Likelihood estimation of consumer preferences in choice-based conjoint analysis

In marketing research the measurement of individual preferences and assessment of utility functions have long traditions. Conjoint analysis, and particularly choice-based conjoint analysis (CBC), is frequently employed for such measurement. The world today appears increasingly customer or user oriented wherefore research intensity in conjoint analysis is rapidly increasing in various fields, OR/MS being no exception. Although several optimization based approaches have been suggested since the introduction of the Hierarchical Bayes (HB) method for estimating CBC utility functions, recent comparisons indicate that challenging HB is hard. Based on likelihood maximization we propose a method called LM and compare its performance with HB using twelve field data sets. Performance comparisons are based on holdout validation, i.e. predictive performance. Average performance of LM indicates an improvement over HB and the difference is statistically significant. We also use simulation based data sets to compare the performance for parameter recovery. In terms of both predictive performance and RMSE a smaller number of questions in CBC appears to favor LM over HB.     

On a class of σ-space with special nets

Strong CP(HCP)-netted spaces are defined and some properties are shown. In particular, the following results are shown.

1. A submetrizable space is strong CP(HCP)-netted provided that the space admits a perfect map onto a strong CP(HCP)-netted space.
2. The image of a strong CP(HCP)-netted space under a perfect map is strong CP(HCP)-netted space.
3. A stratifiable space is strong HCP-netted if the space has a countable closed cover consisting of strong HCP-netted subspaces.

     

Real hypersurfaces of a complex space form

In this paper we are interested in obtaining a condition under which a compact real hypersurface of a complex projective space CP ⁿ is a geodesic sphere. We also study the question as to whether the characteristic vector field of a real hypersurface of the complex projective space CP ⁿ is harmonic, and show that the answer is in negative.     

On orthocomplemented subspaces in p-adic Banach spaces

For linear subspaces of finite-dimensional normed spaces over K, where K is a non-Archimedean complete valued field which is not spherically complete, we study orthocomplementation as related to strictness and the Hahn-Banach property. We prove that there exist finite-dimensional normed spaces which possess non-orthocomplemented, strict HB-subspaces.     

On the influence of the prior distribution in image reconstruction

Two measures of the influence of the prior distribution p(θ) in Bayes estimation are proposed. Both involve comparing with alternative prior distributions proportional to p(θ) ^s , for s  ≥  0. The first one, the influence curve for the prior distribution, is simply the curve of parameter values which are obtained as estimates when the estimation is made using p(θ) ^s instead of p(θ). It measures the overall influence of the prior. The second one, it the influence rate for the prior, is the derivative of this curve at s = 1, and quantifies the sensitivity to small changes or inaccuracies in the prior distribution. We give a simple formula for the influence rate in marginal posterior mean estimation, and discuss how the influence measures may be computed and used in image processing with Markov random field priors. The results are applied to an image reconstruction problem from visual field testing and to a stylized image analysis problem.     

Estimation of the number of iterations in integer programming algorithms using the regular partitions method

We review the results of studying integer linear programming algorithms which exploit properties of problem relaxation sets. The main attention is paid to the estimation of the number of iterations of these algorithms by means of the regular partitions method and other approaches. We present such estimates for some cutting plane, branch and bound (Land and Doig scheme), and L-class enumeration algorithms and consider questions of their stability. We establish the upper bounds for the average number of iterations of the mentioned algorithms as applied to the knapsack problem and the set packing one.     

On Hurwitz numbers and Hodge integrals

In this paper we find an explicit formula for the number of topologically different ramified coverings C → CP¹ (C is a compact Riemann surface of genus g) with only one complicated branching point in terms of Hodge integrals over the moduli space of genus g curves with marked points.     

Double solid twistor spaces: the case of arbitrary signature

In a recent paper ([9]) we constructed a series of new Moishezon twistor spaces which are a kind of variant of the famous LeBrun twistor spaces. In this paper we explicitly give projective models of another series of Moishezon twistor spaces on n CP ² for arbitrary n≥3, which can be regarded as a generalization of the twistor spaces of ‘double solid type’ on 3CP ² studied by Kreußler, Kurke, Poon and the author. Similarly to the twistor spaces of ‘double solid type’ on 3CP ², projective models of the present twistor spaces have a natural structure of double covering of a CP ²-bundle over CP ¹. We explicitly give a defining polynomial of the branch divisor of the double covering, whose restriction to fibers is degree four. If n≥4 these are new twistor spaces, to the best of the author’s knowledge. We also compute the dimension of the moduli space of these twistor spaces. Differently from [9], the present investigation is based on analysis of pluri-(half-)anticanonical systems of the twistor spaces.     

Semi-Parametric Probability-Weighted Moments Estimation Revisited

In this paper, for heavy-tailed models and through the use of probability weighted moments based on the largest observations, we deal essentially with the semi-parametric estimation of the Value-at-Risk at a level p, the size of the loss occurred with a small probability p, as well as the dual problem of estimation of the probability of exceedance of a high level x. These estimation procedures depend crucially on the estimation of the extreme value index, the primary parameter in Statistics of Extremes, also done on the basis of the same weighted moments. Under regular variation conditions on the right-tail of the underlying distribution function F, we prove the consistency and asymptotic normality of the estimators under consideration in this paper, through the usual link of their asymptotic behaviour to the one of the extreme value index estimator they are based on. The performance of these estimators, for finite samples, is illustrated through Monte-Carlo simulations. An adaptive choice of thresholds is put forward. Applications to a real data set in the field of insurance as well as to simulated data are also provided.     

