A survey on multivariate chi-square distributions and their applications in testing multiple hypotheses

We are concerned with three different types of multivariate chi-square distributions. Their members play important roles as limiting distributions of vectors of test statistics in several applications of multiple hypotheses testing. We explain these applications and consider the computation of multiplicity-adjusted p-values under the respective global hypothesis. By means of numerical examples, we demonstrate how much gain in level exhaustion or, equivalently, power can be achieved with corresponding multivariate multiple tests compared with approaches which are only based on univariate marginal distributions and do not take the dependence structure among the test statistics into account. As a further contribution of independent value, we provide an overview of essentially all analytic formulas for computing multivariate chi-square probabilities of the considered types which are available up to present. These formulas were scattered in the previous literature and are presented here in a unified manner.     

Bayesian adaptive dose‐escalation procedures for binary and continuous responses utilizing a gain function

One of the main aims of early phase clinical trials is to identify a safe dose with an indication of therapeutic benefit to administer to subjects in further studies. Ideally therefore, dose‐limiting events (DLEs) and responses indicative of efficacy should be considered in the dose‐escalation procedure. Several methods have been suggested for incorporating both DLEs and efficacy responses in early phase dose‐escalation trials. In this paper, we describe and evaluate a Bayesian adaptive approach based on one binary response (occurrence of a DLE) and one continuous response (a measure of potential efficacy) per subject. A logistic regression and a linear log‐log relationship are used respectively to model the binary DLEs and the continuous efficacy responses. A gain function concerning both the DLEs and efficacy responses is used to determine the dose to administer to the next cohort of subjects. Stopping rules are proposed to enable efficient decision making. Simulation results shows that our approach performs better than taking account of DLE responses alone. To assess the robustness of the approach, scenarios where the efficacy responses of subjects are generated from an E _max model, but modelled by the linear log–log model are also considered. This evaluation shows that the simpler log–log model leads to robust recommendations even under this model showing that it is a useful approximation to the difficulty in estimating E _max model. Additionally, we find comparable performance to alternative approaches using efficacy and safety for dose‐finding. Copyright © 2015 John Wiley & Sons, Ltd.     

PROFIT‐MAXIMIZING GATE REVENUE SHARING IN SPORTS LEAGUES

In this article, I examine how sports leagues can use gate revenue sharing to coordinate talent investments and maximize club profits. Gate revenue sharing reduces incentives to invest in talent. Initially lower investments boost profits, because total costs go down, but investing less also shrinks revenues, which harms profits at higher levels of sharing. The league maximizes profits by setting a sharing rule, which balances these two effects. Gate revenue sharing decreases talent investments more strongly in leagues with heterogeneous rather than homogeneous local market sizes. As a result, the profit‐maximizing level of sharing is higher for relatively homogeneous leagues. This implies that more balanced leagues are expected to share more gate revenues than less balanced leagues. It also explains why gate revenue sharing is widely used in the U.S. major leagues, while it is largely absent in European soccer. (JEL L41, L83)     

Time to Diagnosis: Accounting for Differential Endpoint Follow-up in Multi-Cohort Studies

Cox regression is widely used to analyze discrete survival time data. Differential endpoint follow-up across sub-cohorts where distribution of a covariate varies may cause typical estimators to be biased or inefficient. We demonstrate that with Cardiovascular Health Study data for incident type 2 diabetes. Two cohorts with extremely different race distribution have differential follow-up for fasting glucose levels. We study various scenarios of Cox regression. We suggest an alternative approach, Poisson generalized estimating equations with an offset to accommodate the differential follow-up. We use simulations to contrast the methods.     

Three's a crowd? The Nader vote in the 2000 presidential, election in U.S. metropolitan areas

The 2000 U.S. presidential election resulted in one of the closest and most controversial outcomes in U.S. history. Green Party candidate Ralph Nader had little chance of winning, but nevertheless impacted the race in several close states and arguably swung the race from Al Gore to George W. Bush. This research examines Ralph Nader's “urban strategy” to win 5% of the vote for president and the bases of his electoral support. This study uses the METRO_2000 data set which contains a variety of publicly available variables for 276 U.S. metropolitan statistical areas (MSAs) in the year 2000. The analysis uses OLS regression to examine the determinants of the percentage of the vote for Nader in each MSA. The results indicate that the Nader vote was positively influenced by key electoral variables such as the level of electoral participation, whether Nader was on the ballot or could be written in, and the closeness of the race in state polls leading up to the election. The Nader vote was also higher in MSAs with high percentages of voters who supported Nader programs including environmentalists, those favoring universal health care and gay rights, union members, and MSAs that were college towns or with high percentages of college-educated voters. Ralph Nader's urban strategy effectively mobilized enough of his electoral base to impact the 2000 election, but electoral constraints and the closeness of the race prevented him from achieving his goal of attaining 5% of the vote. This case holds lessons about the limits and possibilities of third party campaigns in U.S. presidential elections.     

CREDIT,WAGES, AND BANKRUPTCY LAWS

We analyze how bankruptcy laws affect the general equilibrium interactions between credit and wages. Soft laws reduce the frequency of liquidations and thus ex post inefficiencies, but they worsen credit rationing ex ante. This hinders firm creation and thus depresses labor demand. Rich agents who need few outside funds can invest even if creditor rights are weak. Hence, they favor soft laws that exclude poorer agents from the credit market and reduce the competition for labor. Such laws can generate greater utilitarian welfare than under perfect contract enforcement: By barring access to credit to some agents, soft laws lower wages, which increases the pledgeable income of richer agents and decreases the liquidation rates they must commit to. When they induce strong credit rationing, however, soft laws are Pareto‐dominated by tougher laws combined with subsidies to entrepreneurs. (JEL: D82, G33, K22)     

Toward a General Theory of Alienation*

In this paper, the author arranges some of the major treatments of alienation within a coherent framework. He introduces a distinction between disassociation (certain specified objective conditions) and alienation (a specified experience) and articulates the relationship between these two by presenting a series of intervening psychological issues. A typology of human association is presented; and it is argued that especially two types of disassociation (i.e., marginality and subordination) and, to some extent, another (i.e., privilege) may be productive of alienation. These conditions are considered at the cultural, social, and psychological levels of analysis. Variables connecting these conditions and alienation include the perception of the condition, evaluation, integration, blame, and response.     

Unconditional Quantile Regressions

We propose a new regression method to evaluate the impact of changes in the distribution of the explanatory variables on quantiles of the unconditional (marginal) distribution of an outcome variable. The proposed method consists of running a regression of the (recentered) influence function (RIF) of the unconditional quantile on the explanatory variables. The influence function, a widely used tool in robust estimation, is easily computed for quantiles, as well as for other distributional statistics. Our approach, thus, can be readily generalized to other distributional statistics.