Efficiency Analysis of Higher Education Institutions: Use of Categorical Variables

This paper focuses on the Data Envelopment Analysis (DEA) based efficiency evaluation to find the impact of two-step categorical impact on the enrollment efficiency of colleges in Bihar, one of the largest states of India. The objective of the study is to find the impact of factors, other than college-specific, on the efficiency of the colleges. The proposed research includes colleges funded and managed through seven state public universities. To follow the homogeneity condition of DEA, colleges providing courses of Arts (languages and humanities only), Science, and Commerce only, have been selected. The numbers of students enrolled in undergraduate and postgraduate courses are considered as two outputs. Numbers of teaching and non-teaching staff are considered as inputs. Colleges have been classified into two categories based on their presence in the rural or urban areas. The efficiency of a college due to any categorical value is calculated as the ratio of overall efficiency and efficiency calculated with similar categorical Decision-Making Units (DMUs) only. The impact of both the categorical variables, affiliation to university and geographical presence, has been analyzed through the hypothesis testing with the null hypothesis that there is no impact of category on the efficiency of DMUs due to a categorical variable.

Solution of the system of nonlinear PDEs characterizing CES property under quasi-homogeneity conditions

The constant elasticity of substitution (CES for short) is a basic property widely used in some areas of economics that involves a system of second-order nonlinear partial differential equations. One of the most remarkable results in mathematical economics states that under homogeneity condition i.e. the production function is a homogeneous function of a certain degree, there are no other production models with the CES property apart from the famous Cobb–Douglas and Arrow–Chenery–Minhas–Solow production functions. In this paper we generalize this classification result to a much wider framework of production functions under quasi-homogeneity conditions, showing in particular the existence of three new classes of production models with the CES property.

On a type of distributivity of lattice ordered groups

Let m be an infinite cardinal. Inspired by a result of Sikorski on m-representability of Boolean algebras, we introduce the notion of r m-distributive lattice ordered group. We prove that the collection of all such lattice ordered groups is a radical class. Using the mentioned notion, we define and investigate a homogeneity condition for lattice ordered groups.

On the 1-homogeneous non-linear connections

In this paper, we show that for every semispray S on a vector bundle (R × TM, π, R × M), there are several sequences of semisprays and correspondingly several nonlinear connections associated to it. It is important to derive conditions on S, which guarantee that a sequence of nonlinear connections associated to S is constant. We show that the homogeneity condition for S yields the result.

A Multilabel Texture Segmentation Based on Local Entropy Signature

We propose a multilabel segmentation that aims to partition a texture image into multiple regions based on a homogeneity condition using local entropy measured at varying scales. For multi-label segmentation, a bipartitioning segmentation scheme is recursively applied to confined regions obtained by previous segmentation steps. The empirical entropy is measured in the local neighbourhoods at varying scales, which is used as a characteristic feature in determining the spatial regularity of elementary texture structures. The experimental results on a variety of texture images demonstrate the efficiency and robustness of the proposed algorithm.

The Kruskal-Wallis Test and Stochastic Homogeneity

For the comparison of more than two independent samples the Kruskal-Wallis H test is a preferred procedure in many situations. However, the exact null and alternative hypotheses, as well as the assumptions of this test, do not seem to be very clear among behavioral scientists. This article attempts to bring some order to the inconsistent, sometimes controversial treatments of the Kruskal-Wallis test. First we clarify that the H test cannot detect with consistently increasing power any alternative hypothesis other than exceptions to stochastic homogeneity. It is then shown by a mathematical derivation that stochastic homogeneity is equivalent to the equality of the expected values of the rank sample means. This finding implies that the null hypothesis of stochastic homogeneity can be tested by an ANOVA performed on the rank transforms, which is essentially equivalent to doing a Kruskal-Wallis H test. If the variance homogeneity condition does not hold then it is suggested that robust ANOVA alternatives performed on ranks be used for testing stochastic homogeneity. Generalizations are also made with respect to Friedman’s G test.