On boundary detection

Given a sample of a random variable supported by a smooth compact manifold $M\subset \mathbb{R}^d$, we propose a test to decide whether the boundary of $M$ is empty or not with no preliminary support estimation. The test statistic is based on the maximal distance between a sample point and the average of its $k_n$-nearest neighbors. We prove that the level of the test can be estimated, that, with probability one, its power is one for $n$ large enough, and that there exists a consistent decision rule. Heuristics for choosing a convenient value for the $k_n$ parameter and identifying observations close to the boundary are also given. We provide a simulation study of the test

Couplage d'un problème de classification et d'estimation de densité par des noyaux gaussiens

La classification et l'estimation de densité d'un nuage de points issu du tirage d'un mélange de lois sont deux problèmes intimement liés. En effet la connaissance de la densité induit une classification naturelle dans laquelle le nombre de classe est connu (et correspond au nombre de modes), d'autre part la connaissance de la classification permet de localiser dans l'espace les points correspondant a chacune des composantes du mélange et simplifie le problème de l'estimation de densité. Dans la pratique aucune de ses deux données n'est disponible. Dans ce papier on propose une méthode permettant de résoudre conjointement ces deux problèmes

Estimation de densité via un algorithme EM-Kernel

International audienceOn s'intéresse, dans ce papier à la construction d'un algorithme automatique d'estimation de densité. Cet algorithme repose sur un modèle de mélange. Chaque composante de ce mélange peut être estimée via une méthode à densité dépendant d'un paramètre $\lambda$ . La valeur de $\lambda$ pour chaque composante du mélange, ainsi que les probabilités d'appartenance seront estimées par une méthode type EM par abus de langage (on maximisera une pseudo vraisemblance en alternant les étapes optimisation sur $\lambda$, optimisation sur les probabilités). Le choix d'une telle méthode sera justifié, pour la dimension 1, en partie 1. Des résultats asymptotiques seront explicités en partie 2. Enfin on présentera l'algorithme proprement dit et quelques résultats, en parties 3 et 4

Density support and intrinsic dimension estimation based on a hierarchical delaunay-type simplicial complex

Let $X_1,...,X_N$, $X_i\in \mathbb{R}^D$ be an uniform drawn on a compact $d-$dimensional manifold $S$ with $d\leq D$. Here is suggested a new way to estimate both $S$ and $d$. The method is based on the computation of a set of simplicial complexes (one for each dimension $d\leq D$) and on an inductive criterion to select the ''good'' one. Each computed complex is a subcomplex of Delaunay's complex computed using $k-$nearest neighbors restriction and local $PCA$. A proposition for the $k$ value is given in the first part and the algorithm is detailed in the second part

The Development of a Quality Scale to Measure the Impact of Quality on Supermarket Fruit Demand

This research examines how fluctuations in quality affect consumer expenditures for fresh fruit at the retail level. This paper examines how consumersÂ’' purchasing behaviors react to changes in fresh fruit quality by quantifying quality characteristics based on weekly observations. A four-point scale was created and used to quantify four different quality characteristics: bruising, markings, brilliance, and maturity. A non-linear Almost Ideal Demand System was used to model the share equations for Gala apples, Fuji apples, Red Delicious apples, other sweet apples, tart apples, pears, bananas, and oranges. Seventy-nine weeks of data on weekly store sales were collected from two grocery stores in the Portland, Oregon metropolitan area. Results from the quality measures are provided and discussed. Suggestions are made for modifications to the quality measures to improve the modeling results of future fruit-demand studies.Demand and Price Analysis,

Collecting Store-Level Data on Retail Supermarket Sales

Primary data-collection methods have been understood and studied to a great degree. For example, volumes can be written on the proper way to conduct a survey-based study. However, the process of collecting data from a retail establishment is not as well documented. This paper covers the tools and strategies used to collect weekly data in a retail environment and makes some suggestions for future researchers so that they may avoid similar problems that occurred during the data collection and entry process.Agribusiness,

Local Convex Hull support and boundary estimation

International audienceIn this paper we introduce a new estimator for the support of a multivariatedensity. It is defined as a union of convex hulls of observations contained in balls of fixed radius.We study the asymptotic behavior of this ``local convex hull" for the estimation of the support and its boundary.When the support is smooth enough, the proposed estimator is proved to be, eventually almost surely, homeomorphic to the support.Numerical simulations on both simulated and real data illustrate the performance of our estimator

Marketing-Management Impacts on Produce Sales

Produce departments are important to the profitability and competitiveness of grocery stores. Understanding how variables beyond price and seasonality impact the demand and ultimately sales for produce is vital. This study finds display size and the use of multiple displays to be the most powerful tools (after price) that produce managers have available to them, but only with the right products. Also, point-of-purchase signage is found to have limited impact. These findings are based on the estimation of a demand system of fruits with prices, advertising size and location, display size (including multiple displays), and product origin among the explanatory variables.Agribusiness, Marketing,

Quantifying water quality improvements through use of precision herbicide application technologies in a dry-tropical, furrow-irrigated cropping system

This study compared water quality effects of using precision herbicide application technologies and traditional spraying approaches across several regulated 'priority' and alternative preand post-emergent herbicides in a northern Australian cane farming system. Use of herbicide banding spray technologies resulted in pre-emergent herbicide load reductions, extending substantially beyond simple proportionate decreases in the amount of herbicide ingredient applied to paddocks. Aquatic risk assessment from resultant chemical mixtures leaving paddocks, and upscaled to local catchment concentrations, highlighted that precision application technologies could markedly reduce the ecological risk of pre-emergent herbicides. These risk reductions were, however, often complicated by the additional toxicity of post-emergent herbicides in mixtures, some associated with the adoption of band-spraying weed treatments. While the currently regulated priority herbicide, diuron, posed the greatest risk to the environment, alternative herbicides could still pose significant environmental risks, although these relative risks were lower at more ecologically relevant concentrations, typically found in the local freshwater ecosystems. Results underline the need for a carefully considered approach to integrating alternative herbicides and precision application technologies into improved weed management by irrigating cane farmers. Recent government changes to the appraisal of water quality improvement progress, from load-based to ecosystem-based targets, involving a much broader suite of herbicides, also appear likely to complicate assessment of the environmental impacts of practice change adoption for the industry