whiteman (1989a,b,c), we do not find that the data overwhelmingly favor the existence of deterministic trends over stochastic trends. In addition, we find evidence supporting Perron's (1989) view that some of the Nelson and Plosser data are best construed as trend stationary with a change in the trend function occurring at 1929.     

The covariance of the number of renewals in a fixed time and the ensuing excess life

The covariance of the number of renewals in a fixed time N ^t and the ensuing excess life time Y ^t is derived using matrix-analytic methods for the stationary PH-renewal process. Specific results for the Erlang and hyperexponential processes are provided to illustrate the ease of computation. Properties concerning the sign and the behavior of the covariance as t→∞ are provided throughout. Parameter estimation for renewal processes which cannot be fully observed serves as the motivation for our derivations. These statistical applications as well as links to estimation for service time distributions in queues shed light on the type of problems for which the covariance is useful.     

Simple inference in multinomial and ordered logit

This paper provides some simple methods of interpreting the coefficients in multinomial logit and ordered logit models. These methods are summarized in Propositions concerning the magnitudes, signs, and patterns of partial derivatives of the outcome probabilities with respect to the exogenousvariables. The paper also provides an empirical example illustrating the use of these Propositions.     

Confidence intervals for the regression coefficient in a simple regression model with a balanced two-fold nested error structure

ABSTRACT

In applications using a simple regression model with a balanced two-fold nested error structure, interest focuses on inferences concerning the regression coefficient. This article derives exact and approximate confidence intervals on the regression coefficient in the simple regression model with a balanced two-fold nested error structure. Eleven methods are considered for constructing the confidence intervals on the regression coefficient. Computer simulation is performed to compare the proposed confidence intervals. Recommendations are suggested for selecting an appropriate method.