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Related Concept Videos

Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
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A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Sieve Maximum Likelihood Estimation for Doubly Semiparametric Zero-Inflated Poisson Models.

Xuming He1, Hongqi Xue, Ning-Zhong Shi

  • 1Department of Statistics, University of Illinois at Urbana-Champaign, Department of Biostatistics and Computational Biology, University of Rochester, School of Mathematics and Statistics, Northeast Normal University, China.

Journal of Multivariate Analysis
|July 31, 2010
PubMed
Summary

This study introduces a flexible doubly semiparametric zero-inflated Poisson model for analyzing count data with excess zeros. The proposed method offers accurate estimation and optimal convergence rates, showing little loss in efficiency.

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Area of Science:

  • Statistics
  • Biostatistics
  • Econometrics

Background:

  • Nonnegative measurements like income or sick days often exhibit a disproportionate number of zero counts.
  • Standard Poisson models may not adequately capture the excess zeros common in such data.
  • Zero-inflated models are frequently used, but semiparametric approaches offer enhanced flexibility.

Purpose of the Study:

  • To propose a doubly semiparametric zero-inflated Poisson model for count data with excess zeros.
  • To develop and analyze a sieve maximum likelihood estimator for regression and nonparametric components.
  • To assess the statistical properties and practical performance of the proposed model.

Main Methods:

  • Development of a doubly semiparametric zero-inflated Poisson model with two partially linear link functions.
  • Application of a sieve maximum likelihood estimator for regression parameters and nonparametric functions.
  • Theoretical analysis of strong consistency and asymptotic normality of the estimators.

Main Results:

  • The proposed estimators are shown to be strongly consistent under routine conditions.
  • Parameter estimators exhibit asymptotic normality and first-order efficiency.
  • Nonparametric components achieve optimal convergence rates, demonstrating the model's efficiency.

Conclusions:

  • The doubly semiparametric zero-inflated Poisson model provides a flexible and statistically sound approach for count data with excess zeros.
  • The sieve maximum likelihood estimator performs well, offering desirable asymptotic properties.
  • The model's flexibility is gained with minimal loss in statistical efficiency, as confirmed by simulations and a public health data application.