Asymptotic normality of nonparametric M-estimators with applications to hypothesis testing for panel count data

Xingqiu Zhao, Ying Zhang

Research output: Contribution to journalArticle

Abstract

In semiparametric and nonparametric statistical inference, the asymptotic normality of estimators has been widely established when they are consistent. In many applications, nonparametric estimators are not able to achieve this rate. We have a result on the asymptotic normality of nonparametric M-estimators that can be used if the rate of convergence of an estimator is n or slower. We apply this to study the asymptotic distribution of sieve estimators of functionals of a mean function from a counting process, and develop nonparametric tests for the problem of treatment comparison with panel count data. The test statistics are constructed with spline likelihood estimators instead of nonparametric likelihood estimators. The new tests have a more general and simpler structure and are easy to implement. Simulation studies show that the proposed tests perform well even for small sample sizes. We find that a new test is always powerful for all the situations considered and is thus robust. For illustration, a data analysis example is provided.

Original languageEnglish (US)
Pages (from-to)931-950
Number of pages20
JournalStatistica Sinica
Volume27
Issue number2
DOIs
StatePublished - Apr 1 2017

Fingerprint

M-estimator
Count Data
Panel Data
Hypothesis Testing
Asymptotic Normality
Estimator
Nonparametric Likelihood
Nonparametric Inference
Counting Process
Sieve
Non-parametric test
Nonparametric Estimator
Small Sample Size
Statistical Inference
Asymptotic distribution
Spline
Test Statistic
Likelihood
Data analysis
Rate of Convergence

Keywords

  • Asymptotic normality
  • M-estimators
  • Nonparametric maximum likelihood
  • Nonparametric maximum pseudo-likelihood
  • Nonparametric tests
  • Spline

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Asymptotic normality of nonparametric M-estimators with applications to hypothesis testing for panel count data. / Zhao, Xingqiu; Zhang, Ying.

In: Statistica Sinica, Vol. 27, No. 2, 01.04.2017, p. 931-950.

Research output: Contribution to journalArticle

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