Median problems in networks

The P-median problem is a classical location model par excellence . In this paper we, firstexamine the early origins of the problem, formulated independently by Louis Hakimi andCharles ReVelle, two of the fathers of the burgeoning multidisciplinary field of researchknown today as Facility Location Theory and Modelling. We then examine some of thetraditional heuristic and exact methods developed to solve the problem. In the third sectionwe analyze the impact of the model in the field. We end the paper by proposing new lines ofresearch related to such a classical problem.

Value and depreciation of mineral resources over the very long run: An empirical contrast of different methods

The paper contrasts empirically the results of alternative methods for estimating thevalue and the depreciation of mineral resources. The historical data of Mexico andVenezuela, covering the period 1920s-1980s, is used to contrast the results of severalmethods. These are the present value, the net price method, the user cost method andthe imputed income method. The paper establishes that the net price and the user costare not competing methods as such, but alternative adjustments to different scenariosof closed and open economies. The results prove that the biases of the methods, ascommonly described in the theoretical literature, only hold under the most restrictedscenario of constant rents over time. It is argued that the difference between what isexpected to happen and what actually did happen is for the most part due to a missingvariable, namely technological change. This is an important caveat to therecommendations made based on these models.

A generalization of Hull and White formula and applications to option pricing approximation

By means of Malliavin Calculus we see that the classical Hull and White formulafor option pricing can be extended to the case where the noise driving thevolatility process is correlated with the noise driving the stock prices. Thisextension will allow us to construct option pricing approximation formulas.Numerical examples are presented.

Exact and approximate stepdown methods for multiple hypothesis testing

Consider the problem of testing k hypotheses simultaneously. In this paper,we discuss finite and large sample theory of stepdown methods that providecontrol of the familywise error rate (FWE). In order to improve upon theBonferroni method or Holm's (1979) stepdown method, Westfall and Young(1993) make eective use of resampling to construct stepdown methods thatimplicitly estimate the dependence structure of the test statistics. However,their methods depend on an assumption called subset pivotality. The goalof this paper is to construct general stepdown methods that do not requiresuch an assumption. In order to accomplish this, we take a close look atwhat makes stepdown procedures work, and a key component is a monotonicityrequirement of critical values. By imposing such monotonicity on estimatedcritical values (which is not an assumption on the model but an assumptionon the method), it is demonstrated that the problem of constructing a validmultiple test procedure which controls the FWE can be reduced to the problemof contructing a single test which controls the usual probability of a Type 1error. This reduction allows us to draw upon an enormous resamplingliterature as a general means of test contruction.

How much structure in empirical models?

This chapter highlights the problems that structural methods and SVAR approaches have when estimating DSGE models and examining their ability to capture important features of the data. We show that structural methods are subject to severe identification problems due, in large part, to the nature of DSGE models. The problems can be patched up in a number of ways but solved only if DSGEs are completely reparametrized or respecified. The potential misspecification of the structural relationships give Bayesian methods an hedge over classical ones in structural estimation. SVAR approaches may face invertibility problems but simple diagnostics can help to detect and remedy these problems. A pragmatic empirical approach ought to use the flexibility of SVARs against potential misspecificationof the structural relationships but must firmly tie SVARs to the class of DSGE models which could have have generated the data.

Local volatility changes in the black-scholes model

In this paper we address a problem arising in risk management; namely the study of price variations of different contingent claims in the Black-Scholes model due to anticipating future events. The method we propose to use is an extension of the classical Vega index, i.e. the price derivative with respect to the constant volatility, in thesense that we perturb the volatility in different directions. Thisdirectional derivative, which we denote the local Vega index, will serve as the main object in the paper and one of the purposes is to relate it to the classical Vega index. We show that for all contingent claims studied in this paper the local Vega index can be expressed as a weighted average of the perturbation in volatility. In the particular case where the interest rate and the volatility are constant and the perturbation is deterministic, the local Vega index is an average of this perturbation multiplied by the classical Vega index. We also study the well-known goal problem of maximizing the probability of a perfect hedge and show that the speed of convergence is in fact dependent of the local Vega index.

Are these classical business cycles?

The aim of this paper is to test formally the classical business cyclehypothesis, using data from industrialized countries for the timeperiod since 1960. The hypothesis is characterized by the view that the cyclical structure in GDP is concentrated in the investment series: fixed investment has typically a long cycle, while the cycle in inventory investment is shorter. To check the robustness of our results, we subject the data for 15 OECD countries to a variety of detrending techniques. While the hypothesis is not confirmed uniformly for all countries, there is a considerably high number for which the data display the predicted pattern. None of the countries shows a pattern which can be interpreted as a clear rejection of the classical hypothesis.

Weighted metric multidimensional scaling

This paper establishes a general framework for metric scaling of any distance measure between individuals based on a rectangular individuals-by-variables data matrix. The method allows visualization of both individuals and variables as well as preserving all the good properties of principal axis methods such as principal components and correspondence analysis, based on the singular-value decomposition, including the decomposition of variance into components along principal axes which provide the numerical diagnostics known as contributions. The idea is inspired from the chi-square distance in correspondence analysis which weights each coordinate by an amount calculated from the margins of the data table. In weighted metric multidimensional scaling (WMDS) we allow these weights to be unknown parameters which are estimated from the data to maximize the fit to the original distances. Once this extra weight-estimation step is accomplished, the procedure follows the classical path in decomposing a matrix and displaying its rows and columns in biplots.

