Partition ratios, Pareto optimal cake division, and related notions

We consider the problem of partitioning a ‘cake' C among n players. Various criteria have been considered for deciding whether a partition P₁,P₂,…,P_n of C, where piece P_i goes to player i, is a ‘good' partition. See, for example, Barbanel (1996) [Barbanel, J.B., 1996. Super envy-free cake division and independence of measures. J. Math. Anal. Appl. 197, 54–60] or Brams and Taylor (1996) [Brams, S.J., Taylor, A.D., 1996. Fair Division: From Cake-Cutting To Dispute Resolution. Cambridge Univ. Press]. In this paper we study certain real numbers (the ‘partition ratios' of this paper's Section 2) which can be associated in a natural way with any partition. We show that various types of products of these numbers provide us with useful information about certain trades and transfers between players.     

Linear performance pricing: A collaborative tool for focused supply cost reduction

Supplier networks and the buyer/supplier relationships that comprise them are becoming increasingly important to effective supply chain management. Trust, collaboration, and efficient sharing of information are critical for true win/win relationships to surface in an environment where there is constant pressure to reduce costs and still maintain reasonable profitability. The use of across-the-board cost reduction demands and simple market clout may not always be the most effective approach in the long run. This paper describes linear performance pricing (LPP), a tool developed for a major automobile OEM in an attempt to effectively and efficiently provide more focused supply cost reductions. LPP is a data-driven methodology relying on a series of regression analyses that McKinsey and Company [2006. Automotive and assembly glossary. http://autoassembly.mckinsey.com/html/resources/glossary/1.asp (accessed 15.01.06)] describes as a “measurement tool that establishes a relationship between the value provided by a given part (performance) and its price.” We maintain that LPP facilitates a collaborative effort on the part of both the buyer and supplier and has the potential for leveraging the increased visibility of the buyer within the supplier network with respect to tier one or tier two suppliers. It helps by focusing cost reduction efforts of the tier one suppliers and provides lateral market visibility they may not have otherwise. Although widely used throughout the automotive industry in the US and Europe, little discussion of LPP is found in the literature. To promote a better understanding of LPP, we present a detailed example and discuss the managerial implications of the approach.     

Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals

This paper considers semiparametric efficient estimation of conditional moment models with possibly nonsmooth residuals in unknown parametric components (θ) and unknown functions (h) of endogenous variables. We show that: (1) the penalized sieve minimum distance (PSMD) estimator can simultaneously achieve root-n asymptotic normality of and nonparametric optimal convergence rate of , allowing for noncompact function parameter spaces; (2) a simple weighted bootstrap procedure consistently estimates the limiting distribution of the PSMD ; (3) the semiparametric efficiency bound formula of [Ai, C., Chen, X., 2003. Efficient estimation of models with conditional moment restrictions containing unknown functions. Econometrica, 71, 1795–1843] remains valid for conditional models with nonsmooth residuals, and the optimally weighted PSMD estimator achieves the bound; (4) the centered, profiled optimally weighted PSMD criterion is asymptotically chi-square distributed. We illustrate our theories using a partially linear quantile instrumental variables (IV) regression, a Monte Carlo study, and an empirical estimation of the shape-invariant quantile IV Engel curves.     

Further remarks on totally ordered representable subsets of Euclidean space

We introduce the property of ? -norm-boundedness on totally ordered subsets of Euclidean spaces. We show that when a closed subset X of the Euclidean space ⁿ, endowed with a continuous total order ?, is ? -norm-bounded, the order topology and the induced Euclidean topology must coincide on X. This generalizes a recent result by Beardon, proved on connected totally ordered subsets of Euclidean space, because on totally ordered closed subsets of ⁿ connectedness is a particular case of ? -norm-boundedness. We also analyze necessary and sufficient conditions for the coincidence of both topologies, and discuss some extension to the infinite-dimensional context.     

A note on the decomposition (at a point) of aggregate excess demand on the Grassmannian

This paper analyzes the properties of aggregate excess demand functions for economies with an arbitrary finite set of N commodities where agents face trading restrictions of a general, abstract form: their budget set is defined by K-dimensional planes in ^N. It is shown that, if there are at least K agents in the economy, the only general property satisfied by the value of aggregate excess demand and its derivative, at any arbitrary point, is Walras Law. The result is established by considering an economy where agents' preferences are of a ‘generalized Leontief' type.     

