Age-test Markov chains for drug testing and detection

Random urinalysis strategies stratified by time since the last test are characterized with a set of Markov chain models. The probability of a person being tested depends on the amount of time since the person's last test. The Nuclear Regulatory Commission (NRC) has proposed a two strata drug testing strategy based on time since last test. The proposal included a high testing rate for people not yet tested in a given time period and a low testing rate for people testing negative in a given time period. Southern California Edison has implemented a variation of the NRC proposal. These strategies can be modeled within a Markov chain framework. Time to detection is calculated as a function of testing probabilities and drug usage levels. Drug user gaming strategies are discussed with illustrations. These models are implemented as part of a U.S. Navy drug policy analysis system.     

Monotone dependence in graphical models for multivariate Markov chains

We show that a deeper insight into the relations among marginal processes of a multivariate Markov chain can be gained by testing hypotheses of Granger noncausality, contemporaneous independence and monotone dependence. Granger noncausality and contemporaneous independence conditions are read off a mixed graph, and the dependence of an univariate component of the chain on its parents—according to the graph terminology—is described in terms of stochastic dominance criteria. The examined hypotheses are proven to be equivalent to equality and inequality constraints on some parameters of a multivariate logistic model for the transition probabilities. The introduced hypotheses are tested on real categorical time series.     

Time reversibility of stationary regular finite-state Markov chains

We propose an alternate parameterization of stationary regular finite-state Markov chains, and a decomposition of the parameter into time reversible and time irreversible parts. We demonstrate some useful properties of the decomposition, and propose an index for a certain type of time irreversibility, applicable to chains whose states are naturally ordered. Two empirical examples illustrate the use of the proposed parameter, decomposition and index. One, on gasoline price mark-ups, involves observed states. The other, on U.S. investment growth, features latent states.     

Some remarks on the construction of independent identically distributed random variables,Markov chains and martingales

In this note, we make some remarks on the construction of sequences of independent identically distributed random variables and of Markov chains concretely on a probability space (Ω,A,P). We also show that there are non non-trivial martingales of exponential type.     

On contracting for uncertain R&D

Using a two‐stage model, this paper studies auctions of research and development (R&D) contracts when the outcome of research is uncertain. The agent is contracted by the principal to invent a new product or a new process. The principal selects the most capable agent through an auction and writes an incentive contract with the winning agent to share risks. The main finding of the paper is that the generally superior incentive contracts might not be desirable under plausible conditions in R&D contracting. In particular, we find that the principal prefers a cost‐plus contract in cases of large R&D projects or rising innovation benefits, but would prefer a fixed‐price contract when the number of bidders increases. An alternate elasticity interpretation of results holds promise for empirical analysis. Public policy implications are finally discussed. Copyright © 1999 John Wiley & Sons, Ltd.     

Expected utility with uncertain probabilities theory

This paper introduces a model of decision making under ambiguity by extending the Bayesian approach to uncertain probabilities. In this model, preferences for ambiguity pertain directly to probabilities such that attitude toward ambiguity is defined as attitude toward mean-preserving spreads in probabilities—analogous to the Rothschild–Stiglitz risk attitude toward mean-preserving spreads in outcomes. The model refines the separations between tastes and beliefs, and between risk and ambiguity. These separations are crucial for the measurement of the degree of ambiguity and for the elicitation and characterization of attitudes toward ambiguity, thereby providing an empirically and experimentally applicable framework.     

Coefficients of correlation for simultaneous equation systems

This paper presents measures of correlation for use with either a single equation within a simultaneous system or for the whole system, which specifically account for the identifying restrictions. The measures lie between zero and one and have the same interpretation as the familiar R² used with classical least squares. When used in conjunction with several common coefficient estimators they have straightforward limiting distributions so that asymptotic tests of significance are possible.     

MRP with high uncertain yield losses

Certain manufacturing systems, notably those in high technology precision casting and integrated circuit production suffer from process yield losses which are both significant in quantity terms and are also highly unpredictable. This poses special problems for the provisioning of materials to support a manufacturing program and for the detailed scheduling necessary to update the priorities of work in process batches as losses occur. This paper establishes a framework of analysis to handle this problem in MRP logic. It describes the mechanisms available and discusses their relevance to the market environments in which the company is operating.The key conclusion of this paper is that different solutions are required for different market circumstances. The four key strategies developed are:

1. A: For continuous schedules, make-for-stock: Use mean yield rate and fixed buffer stocks.

2. B: For continuous schedules, make-to-order: Use mean yield rate, fixed buffers and a yield to finish monitoring system.

