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Intelligent Constructing Efficient Statistical Decisions via Pivot-Based Elimination of Unknown (Nuisance) Parameters from Underlying Models

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Abstract—

The big question in statistics is: How can we eliminate the unknown (nuisance) parameter from an underlying model? Eliminating unknown (nuisance) parameters from an underlying model is universally recognized as a major problem of statistics and has been formally studied in virtually all approaches to inference. A surprisingly large number of elimination methods have been proposed in the literature on this topic. The classical method of elimination of unknown (nuisance) parameters from the model, which is used repeatedly in the large sample theory of statistics, is to replace the unknown (nuisance) parameter by an estimated value. However, this method is not efficient when dealing with small data samples. The Bayesian approach is dependent of the choice of priors. In this paper, a new method is proposed to eliminate the unknown (nuisance) parameter from the underlying model. This method isolates and eliminates unknown (nuisance) parameters from the underlying model as efficiently as possible. Unlike the Bayesian approach, the proposed method is independent of the choice of priors and represents a novelty in the theory of statistical decisions. It allows one to eliminate unknown parameters from the problem and to find the efficient statistical decision rules, which often have smaller risk than any of the well-known decision rules. To illustrate the proposed method, some practical applications are given.

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ACKNOWLEDGMENTS

The authors would like to thank the anonymous reviewers for their valuable comments that helped to improve the presentation of this paper.

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Authors and Affiliations

  1. BVEF Research Institute, University of Latvia, 1586, Riga, Latvia

    N. A. Nechval & G. Berzins

  2. Transport and Telecommunication Institute, 1019, Riga, Latvia

    K. N. Nechval

  3. Baltic International Academy, 1019, Riga, Latvia

    Zh. Tsaurkubule

Authors
  1. N. A. Nechval
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  2. G. Berzins
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  3. K. N. Nechval
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  4. Zh. Tsaurkubule
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Correspondence to N. A. Nechval.

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Nechval, N.A., Berzins, G., Nechval, K.N. et al. Intelligent Constructing Efficient Statistical Decisions via Pivot-Based Elimination of Unknown (Nuisance) Parameters from Underlying Models. Aut. Control Comp. Sci. 55, 469–489 (2021). https://doi.org/10.3103/S0146411621050060

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