Wild Bootstrapping in Finite Populations with Auxiliary Information

Consider a finite population u , which can be viewed as a realization of a super-population model. A simple ratio model (linear regression, without intercept) with heteroscedastic errors is supposed to have generated u . A random sample is drawn without replacement from u . In this set-up a two-stage wild bootstrap resampling scheme as well as several other useful forms of bootstrapping in finite populations will be considered. Some asymptotic results for various bootstrap approximations for normalized and Studentized versions of the well-known ratio and regression estimator are given. Bootstrap based confidence interval s for the population total and for the regression parameter of the underlying ratio model are also discussed     

Inventory placement problems in dynamic supply chains

Summary  In this paper a basic model for analyzing the inventory placement problem in a supply chain is developed. The problem will be studied for a capacitated, multi-stage supply chain facing a continuous, stochastic demand for a single period for a single product — a specialty item with a very short selling season. The objective is to maximize the probability of achieving a set profit level. We prove that finding an optimal stock investment at the stages entails solving a mixed binary integer linear program. We characterize properties of the stock investment, examine two interesting cases where the stock investments have a simple structure, and develop a branch and bound approach for solving the more general case.

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Zusammenfassung  In diesem Beitrag wird ein Grundmodell entwickelt, um das Problem der Lagerplatzierung in einer Lieferkette analysieren zu k?nnen. Das Problem wird für eine kapazitierte mehrstufige Lieferkette untersucht, wobei unterstellt wird, dass es um die Nachfrage nach einem einzigen Produkt für eine einzige Periode (einen Sonderartikel mit sehr kurzer Verkaufszeit) geht und diese Nachfrage stetig und stochastisch ist. Unter diesen Bedingungen soll die Wahrscheinlichkeit maximiert werden, ein vorgegebenes Gewinnniveau zu erreichen. Die Suche nach der optimalen Vorratsinvestition auf den Stufen der Lieferkette führt zur Formulierung eines gemischten ganzzahligen linearen Programmierungsproblems mit Bin?rvariablen. Die Eigenschaften der Bevorratungsinvestition werden charakterisiert, zwei interessante F?lle mit einer einfachen Struktur der Bevorratungsinvestition untersucht und ein Branch-and-Bound-Ansatz zur L?sung eines allgemeineren Problemfalls entwickelt.

     

The Berry-Esseen bound for Studentized U-statistics

Callaert and Veraverbeke (1981) recently obtained a Berry-Esseen-type bound of order n^–1/2 for Studentized nondegenerate U-statistics of degree two. The condition these authors need to obtain this order bound is the finiteness of the 4.5th absolute moment of the kernel h. In this note it is shown that this assumption can be weakened to that of a finite (4 + ?)th absolute moment of the kernel h, for some ? > 0. Our proof resembles part of Helmers and van Zwet (1982), where an analogous result is obtained for the Student t-statistic. The present note extends this to Studentized U-statistics.     

A non-parametric estimator for the doubly periodic Poisson intensity function

In a series of papers, J. Garrido and Y. Lu have proposed and investigated a doubly periodic Poisson model, and then applied it to analyze hurricane data. The authors have suggested several parametric models for the underlying intensity function. In the present paper we construct and analyze a non-parametric estimator for the doubly periodic intensity function. Assuming that only a single realization of the process is available in a bounded window, we show that the estimator is consistent and asymptotically normal when the window expands indefinitely. In addition, we calculate the asymptotic bias and variance of the estimator, and in this way gain helpful information for optimizing the performance of the estimator.