3. C1: For single batch production make-to-order: As for B but using a desired service level yield rate.

4. C2: For multiple batch production, make-to-order: As B but using a variable yield rate by batch.

The implementation of each of these is described in relation to the business objectives of cost effectiveness and customer satisfaction.     

Testing the independence of forecast errors in the forward foreign exchange market using Markov chains: A cross-country comparison

In this paper, we apply the theory of finite state Markov chains to test the cross-country and temporal independence of forecast errors in the forward foreign exchange market. Specifically, we consider the month-end thirty day foreign exchange data for Canada, France, Italy, Japan, United Kingdom and West Germany for the period 1974–1981. Using pairwise comparisons for the various countries, we find that except for Canada, the hypothesis that the probability distribution of the forecast error of one country is independent of the forecast error of another is rejected. Further tests indicate that the temporal independence for most countries is also rejected. Based upon these results, we conclude that for these six countries, there is current information available which is ‘useful’ in predicting the future forward exchange forecast errors.     

Sequential estimate for linear regression models with uncertain number of effective variables

As a result of novel data collection technologies, it is now common to encounter data in which the number of explanatory variables collected is large, while the number of variables that actually contribute to the model remains small. Thus, a method that can identify those variables with impact on the model without inferring other noneffective ones will make analysis much more efficient. Many methods are proposed to resolve the model selection problems under such circumstances, however, it is still unknown how large a sample size is sufficient to identify those “effective” variables. In this paper, we apply sequential sampling method so that the effective variables can be identified efficiently, and the sampling is stopped as soon as the “effective” variables are identified and their corresponding regression coefficients are estimated with satisfactory accuracy, which is new to sequential estimation. Both fixed and adaptive designs are considered. The asymptotic properties of estimates of the number of effective variables and their coefficients are established, and the proposed sequential estimation procedure is shown to be asymptotically optimal. Simulation studies are conducted to illustrate the performance of the proposed estimation method, and a diabetes data set is used as an example.     

Comparative statics for markov chains

For a finite ergodic Markov chain, the effects of a change in the transition matrix on the equilibrium probability vector and on the mean first passage matrix are described.     

An Approximate Test for Homogeneity of Correlated Correlation Coefficients

This paper develops and evaluates an approximate procedure for testing homogeneity of an arbitrary subset of correlation coefficients among variables measured on the same set of individuals. The sample may have some missing data. The simple test statistic is a multiple of the variance of Fisher r-to-z transformed correlation coefficients relevant to the null hypothesis being tested and is referred to a chi-square distribution. The use of this test is illustrated through several examples. Given the approximate nature of the test statistics, the procedure was evaluated using a simulation study. The accuracy in terms of the nominal and the actual significance levels of this test for several null hypotheses of interest were evaluated. This revised version was published online in June 2006 with corrections to the Cover Date.     

Nonparametric model validations for hidden Markov models with applications in financial econometrics

We address the nonparametric model validation problem for hidden Markov models with partially observable variables and hidden states. We achieve this goal by constructing a nonparametric simultaneous confidence envelope for transition density function of the observable variables and checking whether the parametric density estimate is contained within such an envelope. Our specification test procedure is motivated by a functional connection between the transition density of the observable variables and the Markov transition kernel of the hidden states. Our approach is applicable for continuous-time diffusion models, stochastic volatility models, nonlinear time series models, and models with market microstructure noise.     

On Testing for the Nullity of Some Skewness Coefficients

Three tests for the skewness of an unknown distribution are derived for iid data. They are based on suitable normalization of estimators of some usual skewness coefficients. Their asymptotic null distributions are derived. The tests are next shown to be consistent and their power under some sequences of local alternatives is investigated. Their finite sample properties are also studied through a simulation experiment, and compared to those of the √ b ₂-test.     

Estimation of Non-Stationary Social Accounting Matrix Coefficients with Supply-Side Information

Given aggregated data, a framework for estimating the entries of a social accounting matrix (SAM), or any large matrix of expenditures, trade or income flows, is developed. Under this framework it is possible to evaluate the contribution of structural and supply-side information, as well as policy variables, within the generalized context of a non-stationary SAM. Inference and diagnostic properties are developed as well. This new estimator can be viewed as a generalized maximum likelihood estimator. Stationary and non-stationary estimates of the US SAM for the years 1987-1994 together with the effects of supply-side variables are analyzed.     

Goodness-of-fit tests for parametric nonhomogeneous Markov processes

Tests for parametric nonhomogeneous and homogeneous Markov processes are given. Asymptotic distribution of test statistics is investigated. Tests for various well-known models are discussed as examples.