Some recent results for series system reliability

Asymptotic properties of key test results ate obtained. Some further results on the Lindstrom-Madden method are given, including a binomial-Poisson inequality, together with some numerical examples. Simplified proofs of some results of Pledger and Proschan (1971) and Nevius, Proschan and Sethuraman (1977) are provided and the listing of a FORTRAN program to calculate a lower bound to the 1-α lower confidence limit on the system reliability is given.     

Binomial confidence limits adjusted for a confounding variable

A simple transformation of classical binomial confidence limits provides exact confidence limits in situations where a confounding variable is present. An example is the multiple-choice test, where a correct answer may represent either knowledge or guesswork, the latter being the confounding variable.     

On the maximum likelihood estimation of parameters of a spatial discrimination model

Consideration is given here to the problem of maximum likelihood estimation of parameters in a sparial discrimination model which was proposed by switzer (1980). some moments of these estimators are derived. These results extend the work of Mardia (1984) who gave expressions for these estimators without their moments.     

Stratified analysis of correlated binary outcome data: a comparison of model dependent and robust tests of significance

Model dependent and robust test statistics constructed using a generalized estimating equations extension of logistic regression applicable to the analysis of correlated binary outcome data are shown to have relatively simple algebraic expressions in stratified analyses where all variables are measured at the cluster level These expressions are used to demonstrate the close relationship to standard procedures which assume that subjects responses are independent, to prove that the asymptotic validity of model dependent test statistics is assured if the average correlation between cluster members is constant, and that this assumption can be relaxed when there are the same number of subjects in each cluster.     

Understanding the Risk-Return Relation: The Aggregate Wealth Proxy Actually Matters

ABSTRACT

The ICAPM implies that the market’s conditional expected return is proportional to its conditional variance and that the reward-to-risk ratio equals the representative investor’s coefficient of relative risk aversion. Prior studies examine this relation using the stock market to proxy for aggregate wealth and find mixed results. We show, however, that stock-based tests suffer from low power and lead to biased estimates of the risk-return tradeoff when stocks are an imperfect market proxy. Tests designed to mitigate this bias by incorporating a more comprehensive measure of aggregate wealth produce large, positive estimates of the risk-aversion coefficient around seven to nine. Supplementary materials for this article are available online.     

Modeling Dependence in High Dimensions With Factor Copulas

This article presents flexible new models for the dependence structure, or copula, of economic variables based on a latent factor structure. The proposed models are particularly attractive for relatively high-dimensional applications, involving 50 or more variables, and can be combined with semiparametric marginal distributions to obtain flexible multivariate distributions. Factor copulas generally lack a closed-form density, but we obtain analytical results for the implied tail dependence using extreme value theory, and we verify that simulation-based estimation using rank statistics is reliable even in high dimensions. We consider “scree” plots to aid the choice of the number of factors in the model. The model is applied to daily returns on all 100 constituents of the S&P 100 index, and we find significant evidence of tail dependence, heterogeneous dependence, and asymmetric dependence, with dependence being stronger in crashes than in booms. We also show that factor copula models provide superior estimates of some measures of systemic risk. Supplementary materials for this article are available online.     

Properties of estimators for the gamma distribution

Accurate moments of maximum likelihood and moment estimators for the scale and shape parameters of a two parameter gamma density are given, the former being tabulated over a segment of the parameter space. In addition, joint acceptance regions are given for a particular case. The three parameter model is also considered and comments made on second order asymptotics for the maximum likelihood estimators     

Generalizations of a contamination model for continuous type random variables

In 1965, Stanley Warner (Warner, 1965) introduced a model for contaminating discrete type random variables. He presented this scheme as being potentially useful in survevs where sensitive in-formation is being gathered. Since that time much research has been conducted and many papers written on the development of these discrete type randomized response models. More recently, atten-tion has been focused on the application of randomized response type models for preservation of confidentiality in existing data files (Boruch 1971 and 1972, Ranney 1975, Felligi 1974, and Inge-marsson 1975). In 1974, Poole (Poole, 1974) introduced a randomized response model for a positive continuous type random variable which was basically a continuous variable analog of the discrete variable Warner model. In this paper the results of the 1974 paper are extended to a lt-dimensional continuous type random variable in k-dimensional Euclidean space.     

Test procedures in coyariamce analysis assuming a general correlation pattern

The analysis of covariance procedure is considered when the observations in each cell are equicorrelated. A correction procedure is given, A computationally easier conservative test statistic is also given. The conservative test statistic allows one to more readily determine the consequences of ignoring correlations, even slight correlations, in the analysis of covariance procedure. The difference of the corrected test and the conservative test is shown to converge in probability to zero. This conservative test is easy to implement on statistical computer packages, It is shown, that for the general correlation pattern, any test involving the regression coefficients of the covariables is an exact test. An example illustrates the procedure