Yang, Bill Huajian
(2019):
*Monotonic Estimation for Probability Distribution and Multivariate Risk Scales by Constrained Minimum Generalized Cross-Entropy.*
Forthcoming in: International Journal of Machine Learning and Computing

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## Abstract

Minimum cross-entropy estimation is an extension to the maximum likelihood estimation for multinomial probabilities. Given a probability distribution {r_i }_(i=1)^k, we show in this paper that the monotonic estimates {p_i }_(i=1)^k for the probability distribution by minimum cross-entropy are each given by the simple average of the given distribution values over some consecutive indexes. Results extend to the monotonic estimation for multivariate outcomes by generalized cross-entropy. These estimates are the exact solution for the corresponding constrained optimization and coincide with the monotonic estimates by least squares. A non-parametric algorithm for the exact solution is proposed. The algorithm is compared to the “pool adjacent violators” algorithm in least squares case for the isotonic regression problem. Applications to monotonic estimation of migration matrices and risk scales for multivariate outcomes are discussed.

Item Type: | MPRA Paper |
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Original Title: | Monotonic Estimation for Probability Distribution and Multivariate Risk Scales by Constrained Minimum Generalized Cross-Entropy |

Language: | English |

Keywords: | maximum likelihood, cross-entropy, least squares, isotonic regression, constrained optimization, multivariate risk scales |

Subjects: | C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C18 - Methodological Issues: General C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C44 - Operations Research ; Statistical Decision Theory C - Mathematical and Quantitative Methods > C5 - Econometric Modeling C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C52 - Model Evaluation, Validation, and Selection C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C54 - Quantitative Policy Modeling C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C55 - Large Data Sets: Modeling and Analysis C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C58 - Financial Econometrics C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling |

Item ID: | 93400 |

Depositing User: | Dr. Bill Huajian Yang |

Date Deposited: | 24 Apr 2019 14:58 |

Last Modified: | 26 Sep 2019 17:06 |

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URI: | https://mpra.ub.uni-muenchen.de/id/eprint/93400 |