Search results

When a parameter of interest is nondifferentiable in the probability, the existing theory of semiparametric efficient estimation is not applicable, as it does not have an influence function. Song (2014) recently developed a local asymptotic minimax estimation theory for a parameter that is a nondifferentiable transform of a regular parameter, where the transform is a composite map of a continuous piecewise linear map with a single kink point and a translation-scale equivariant map. The contribution of this paper is twofold. First, this paper extends the local asymptotic minimax theory to nondifferentiable transforms that are a composite map of a Lipschitz continuous map having a finite set of nondifferentiability points and a translation-scale equivariant map. Second, this paper investigates the discontinuity of the local asymptotic minimax risk in the true probability and shows that the proposed estimator remains to be optimal even when the risk is locally robustified not only over the scores at the true probability, but also over the true probability itself. However, the local robustification does not resolve the issue of discontinuity in the local asymptotic minimax risk.

A new method of designing electromagnetic devices is presented in this paper. As a result of applying a very effective algorithm for non‐linear minimax optimization, a flexible method for Computer Aided Design (CAD) of electromagnetic devices has been obtained. The algorithm is based on successive linear approximation of the functions defining the problem. In each iteration step those functions are computed with the aid of the Finite Element Method (FEM). The resulting linear sub‐problems are solved in the minimax sense subject to the linear equality and inequality constraints. The application of the new method for the design of two different examples are presented. The first example is a classical case of shape designing with the aid of the independent nodes movement (INM) method. In the second example the applied equality constraints added to INM have reduced the problem to the optimal location. In both cases the method proved its flexibility and usefulness in CAD.

A new computational noniterative algorithm which gives the solution to a linear deconvolution‐inverse filtering problem is proposed and its properties are studied. It is proved, in some specific cases of input signal, that the algorithm discussed gives the solution, which is equal to that with the Chebyshev minimax norm for the approximation error. In a general case of input signal the solution obtained provides a good prompt for determining an “appropriate subsystem” of n + 1 linear equations of n unknowns, which directly gives the Chebyshev minimax norm based solution.

These moments of the asymptotic distribution of the least-squares estimator of the local-to-unity autoregressive model are computed using computationally simple integration. These calculations show that conventional simulation estimation of moments can be substantially inaccurate unless the simulation sample size is very large. We also explore the minimax efficiency of autoregressive coefficient estimation, and numerically show that a simple Stein shrinkage estimator has minimax risk which is uniformly better than least squares, even though the estimation dimension is just one.

Planning inventories for emergency supplies such as bottled water, non‐perishable foods, batteries, and flashlights can be challenging for retailers situated within the projected path of a severe storm. The retailer's inventory decisions are complicated by the inherent volatility of storm forecasts and the corresponding demand predictions. The purpose of this paper is to explore both proactive and reactive inventory control policies within the context of probable pre‐storm demand surge for a fast‐moving emergency supply item, and identify the conditions that are most conducive to each strategy according to the minimax decision criterion.

The inventory system is formulated based on an underlying economic order quantity framework. Minimax decision rules are developed analytically. Sensitivity analysis is facilitated by both analytic and numerical methods.

The conditions that are conducive to a proactive ordering strategy are limited supplier flexibility, acute demand surge, and exorbitant reorder costs; otherwise, the minimax inventory control policy is given by a reactive ordering strategy.

The above‐mentioned findings are based on a stylized inventory model characterized by assumptions that are consistent with the academic literature. In order to assess the implications of these results in practice, the model should be extended according to the relevance of each assumption to specific real‐world inventory systems.

Householders preparing for probable evacuation or post‐storm power outages typically overwhelm grocery and home improvement stores during a brief period prior to the impact of an approaching weather system. This phenomenon triggers a temporary spike in demand for several stock keeping units, which is oftentimes accompanied by pervasive inventory shortages that proliferate community vulnerability and engender a sense of disarray throughout the local populace. Effective inventory management of emergency supply items during this period can help alleviate some of these social dilemmas.

Few academic publications address inventory management from the perspective of humanitarian relief. Among existing studies, the emphasis has been coordination of emergency supplies for post‐disaster relief and recovery activities. This paper appears to be the first academic investigation of an inventory system driven by the pre‐storm demand surge for emergency supplies that typically occurs in the presence of an ominous and potentially devastating weather system. Additionally, this study conceivably represents the first minimax distribution free approach to inventory control within the context of humanitarian logistics and disruption management.

A solution of a discrete minimax problem is derived, using the standard methods of approximation theory. It represents a problem of the deconvolution‐inverse filtering of a three‐element discrete even signal, subject to a constraint on the output signal sidelobe level. Consequently, properties of this solution, in particular the asymptotic behaviour of the parameter, which represents the degradation of signal‐to‐noise ratio due to the filtering are examined.

A new method of designing electromagnetic devices especially high‐voltage ones, is presented. As a result of applying a sequential quadratic programing algorithm and a very effective algorithm for non‐linear minimax optimization, a flexible method for computer aided design of high‐voltage and semiconductor devices has been obtained. The minimax algorithm is based on a successive linear approximation of the functions defining the problem. In each iteration step these functions are computed with the aid of the finite element method. The resulting linear subproblems are solved in the minimax sense subject to the linear equality and inequality constraints. Applications of these two methods for the designing some parts of the high‐voltage devices are presented.

The aim of this paper is to show that in the case of even input signals with sidelobes of equal amplitude and arbitrary sign the D‐algorithm introduced in the first part of this paper subtitled “Theory”, may give a solution which is equal to that with the Chebyshev minimax norm for the approximation error. It is proved that, with some restrictions, in the case of two, four, and six sidelobe even input signals, the algorithm discussed gives exactly the Chebyshev minimax solution—CMS. Also, properties of the algorithm in the case of more general input signal are discussed.

In this note we correct the flow diagram of the ascent algorithm for the linear minimax problem which was shown by Cheney on p. 50.

This paper presents a closed form analytic solution for the impulse response of an optimum FIR deconvolution filter intended for a pair of discrete pulses of arbitrary amplitude and sign, subject to the minimisation of Chebyshev maximum norm for the approximation error. The tradeoff between the approximation error and the degradation of signal‐to‐noise ratio, is examined.