Examples of the use of an equivalence theorem in constructing optimum experimental designs for random-effects nonlinear regression models

The problem considered is that of finding an optimum measurement schedule to estimate population parameters in a nonlinear model when the patient effects are random. The paper presents examples of the use of sensitivity functions, derived from the General Equivalence Theorem for D-optimality, in the construction of optimum population designs for such schedules. With independent observations, the theorem applies to the potential inclusion of a single observation. However, in population designs the observations are correlated and the theorem applies to the inclusion of an additional measurement schedule. In one example, three groups of patients of differing size are subject to distinct schedules. Numerical, as opposed to analytical, calculation of the sensitivity function is advocated. The required covariances of the observations are found by simulation.     

Efficient designs based on orthogonal arrays of type I and type II for experiments using units ordered over time or space

For a wide variety of applications, experiments are based on units ordered over time or space. Models for these experiments generally may include one or more of: correlations, systematic trends, carryover effects and interference effects. Since the standard optimal block designs may not be efficient in these situations, orthogonal arrays of type I and type II, which were introduced in 1961 by C.R. Rao [Combinatorial arrangements analogous to orthogonal arrays, Sankhya A 23 (1961) 283–286], have been recently used to construct optimal and efficient designs for many of these experiments. Results in this area are unified and the salient features are outlined.     

The repeated public goods game: A solution using Tit-for-Tat and the Lindahl point

This paper demonstrates how a repeated public goods problem may be solved by using Tit-for-Tat (TFT) on the Lindahl point. The general solution is developed; geometric and numerical examples are offered.I wish to thank an anonymous reviewer for very helpful comments on earlier drafts of this paper.     

多功能开放型企业供需网成员企业合作关系的经济模型

多功能开放型企业供需网(SDN)合作伙伴关系的稳定性，将直接决定SDN创新管理理念的生命力和未来发展前景，传统企业间的一次性静态博弈和供应链(SC)盟员间的有限次重复博弈，都是低效的合作关系，因而其稳定性较差，无限次重复博弈以及由此而引发的触发策略，能够实现帕累托最优的纳什均衡，是SDN合作伙伴关系稳定发展的深层经济学原因，通过建立SDN成员企业合作关系的经济模型，论证了SDN的稳定性。     

An affine‐invariant multivariate sign test for cluster correlated data

The author presents a multivariate location model for cluster correlated observations. He proposes an affine‐invariant multivariate sign statistic for testing the value of the location parameter. His statistic is an adaptation of that proposed by Randles (2000). The author shows, under very mild conditions, that his test statistic is asymptotically distributed as a chi‐squared random variable under the null hypothesis. In particular, the test can be used for skewed populations. In the context of a general multivariate normal model, the author obtains values of his test's Pitman asymptotic efficiency relative to another test based on the overall average. He shows that there is an improvement in the relative performance of the new test as soon as intra‐cluster correlation is present Even in the univariate case, the new test can be very competitive for Gaussian data. Furthermore, the statistic is easy to compute, even for large dimensional data. The author shows through simulations that his test performs well compared to the average‐based test. He illustrates its use with real data.     

Conditional Likelihood Estimators for Hidden Markov Models and Stochastic Volatility Models

ABSTRACT.  This paper develops a new contrast process for parametric inference of general hidden Markov models, when the hidden chain has a non-compact state space. This contrast is based on the conditional likelihood approach, often used for ARCH-type models. We prove the strong consistency of the conditional likelihood estimators under appropriate conditions. The method is applied to the Kalman filter (for which this contrast and the exact likelihood lead to asymptotically equivalent estimators) and to the discretely observed stochastic volatility models.     