A review of estimates of the schooling/earnings relationship, with tests for publication bias

In this paper we provide an analytical review of previous estimates of the rate of return on schooling investments and measure how these estimates vary by country, over time, and by estimation method. We find evidence of reporting (or “file drawer”) bias in the estimates and, after due account is taken of this bias, we find that differences due to estimation method are much smaller than is sometimes reported, although some are statistically significant. We also find that estimated returns are higher in the US and they have increased in the last two decades.     

Consistent estimation of a general nonparametric regression function in time series

We propose an estimator of the conditional distribution of X_t|X_t−1,X_t−2,…, and the corresponding regression function , where the conditioning set is of infinite order. We establish consistency of our estimator under stationarity and ergodicity conditions plus a mild smoothness condition.     

Earnings disaggregation and analysts＇ forecasts

Accounting concepts dictate that separately disclosed components should contain separate useful information. This paper examines the relations between income statement components and analysts＇ earnings forecasts and forecast errors. Regressions explaining earnings forecasts using earnings components provide a better fit than regression using just aggregate income to explain forecasts. We interpret this as consistent with the hypothesis that analysts use incremental information in components not available in aggregate income. However, additional tests based on predictability of forecast errors indicate that analysts do not incorporate all information available in components into earnings forecasts. In addition, this inefficiency appears to increase at longer forecast horizons.     

Transformationen,die die Normalverteilung charakterisieren

Zusammenfassung Es sei A: R ⁿ R ⁿ eine Abbildung mit für jedes sei einn-dimensionaler Zufallsvektor. Wir beschreiben die Klasse aller TransformationenA, für die unabhängige, nachN(0, 1) verteilte Komponenten hat, sofern nur die KomponentenX ₁,...,X _n des Zufallsvektors ebenfalls unabhängig und identish Gaußisch verteilt sind mit Erwartungswert Null und Varianz 1. Weiter sind Bedingungen angegeben, die sicherstellen, daß nachN(O, ²) verteilte KomponentenX ₁,...,X _n hat, sofern dieX ₁,...,X _n unabhängig und und identisch verteilt sind. Zwei vonBeer undLukacs behandelte Transformationen sind Spezialfälle der hier untersuchten Transformationen.

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Summary Let A: R ⁿ R ⁿ be a transformation with the property for every . We consider a random vector and characterize the class of all transformationsA such that has independentN (0, 1) distributed componentsY ₁,...,Y _n if has the same distribution. Furthermore in the paper there are given conditions which ensure that hasN(O, ² distributed components if and are identically distributed and the componentsX ₁,...,X _n are independent, identically distributed random variables. Two of the transformations tried byBeer andLukacs are special cases of our transformations.

     

Die messende Prüfung bei Abweichung von der Normalverteilungsannahme

Summary For sampling inspection by variables in the one-sided case (item bad if variablex>a) under the usual assumption of normality with known variance ₂ the operating characteristic is given by , wherep denotes the fraction defective. If instead of a normal distribution ((·–a–)/) there is a distributionF((·–a–)/) whereF is sufficiently regular and normed like , one has the approximative operating characteristic . It is shown that for arbitrarily fixed parametersn andc the function takes the valueL _n,c ⁽⁾ (p) at the pointp _F (p)=1–F(–^–1(p)). Sufficient conditions for a simple behavior of the differencep _F (p)–p are given. In the cases of rectangular and symmetrically truncated normal distribution these conditions are shown to be fulfilled.     

Contributions to nonparametric generalized failure rate function estimation

For a specified distribution functionG with densityg, and unknown distribution functionF with densityf, the generalized failure rate function (x)=f(x)/gG ^–1 F(x) may be estimated by replacingf andF byf _n and , wheref _n is an empirical density function based on a sample of sizen from the distribution functionF, and . Under regularity conditions we show and, under additional restrictions whereC is a subset ofR and _n. Moreover, asymptotic normality is derived and the Berry-Esséen type bound is shown to be related to a theorem which concerns the sum of i.i.d. random variables. The order boundO(n^–1/2+c _n ^1/2 ) is established under mild conditions, wherec _n is a sequence of positive constants related tof _n and tending to 0 asn.Research was supported in part by the Army, Navy and Air Force under Office of Naval Research contract No. N00014-76-C-0608. AMS 1970 subject classifications. Primary 62G05. Secondary 60F15.