A model for a Mixed Continuous-Periodic Review One-Warehouse,N-Retailer inventory system

This paper analyzes a Mixed Continuous-Periodic Review One-Warehouse, N-Retailer inventory system for a single, consumable item. In this system, the warehouse holds stock and the retailers experience independent, stationary field demand. Each retailer follows a continuous review (Q, r) policy. However, the warehouse reviews each retailer according to a review interval T. We discuss the motivation for this warehouse policy and show how its impact on the retailers can be modeled with an (nQ, r, T) policy at the retailers and the warehouse. Then we present an approximate analytical model to predict the performance of such a system under different operating conditions. An interesting aspect of the model is the estimation of warehouse demand variance via a closed form expression derived using renewal theory. We compare the approximate model with a simulation model to test its accuracy. The comparison indicates that the approximate model predicts quite accurately in high fill rate ranges (retailer fill rates of 90% and more). Finally, we propose several extensions to this research.     

On-line robust nonlinear state estimators for nonlinear bioprocess systems

This paper presents the design of a new robust nonlinear estimator for estimation of states of nonlinear systems. Two approaches are considered based on the state-dependent Riccati equation formulation and the technique of H-infinity control design. The proposed method differs from other well-known state estimators, because not only nonlinear dynamics but also the robustness is taken into account. The proposed method is implemented and tested on a biological wastewater system. The simulation study compares the Extended Kalman Estimator (EKE), the State-Dependent Riccati Estimator (SDRE), and the Extended H-infinity Estimator (EHE) with a new proposed State Dependent H-infinity Estimator (SDHE). The results are compared for different weather conditions, i.e. dry, rain and storm, showing a superior performance of the proposed method.     

Spaces of rational maps and the Stone-Weierstrass theorem

It is shown that Segal's theorem on the spaces of rational maps from CP¹ to CPⁿ can be extended to the spaces of continuous rational maps from CP^m to CPⁿ for any m?n. The tools are the Stone-Weierstrass theorem and Vassiliev's machinery of simplicial resolutions.     

Lagrangian submanifolds in complex projective space CP n

We first prove a basic theorem with respect to the moving frame along a Lagrangian immersion into the complex projective space CP ⁿ . Applying this theorem, we study the rigidity problem of Lagrangian submanifolds in CP ⁿ .     

A Lagrangian relaxation approach to the edge-weighted clique problem

The b-clique polytope CPⁿ_b is the convex hull of the node and edge incidence vectors of all subcliques of size at most b of a complete graph on n nodes. Including the Boolean quadric polytope QPⁿ=CPⁿ_n as a special case and being closely related to the quadratic knapsack polytope, it has received considerable attention in the literature. In particular, the max-cut problem is equivalent with optimizing a linear function over CPⁿ_n. The problem of optimizing linear functions over CPⁿ_b has so far been approached via heuristic combinatorial algorithms and cutting-plane methods.We study the structure of CPⁿ_b in further detail and present a new computational approach to the linear optimization problem based on the idea of integrating cutting planes into a Lagrangian relaxation of an integer programming problem that Balas and Christofides had suggested for the traveling salesman problem. In particular, we show that the separation problem for tree inequalities becomes polynomial in our Lagrangian framework. Finally, computational results are presented.     

On Fubini-Study form and Reidemeister torsion

For a general chain complex (C_*,_∂*), one can associate the Reidemeister torsion of it. We prove the relation between Reidemeister torsion and Fubini-Study 2-form ωFS of the complex projective space CPn.     

Heuristic solution methods for the stochastic flow shop problem

We investigate the stochastic flow shop problem with m machines and general distributions for processing times. No analytic method exists for solving this problem, so we looked instead at heuristic methods. We devised three constructive procedures with modest computational requirements, each based on approaches that have been successful at solving the deterministic counterpart. We compared the performance of these procedures experimentally on a set of test problems and found that all of them achieve near-optimal performance.     

Fundamental groups of the complements of certain plane non-tame torus sextics

The moduli space of torus sextics with the configuration of singularities {A₂+A₅+2E₆} has two connected components. We compute the fundamental groups π₁(CP²−C) for sextics C in both components and study their differences.     

New approaches to due date assignment in job shops

In this study, two new approaches for due date assignment in job shops are evaluated. Proposed approaches use statistical prediction techniques for dynamic prediction of job flowtimes in a job shop environment as the job arrives to the shop floor. Primary objective of this research is to compare the performance of the proposed due date assignment model (PDDAM) with several conventional due date assignment models (CDDAM). For this purpose, simulation models are developed and comparisons of the PDDAM and CDDAM are made in terms of the mean absolute percent error (MAPE), mean percent error (MPE) and mean tardiness (MT). Simulation experiments showed that for many test conditions, PDDAM dominates CDDAM. Therefore, case by case findings are summarized in the paper.     

Optimal testing for additivity in multiple nonparametric regression

We consider the problem of testing for additivity in the standard multiple nonparametric regression model. We derive optimal (in the minimax sense) non- adaptive and adaptive hypothesis testing procedures for additivity against the composite nonparametric alternative that the response function involves interactions of second or higher orders separated away from zero in L ²([0, 1] ^d )-norm and also possesses some smoothness properties. In order to shed some light on the theoretical results obtained, we carry out a wide simulation study to examine the finite sample performance of the proposed hypothesis testing procedures and compare them with a series of other tests for additivity available in the literature.     

The resolvent average for positive semidefinite matrices

We define a new average - termed the resolvent average - for positive semidefinite matrices. For positive definite matrices, the resolvent average enjoys self-duality and it interpolates between the harmonic and the arithmetic averages, which it approaches when taking appropriate limits. We compare the resolvent average to the geometric mean. Some applications to matrix functions are also given.