Far-sighted equilibria in 2 × 2, non-cooperative,repeated games

Consider a two-person simultaneous-move game in strategic form. Suppose this game is played over and over at discrete points in time. Suppose, furthermore, that communication is not possible, but nevertheless we observe some regularity in the sequence of outcomes. The aim of this paper is to provide an explanation for the question why such regularity might persist for many (i.e., infinite) periods.Each player, when contemplating a deviation, considers a sequential-move game, roughly speaking of the following form: if I change my strategy this period, then in the next my opponent will take his strategy b and afterwards I can switch to my strategy a, but then I am worse off since at that outcome my opponent has no incentive to change anymore, whatever I do. Theoretically, however, there is no end to such reaction chains. In case that deviating by some player gives him less utility in the long run than before deviation, we say that the original regular sequence of outcomes is far-sighted stable for that player. It is a far-sighted equilibrium if it is far-sighted stable for both players.     

An analytic method for randomized trials with informative censoring: Part 1

Consider a randomized trial in which time to the occurrence of a particular disease, say pneumocystis pneumonia in an AIDS trial or breast cancer in a mammographic screening trial, is the failure time of primary interest. Suppose that time to disease is subject to informative censoring by the minimum of time to death, loss to and end of follow-up. In such a trial, the censoring time is observed for all study subjects, including failures. In the presence of informative censoring, it is not possible to consistently estimate the effect of treatment on time to disease without imposing additional non-identifiable assumptions. The goals of this paper are to specify two non-identifiable assumptions that allow one to test for and estimate an effect of treatment on time to disease in the presence of informative censoring. In a companion paper (Robins, 1995), we provide consistent and reasonably efficient semiparametric estimators for the treatment effect under these assumptions. In this paper we largely restrict attention to testing. We propose tests that, like standard weighted-log-rank tests, are asymptotically distribution-free -level tests under the null hypothesis of no causal effect of treatment on time to disease whenever the censoring and failure distributions are conditionally independent given treatment arm. However, our tests remain asymptotically distribution-free -level tests in the presence of informative censoring provided either of our assumptions are true. In contrast, a weighted log-rank test will be an -level test in the presence of informative censoring only if (1) one of our two non-identifiable assumptions hold, and (2) the distribution of time to censoring is the same in the two treatment arms. We also extend our methods to studies of the effect of a treatment on the evolution over time of the mean of a repeated measures outcome, such as CD-4 count.     

A Multivariate Model for Repeated Failure Time Measurements

A parametric multivariate failure time distribution is derived from a frailty-type model with a particular frailty distribution. It covers as special cases certain distributions which have been used for multivariate survival data in recent years. Some properties of the distribution are derived: its marginal and conditional distributions lie within the parametric family, and association between the component variates can be positive or, to a limited extent, negative. The simple closed form of the survivor function is useful for right-censored data, as occur commonly in survival analysis, and for calculating uniform residuals. Also featured is the distribution of ratios of paired failure times. The model is applied to data from the literature     

Nonparametric analysis of treatment effects with missing observations

This paper develops a test for comparing treatment effects when observations are missing at random for repeated measures data on independent subjects. It is assumed that missingness at any occasion follows a Bernoulli distribution. It is shown that the distribution of the vector of linear rank statistics depends on the unknown parameters of the probability law that governs missingness, which is absent in the existing conditional methods employing rank statistics. This dependence is through the variance–covariance matrix of the vector of linear ranks. The test statistic is a quadratic form in the linear rank statistics when the variance–covariance matrix is estimated. The limiting distribution of the test statistic is derived under the null hypothesis. Several methods of estimating the unknown components of the variance–covariance matrix are considered. The estimate that produces stable empirical Type I error rate while maintaining the highest power among the competing tests is recommended for implementation in practice. Simulation studies are also presented to show the advantage of the proposed test over other rank-based tests that do not account for the randomness in the missing data pattern. Our method is shown to have the highest power while also maintaining near-nominal Type I error rates. Our results clearly illustrate that even for an ignorable missingness mechanism, the randomness in the pattern of missingness cannot be ignored. A real data example is presented to highlight the effectiveness of the proposed method.