Evidence of Multi-Dimensional Herfindahl Hirschman Index from Linear Additive Directional Distance Function

EasyChair Preprint 2366

Abstract

Since its inception, application of Directional Distance Models has been found in abundance. Such concepts are invaluable for assessing performance of a firm in the midst of other rivals. Ample directions have been developed to satisfy a diverse set of criteria. The extant research is aimed to fulfil the sole objective of investigating and obtaining an inherent Direction Vector emerging from the Directional Distance Additive Model (DDAM). In this process, the existence of a Multi-Dimensional Herfindahl Hirschman Index (MHHI) is evidenced. The first Eigen-vector of MHHI is proved to be legitimate owing to its fulfilment of properties to symbolize a Directional Distance vector. This newly devised vector possesses the merit of corroborating the competitive position of a set of firms. In this regard, the output oriented form of DDAM is designed to foretell the volume of desirable outputs to be escalated in view of attaining a superior position in the selling market while implicating the same amount of resources. Principal Component Analysis plays a key role to identify the output-oriented directions from the non-central covariance matrix (MHHI) obtained from the output vectors.

Keyphrases: Multi-Dimensional Herfindahl Hirschman Index Directional Distance Additive Model, Principal Component Analysis, noncentral covariance matrix

@booklet{EasyChair:2366,
  author    = {Subhadip Sarkar},
  title     = {Evidence of Multi-Dimensional Herfindahl Hirschman Index from Linear Additive Directional Distance Function},
  howpublished = {EasyChair Preprint 2366},
  year      = {EasyChair, 2020}}