Monotonic multigamma coupling for perfect sampling

We consider a monotonic version of the multigamma coupler introduced by Murdoch and Green in ‘Exact Sampling from a Continuous State Space’ (Scandinavian Journal of Statistics, 1998) in the context of bounded multivariate distributions. Monotonicity greatly increases the efficiency of the coupler. We prove the validity of the multigamma coupler when the coalescence probability ρ is variable; specifically, a function of the bounding chains. This variation is more efficient than the fixed ρ version, and can always be used when the multigamma coupler is monotonic. We apply our algorithm to two examples.     

英语数量词的语用与心理理解

对数量词的理解过程涉及数学领域的补集概念和单调性理论。人们在理解数量词的过程中会潜意识考虑其指称集合及其指称补集,然后推理其所指的对象。数量词的单调性可分为单调递增和单调递减。单调递增数量词的取值极点是这句话的指称全集,对单调递减数量词的理解涉及它的指称补集。     

The role of reversals in order‐restricted inference

A statistical model is said to be an order‐restricted statistical model when its parameter takes its values in a closed convex cone C of the Euclidean space. In recent years, order‐restricted likelihood ratio tests and maximum likelihood estimators have been criticized on the grounds that they may violate a cone order monotonicity (COM) property, and hence reverse the cone order induced by C. The authors argue here that these reversals occur only in the case that C is an obtuse cone, and that in this case COM is an inappropriate requirement for likelihood‐based estimates and tests. They conclude that these procedures thus remain perfectly reasonable procedures for order‐restricted inference.     

Comparison of some goodness of fit tests for a single non-isotropic hypothetical principal component

Kshirsagar (1961) proposed a t e s t criterion for the null hypothesis that a covariance matrix with known smaller latent root of mu1tip1icity p?1 has its single non-isotropic principal component in a specified direction. It is shown that the power function of this criterion lacks some desirable properties. Another test criterion is proposed. The case in which the covariance matrix has an unknown smaller latent root of multi-plicity p?1 is also investigated.     

Axioms for Deferred Acceptance

The deferred acceptance algorithm is often used to allocate indivisible objects when monetary transfers are not allowed. We provide two characterizations of agent‐proposing deferred acceptance allocation rules. Two new axioms—individually rational monotonicity and weak Maskin monotonicity—are essential to our analysis. An allocation rule is the agent‐proposing deferred acceptance rule for some acceptant substitutable priority if and only if it satisfies non‐wastefulness and individually rational monotonicity. An alternative characterization is in terms of non‐wastefulness, population monotonicity, and weak Maskin monotonicity. We also offer an axiomatization of the deferred acceptance rule generated by an exogenously specified priority structure. We apply our results to characterize efficient deferred acceptance rules.     

A No-Trade Theorem under Knightian Uncertainty with General Preferences

This paper derives a no-trade theorem under Knightian uncertainty, which generalizes the theorem of Milgrom and Stokey (1982, Journal of Economic Theory 26, 17) by allowing general preference relations. It is shown that the no-trade theorem holds true as long as agents' preferences are dynamically consistent in the sense of Machina and Schmeidler (1991, Econometrica 60, 745), and satisfies the so-called piece-wise monotonicity axiom. A preference satisfying the piece-wise monotonicity axiom does not necessarily imply the additive utility representation, nor is necessarily based on beliefs. This revised version was published online in June 2006 with corrections to the Cover Date.     

Closest targets and strong monotonicity on the strongly efficient frontier in DEA

The determination of closest efficient targets has attracted increasing interest of researchers in recent Data Envelopment Analysis (DEA) literature. Several methods have been introduced in this respect. However, only a few attempts exist that analyze the implications of using closest targets on the technical inefficiency measurement. In particular, least distance measures based on Hölder norms satisfy neither weak nor strong monotonicity on the strongly efficient frontier. In this paper, we study Hölder distance functions and show why strong monotonicity fails. Along this line, we provide a solution for output-oriented models that allows assuring strong monotonicity on the strongly efficient frontier. Our approach may also be extended to the most general case, i.e. non-oriented models, under some conditions of regularity.     

Preference Monotonicity and Information Aggregation in Elections

If voter preferences depend on a noisy state variable, under what conditions do large elections deliver outcomes “as if” the state were common knowledge? While the existing literature models elections using the jury metaphor where a change in information regarding the state induces all voters to switch in favor of only one alternative, we allow for more general preferences where a change in information can induce a switch in favor of either alternative. We show that information is aggregated for any voting rule if, for a randomly chosen voter, the probability of switching in favor of one alternative is strictly greater than the probability of switching away from that alternative for any given change in belief over states. If the preference distribution violates this condition, there exist equilibria that produce outcomes different from the full information outcome with high probability for large classes of voting rules. In other words, unless preferences closely conform to the jury metaphor, information aggregation is not guaranteed to obtain.     

A “Reverse Order” Elementary Statistics Course

A family of coefficients for measuring monotone association is presented. These include measures of association of ordinal or interval variables such as gamma of Goodman and Kruskal, Somers's d_yx , Kendall's tau, or Spearman's rho as special cases. The article shows how a large number of measures of association can be put into a single general form. These coefficients are used as a basis for defining a variety of data analysis techniques.     

Monotonicity of certain multivariate normal probabilities

Let (X, Y) have a (p+q)-dimensional normal distribution and let C, K be convex symmetric sets of dimensions p, q respectively. Under certain restrictions on the mean vector it is shown that P(X ε C, Y ε K) is a monotonically increasing function of the first canonical correlation coefficient between X and Y, provided the remaining coefficients are zero.