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Weak separability is an important concept in many fields of economic theory. This chapter uses Monte Carlo experiments to investigate the performance of newly developed nonparametric revealed preference tests for weak separability. A main finding is that the bias of the sequentially implemented test for weak separability proposed by Fleissig and Whitney (2003) is low. The theoretically unbiased Swofford and Whitney test (1994) is found to perform better than all sequentially implemented test procedures but is found to suffer from an empirical bias, most likely because of the complexity in executing the test procedure. As a further source of information, we also perform sensitivity analyses on the nonparametric revealed preference tests. It is found that the Fleissig and Whitney test seems to be sensitive to measurement errors in the data.

A new nonparametric procedure is developed to evaluate the significance of violations of weak separability. The procedure correctly detects weak separability with high probability using simulated data that have violations of weak separability caused by adding measurement error. Results are not very sensitive when the amount of measurement error is miss-specified by the researcher. The methodology also correctly rejects weak separability for nonseparable simulated data. We fail to reject weak separability for a monetary and consumption data set that has violations of revealed preference, which suggests that measurement error may be the source of the observed violations.

The purpose of this paper is to provide Korean merchants and practitioners who are not English native speakers with the practical advices and suggestions in drafting arbitration agreements.

The doctrine of separability of arbitration and the competence-competence principle are studied based on the rules of international conventions and internationally recognized arbitral institutes. In addition, the laws of two common law jurisdictions, which are the USA and the UK are discussed with the Korean arbitration law, which follows the civil law system. This study also includes analysis of cases in order to show application of these two principles to practice and to give practical advices and implications to practitioners.

Most national legislatures and jurisdictions approve the doctrine of separability of arbitration agreement and the competence-competence principle under international commercial arbitration. When there is a dispute regarding the existence or the validity of arbitration agreement, it is determined based on the prima facie test without being affected by the main contract in which the arbitration agreement is inserted. In practice, however, there are many occasions where the arbitration agreements are void or inoperable because of its contents. Many practical advices and suggestions are provided.

This paper analyzes arbitration agreements which are used in practice so that it provides many practical advices to practitioners in terms of legal effects of languages and linguistic use.

The selection of wavelength region and number of bands is a research problem for remote sensing experts for utilization of data provided by the sensor system. The present study proposes to make an evaluation for optimum band selection and classification accuracy.

The entropy, brightness value overlap index (BVOI), optimum index factor (OIF) and spectral separability analysis, i.e. Euclidean distance (ED), divergence, transformed divergence (TD) and Jefferies‐Matusita (JM) distance and accuracy of MLC classification were carried out. For the present study Terra ASTER, Landsat ETM⁺ and IRS 1D LISS III dataset has been used. The first three methods were for the spectral evaluation of the three satellite data used and for determination of information content, variance and spectral overlap among the classes present in the natural and man‐made landscape. The fourth method is for selection of spectral band combinations with highest separability of classes using divergence matrices. These band combinations are selected for the classification and subsequent accuracy assessment.

The OIF values are clearly indicating that the performance of ASTER data is the best, having the lowest correlation between the bands; hence the separability of the feature is also highest, while LISS III have shown high correlation between the bands, with the poor separability of the features. Landsat ETM⁺ data are in between these two sensors, better than LISS III but poorer than ASTER. The BVOI outputs of the three datasets of man‐made landscape show that band 3 of ASTER has the least overlap of the classes, followed by band 4 of ETM⁺. Very high overlap of the classes has been found in LISS III data. It has been found from spectral separability analysis of all the three datasets for the man‐made landscape that ASTER data with band combination of spectral bands 123468 contains the highest value of all the measures of spectral separability, i.e. ED (291.72), divergence (2,133.37), TD (2,000.00) and JM distance (1,414.10).

It can be inferred from the present study that spectral resolution plays a very important role in discrimination of vegetation features. ASTER data which are with the highest number of the bands amongst the satellite data used had shown highest classification accuracy, while LISS III data with lowest number of bands had shown lowest accuracy, and Landsat ETM⁺ stood in between the two sensors.

It is important to evaluate the sensor systems and their spectral regions for discrimination of vegetation features. The number of bands present in a particular sensor and the spectral regions used in it are some of the crucial factors which decide the usefulness of the data for different applications, including vegetation‐related studies. The selection of spectral wavelength region, i.e. spectral bands and the sensor system, presents the research problem for remote sensing experts to suggest the best spectral regions and satellite sensor for the discrimination of the vegetation features in different landscapes, namely man‐made and natural.

In the present study all the three datasets are extensively examined and tested for their vegetation discrimination capabilities using well‐established methodologies. All the parameters applied on the datasets revealed that spectral resolution definitely plays a role in the performance of the data as far as discrimination of features is concerned both in natural and man‐made landscape with desirable accuracy.

Revealed preference axioms provide a simple way of testing data from consumers or firms for consistency with optimizing behavior. The resulting non-parametric tests are very attractive, since they do not require any ad hoc functional form assumptions. A weakness of such tests, however, is that they are non-stochastic. In this paper, we provide a detailed analysis of two non-parametric approaches that can be used to derive statistical tests for utility maximization, which account for random measurement errors in the observed data. These same approaches can also be used to derive tests for separability of the utility function.