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A Gaussian Process Arising from Likert-Type Scaling

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Abstract

Convergence of a sequence of stochastic processes obtained from Likert-Type scaling with increasing number of categories with increasing sample sizes is considered. Conditions are exhibited under which the sequence constructed from cumulative class frequencies by linear interpolation with respect to the class boundaries converges to a Gaussian process in law when the support of latent distribution is a bounded interval. We then extend the result to more general unbounded support. Quadratic variation of the limiting process is derived.

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Acknowledgements

The authors wish to thank Prof. Suman Majumdar for useful conversations.

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Authors and Affiliations

  1. Department of Statistics, Haldia Government College, P.O. Debhog, Haldia, Purba Medinipur, West Bengal, 721657, India

    Tuhinsubhra Bhattacharya

  2. Department of Statistics, University of Calcutta, Circular Rd., Ballygunge, Kolkata, West Bengal, 700019, India

    Arindam Sengupta

Authors
  1. Tuhinsubhra Bhattacharya
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  2. Arindam Sengupta
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Correspondence to Tuhinsubhra Bhattacharya.

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Bhattacharya, T., Sengupta, A. A Gaussian Process Arising from Likert-Type Scaling. J Indian Soc Probab Stat 18, 77–87 (2017). https://doi.org/10.1007/s41096-016-0015-3

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  • DOI: https://doi.org/10.1007/s41096-016-0015-3

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