Dynamic graphics of parametrically linked multivariate methods used in compositional data analysis

Many multivariate methods that are apparently distinct can be linked by introducing oneor more parameters in their definition. Methods that can be linked in this way arecorrespondence analysis, unweighted or weighted logratio analysis (the latter alsoknown as "spectral mapping"), nonsymmetric correspondence analysis, principalcomponent analysis (with and without logarithmic transformation of the data) andmultidimensional scaling. In this presentation I will show how several of thesemethods, which are frequently used in compositional data analysis, may be linkedthrough parametrizations such as power transformations, linear transformations andconvex linear combinations. Since the methods of interest here all lead to visual mapsof data, a "movie" can be made where where the linking parameter is allowed to vary insmall steps: the results are recalculated "frame by frame" and one can see the smoothchange from one method to another. Several of these "movies" will be shown, giving adeeper insight into the similarities and differences between these methods.

A decomposition formula for option prices in the Heston model and applications to option pricing approximation

By means of classical Itô's calculus we decompose option prices asthe sum of the classical Black-Scholes formula with volatility parameterequal to the root-mean-square future average volatility plus a term dueby correlation and a term due to the volatility of the volatility. Thisdecomposition allows us to develop first and second-order approximationformulas for option prices and implied volatilities in the Heston volatilityframework, as well as to study their accuracy. Numerical examples aregiven.

Variance reduction methods for simulation of densities on Wiener space

We develop a general error analysis framework for the Monte Carlo simulationof densities for functionals in Wiener space. We also study variancereduction methods with the help of Malliavin derivatives. For this, wegive some general heuristic principles which are applied to diffusionprocesses. A comparison with kernel density estimates is made.

A data-dependent skeleton estimate and a scale-sensitive dimension for classification

The classical binary classification problem is investigatedwhen it is known in advance that the posterior probability function(or regression function) belongs to some class of functions. We introduceand analyze a method which effectively exploits this knowledge. The methodis based on minimizing the empirical risk over a carefully selected``skeleton'' of the class of regression functions. The skeleton is acovering of the class based on a data--dependent metric, especiallyfitted for classification. A new scale--sensitive dimension isintroduced which is more useful for the studied classification problemthan other, previously defined, dimension measures. This fact isdemonstrated by performance bounds for the skeleton estimate in termsof the new dimension.

Weighted Euclidean biplots

We construct a weighted Euclidean distance that approximates any distance or dissimilarity measure between individuals that is based on a rectangular cases-by-variables data matrix. In contrast to regular multidimensional scaling methods for dissimilarity data, the method leads to biplots of individuals and variables while preserving all the good properties of dimension-reduction methods that are based on the singular-value decomposition. The main benefits are the decomposition of variance into components along principal axes, which provide the numerical diagnostics known as contributions, and the estimation of nonnegative weights for each variable. The idea is inspired by the distance functions used in correspondence analysis and in principal component analysis of standardized data, where the normalizations inherent in the distances can be considered as differential weighting of the variables. In weighted Euclidean biplots we allow these weights to be unknown parameters, which are estimated from the data to maximize the fit to the chosen distances or dissimilarities. These weights are estimated using a majorization algorithm. Once this extra weight-estimation step is accomplished, the procedure follows the classical path in decomposing the matrix and displaying its rows and columns in biplots.

Basis set effects on the energy and hardness profiles of the hydrogen fluoride dimer

In earlier work, the present authors have shown that hardness profiles are less dependent on the level of calculation than energy profiles for potential energy surfaces (PESs) having pathological behaviors. At variance with energy profiles, hardness profiles always show the correct number of stationary points. This characteristic has been used to indicate the existence of spurious stationary points on the PESs. In the present work, we apply this methodology to the hydrogen fluoride dimer, a classical difficult case for the density functional theory methods

Simple and fast methods based on solid-phase extraction coupled to liquid chromatography with UV detection for the monitoring of caffeine in natural and waste waters as marker of anthropogenic impact

Two concentration methods for fast and routine determination of caffeine (using HPLC-UV detection) in surface, and wastewater are evaluated. Both methods are based on solid-phase extraction (SPE) concentration with octadecyl silica sorbents. A common “offline” SPE procedure shows that quantitative recovery of caffeine is obtained with 2 mL of an elution mixture solvent methanol-water containing at least 60% methanol. The method detection limit is 0.1 μg L−1 when percolating 1 L samples through the cartridge. The development of an “online” SPE method based on a mini-SPE column, containing 100 mg of the same sorbent, directly connected to the HPLC system allows the method detection limit to be decreased to 10 ng L−1 with a sample volume of 100 mL. The “offline” SPE method is applied to the analysis of caffeine in wastewater samples, whereas the “on-line” method is used for analysis in natural waters from streams receiving significant water intakes from local wastewater treatment plants