On the structure of the equilibrium manifold

An elementary proof is given of Y. Balasko's theorem that the equilibrium manifold is diffeomorphic to R^lm. Our proof includes the case (l,m)=(2,2), which the original proof does not cover.     

Asymptotic normality of the NPMLE of linear functionals for interval censored data, case 1

We give a new proof of the asymptotic normality of a class of linear functionals of the nonparametric maximum likelihood estimator (NPMLE) of a distribution function with "case 1" interval censored data. In particular our proof simplifies the proof of asymptotic normality of the mean given in Groeneboom and Wellner (1992). The proof relies strongly on a rate of convergence result due to van de Geer (1993), and methods from empirical process theory.     

Constructive identification of the mixed proportional hazards model

We give a new proof of the identifiably of the MPH model. This proof is constructive: it is a recipe for constructing the triple—regression function, base-line hazard, and distribution of the individual effect—from the observed cumulative distribution functions.
We then prove that the triples do not depend continuously on the observed cumulative distribution functions. Uniformly consistent estimators do not exist.
Finally we show that the MPH model is even identifiable from two-sided censored observations. This proof is constructive, too.     

On the expected length of the least squares coefficient vector

As a motivation for biased estimation procedures, it is often stated that the vector of the least squares estimator is too long on average. Some authors have given an invalid proof of this statement. In this note a proof is given and comments added to indicate how large is this average length.     

对桥梁工程抗震分析方法的探讨

文章介绍了目前用于桥梁抗震设计的几种主要分析方法，包括静力法、推倒分析法、反应谱法、动力时程分析法，为在今后的抗震设计中选择合适的设计方法提供了依据。     

Profit-maximizing communities and the theory of local public expenditures: Comment

It is argued that Sonstelie and Portney's proof that property-value maximization by each local community leads to Pareto efficient supplies of public goods is incorrect. In their analysis, property-value maximization is equivalent to profit maximization by communities. They contend that less than maximum levels of profits would lead to lower utility levels for consumers. However, in their proof, Sonstelie and Portney do not correctly characterize the implications of utility maximization. When those implications are correctly stated, their proof no longer holds.     

On the existence of equilibria in economies with an infinite dimensional commodity space

We prove an infinite dimensional extension of the Gale–Nikaido–Debreu lemma which includes all necessary limiting processes and allows a proof of the existence of equilibria under standard assumptions in an economy with infinitely many commodities which exactly parallels the proof of Debreu (1959) for the finite dimensional case.     

An elementary proof that additive i-likelihood characterizes the supports of consistent assessments

I prove a convenient reformulation of Kreps and Wilson (1982, Lemma A1), whose proof has a nontrivial gap. Essentially, the support of a consistent assessment is characterized by the additive representability of the infinite-relative-likelihood relation that the support implies. My proof is unexpectedly elementary, for it relies solely on a classic result about additive representation, which in turn relies solely on Farkas’ Lemma.     

A Central Limit Theorem for M-estimators by the von Mises Method

Asymptotic normality of M- or maximum likelihood type estimators was established in a classic paper by Huber (1967). Reeds (1976) argued that this could have been obtained simply as an application of the delta-method, using the tool of compactly differentiating von Mises functionals with respect to the empirical distribution function F_n. His proof however contains some errors and has been largely ignored. A corrected version of the proof is given.     

A Turnpike Theorem in the Closed Dynamic Leontief Model with a Singular Matrix of Capital Coefficients

The paper refers to the well-known Tsukui turnpike theorem on convergence of optimal growth trajectories in the closed dynamic Leontief model to the maximum balanced growth trajectory, called turnpike. In the original proof of this theorem, the assumption that the matrix B of capital coefficients is non-singular plays an essential role. For many reasons this assumption, very convenient for theoretical analysis, is not always satisfied in input-output systems built for empirical purposes. This paper fills the gap between theory and empirical studies, presenting a proof that convergence of optimal trajectories towards the turnpike is also a characteristic feature of the closed Leontief model in the case when matrix B is singular. The general idea of the proof is based on the approximation of a singular matrix B by an infinite sequence of non-singular matrices.