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Open Access Publications from the University of California

Scholarly Works (93 results)

  • Article
  • Peer Reviewed
UC Santa Barbara Previously Published Works (2021)
This paper summarizes a talk given by the author at the Indian Academy of Sciences, Bengaluru on December 12, 2019. It outlines the multiplicity of situations where measurements on directions in two, three, or more dimensions are observed, and form the basis for answering various scientific questions. After briefly outlining the novelty in dealing with such data and the need for an entirely different set of analytical tools, one of the basic questions that arises before any further inference viz. testing isotropy of circular data, is addressed. The author was initiated into this topic of directional statistics by Professor C R Rao during the 1960s and is pertinent to this occasion celebrating him.
    Cover page: A matter of direction
    • Article
    • Peer Reviewed
    UC Santa Barbara Previously Published Works (2020)
      Cover page: A matter of direction
      • Article
      • Peer Reviewed
      UC Santa Barbara Previously Published Works (1991)
        Cover page: ON A PROBLEM IN SEMIPARAMETRIC ESTIMATION
        • Article
        • Peer Reviewed
        UC Santa Barbara Previously Published Works (2014)
          Cover page: On Edgeworth Expansions in Generalized Urn Models
          • Article
          • Peer Reviewed
          UC Santa Barbara Previously Published Works (2017)
          We show that the operations of mixing and wrapping linear distributionsaround a unit circle commute, and can produce a wide variety of circularmodels. In particular, we show that many wrapped circular models studied inthe literature can be obtained as scale mixtures of just the wrapped Gaussianand the wrapped exponential distributions, and inherit many properties fromthese two basic models. We also point out how this general approach canproduce flexible asymmetric circular models, the need for which has beennoted by many authors.
            Cover page: A General Approach for obtaining wrapped circular distributions via mixtures
            • Article
            • Peer Reviewed
            UC Santa Barbara Previously Published Works (2022)
            This paper provides a Bayesian framework for testing the number of modes in a two-component Gaussian mixture. The test is done by first setting up conjugate priors and computing the corresponding posteriors, which are then integrated over the restricted subspace of unimodal parameter space for the mixture distribution, thus obtaining the prior and posterior probabilities of unimodality. Monte Carlo and Gibbs sampling methods are employed to numerically compute these probabilities due to the difficulty in finding analytical solutions. A conclusion on unimodality for the given data is arrived at based on the Bayes factor. Effectiveness of the proposed Bayes test is demonstrated via simulations, and applied to a practical data set on adult human heights in order to answer the question whether the combined height data for men and women is bimodal.
              Cover page: A Bayesian Test for the Number of Modes in a Gaussian Mixture
              • Book
              • Peer Reviewed
              UC Santa Barbara Previously Published Works (2019)
                Cover page: Essential Statistics with Python and R
                • Thesis
                • Peer Reviewed
                UC Santa Barbara Electronic Theses and Dissertations (2016)

                Stable distributions are important family of parametric distributions widely used in signal processing as well as in mathematical finance.

                Estimation of the parameters of this model, is not quite straightforward due to the fact that there is no closed-form expression for their probability density function. Besides the computationally intensive maximum likelihood method where the density has to be evaluated numerically, there are some existing adhoc methods such as the quantile method, and a regression based method. These are introduced in Chapter 2.

                In this thesis, we introduce two new approaches: One, a spacing based estimation method introduced in Chapter 3 and two, an indirect inference method considered in Chapter 4.

                Simulation studies show that both these methods are very robust and efficient and do as well or better than the existing methods in most cases.

                Finally in Chapter 5, we use indirect inference approach to estimate the best fitting income distribution based on limited information that is often available.

                  Cover page: Parameter Estimation for Stable Distribution: Spacing based and Indirect Inference
                  • Article
                  • Peer Reviewed
                  UC Santa Barbara Previously Published Works (2003)
                    Cover page: Testing exponentiality by comparing the empirical distribution function of the normalized spacings with that of the original data.
                    • Article
                    • Peer Reviewed
                    UC Santa Barbara Previously Published Works (1984)
                      Cover page: ASYMPTOTIC RESULTS ON THE GREENWOOD STATISTIC AND SOME OF ITS GENERALIZATIONS
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