Radix-2 x 2 x 2 algorithm for the 3-D discrete hartley transform

The discrete Hartley transform (DHT) has proved to be a valuable tool in digital signal/image processing and communications and has also attracted research interests in many multidimensional applications. Although many fast algorithms have been developed for the calculation of one- and two-dimensional (1-D and 2-D) DHT, the development of multidimensional algorithms in three and more dimensions is still unexplored and has not been given similar attention; hence, the multidimensional Hartley transform is usually calculated through the row-column approach. However, proper multidimensional algorithms can be more efficient than the row-column method and need to be developed. Therefore, it is the aim of this paper to introduce the concept and derivation of the three-dimensional (3-D) radix-2 2X 2X algorithm for fast calculation of the 3-D discrete Hartley transform. The proposed algorithm is based on the principles of the divide-and-conquer approach applied directly in 3-D. It has a simple butterfly structure and has been found to offer significant savings in arithmetic operations compared with the row-column approach based on similar algorithms

Multidimensional Nature of Undernutrition: A Statistical Approach

The statistical assessment of undernutrition is usually restricted to a pairwise analysis of anthropometric indicators. The main objective of this study was to model the associations between underweight, stunting and wasting and to check whether multidimensionality of undernutrition can be justified from a purely statistical point of view. 3742 children aged 0 to 59 months were enrolled in a cross-sectional household survey (2004 Cameroon Demographic and Health Surveys (DHS)). The saturated loglinear model and the multiple correspondence analysis (MCA) showed no interaction and a highly significant association between underweight and stunting (P=0), underweight and wasting (P=0); but not between stunting and wasting (P=0.430). Cronbach's alpha coefficient between weight-for-age, height-for-age and weight-for-height was 0.62 (95% CI 0.59, 0.64). Thus, the study of these associations is not straightforward as it would appear in a first instance. The lack of three-factor interaction and the value of the Cronbach's alpha coefficient indicate that undernutrition is indeed (statistically) multidimensional. The three indicators are not statistically redundant; thus for the case of Cameroon the choice of a particular anthropometric indicator should depend on the goal of the policy maker, as it comes out of this study that no single indicator is to be used for all situations.Stunting; Wasting; Underweight; anthropometric measures; Z-score; Loglinear models

A stability approach for solving multidimensional quadratic BSDEs

We establish an existence and uniqueness result for a class of multidimensional quadratic backward stochastic differential equations (BSDE). This class is characterized by constraints on some uniform a priori estimate on solutions of a sequence of approximated BSDEs. We also present effective examples of applications. Our approach relies on the strategy developed by Briand and Elie in [Stochastic Process. Appl. 123 2921--2939] concerning scalar quadratic BSDEs.Comment: This update contains corrections for Propositions 5.1 and 5.

Shortfall Risk Approximations for American Options in the multidimensional Black--Scholes Model

We show that shortfall risks of American options in a sequence of multinomial approximations of the multidimensional Black--Scholes (BS) market converge to the corresponding quantities for similar American options in the multidimensional BS market with path dependent payoffs. In comparison to previous papers we consider the multi assets case for which we use the weak convergence approach

Intensity of Time and Income Interdependent Multidimensional Poverty: Well-Being and Minimum 2DGAP ; German Evidence

Extending the traditional income poverty concept by multidimensional poverty has been of growing interest within the last years. This paper contributes with an analysis of interdepend-ent multidimensional (IMD) poverty intensity of time and income, which in particular restricts social participation. The interdependency of the multiple poverty dimensions under a strong (union approach) and weak focus axiom (compensation approach) are regarded in particular when measuring the intensity of multidimensional poverty. In addition to various poverty gap measures including the multidimensional well-being gap, for the first time we propose a minimum multidimensional poverty gap (2DGAP).. - To respect Sen's capability approach with its social participation aspects we define the time dimension as genuine personal leisure time. Based on a CES well-being function and a multi-dimensional poverty line evaluated by the German population (estimated with the German Socio-Economic Panel) the individual poverty intensity of the active population is analysed for various regimes of multiple poverty. For this purpose the German Time Use Surveys 1991/92 and 2001/02 and its time use diary data are used. Analysing the active population this paper contributes too to the poverty situation of the working poor. . - All the empirical results, including the microeconometric Heckman type estimation of the IMD poverty intensity (2DGAP) and the IMD poverty risk, indicate the overall importance of the time dimension with its social participation aspect incorporated within an interdependent multidimensional time and income poverty approach. An important dimension would be ne-glected in the poverty analysis and in targeted poverty policies if time additional to income would is not respected.Intensity of time and income poverty, interdependent multidimensional time and income poverty, union and compensation approach, minimum multidimensional poverty gap (2DGAP), extended economic well-being, satisfaction/happiness, working poor

Multidimensional Quasi-Monte Carlo Malliavin Greeks

We investigate the use of Malliavin calculus in order to calculate the Greeks of multidimensional complex path-dependent options by simulation. For this purpose, we extend the formulas employed by Montero and Kohatsu-Higa to the multidimensional case. The multidimensional setting shows the convenience of the Malliavin Calculus approach over different techniques that have been previously proposed. Indeed, these techniques may be computationally expensive and do not provide flexibility for variance reduction. In contrast, the Malliavin approach exhibits a higher flexibility by providing a class of functions that return the same expected value (the Greek) with different accuracies. This versatility for variance reduction is not possible without the use of the generalized integral by part formula of Malliavin Calculus. In the multidimensional context, we find convenient formulas that permit to improve the localization technique, introduced in Fourni\'e et al and reduce both the computational cost and the variance. Moreover, we show that the parameters employed for variance reduction can be obtained \textit{on the flight} in the simulation. We illustrate the efficiency of the proposed procedures, coupled with the enhanced version of Quasi-Monte Carlo simulations as discussed in Sabino, for the numerical estimation of the Deltas of call, digital Asian-style and Exotic basket options with a fixed and a floating strike price in a multidimensional Black-Scholes market.Comment: 22 pages, 6 figure