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Asymptotic normality of generalized maximum spacing estimators for multivariate observations

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  • Kristi Kuljus
  • Bo Ranneby

Abstract

In this paper, the maximum spacing method is considered for multivariate observations. Nearest neighbor balls are used as a multidimensional analogue to univariate spacings. A class of information‐type measures is used to generalize the concept of maximum spacing estimators of model parameters. Asymptotic normality of these generalized maximum spacing estimators is proved when the assigned model class is correct, that is, the true density is a member of the model class.

Suggested Citation

  • Kristi Kuljus & Bo Ranneby, 2020. "Asymptotic normality of generalized maximum spacing estimators for multivariate observations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 968-989, September.
    • Handle: RePEc:bla:scjsta:v:47:y:2020:i:3:p:968-989
    DOI: 10.1111/sjos.12436
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    References listed on IDEAS

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    1. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, Enero-Abr.
    2. Kristi Kuljus & Bo Ranneby, 2015. "Generalized Maximum Spacing Estimation for Multivariate Observations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 1092-1108, December.
    3. Pollard, David, 1985. "New Ways to Prove Central Limit Theorems," Econometric Theory, Cambridge University Press, vol. 1(3), pages 295-313, December.
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    Cited by:

    1. Kristi Kuljus & Bo Ranneby, 2021. "Maximum spacing estimation for continuous time Markov chains and semi-Markov processes," Statistical Inference for Stochastic Processes, Springer, vol. 24(2), pages 421-443, July.
    2. Kuljus, Kristi & Bao, Han & Ranneby, Bo, 2025. "Maximum spacing estimation for multivariate observations under a general class of information-type measures," Journal of Multivariate Analysis, Elsevier, vol. 208(C).
    3. Kristi Kuljus & Bo Ranneby, 2025. "Maximum spacing estimation for hidden Markov models," Statistical Inference for Stochastic Processes, Springer, vol. 28(1), pages 1-31, April.
    4. Rahul Singh & Neeraj Misra, 2023. "Some parametric tests based on sample spacings," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 211-231, March.

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