## An Introduction to Bartlett Correction and Bias ReductionThis book presents a concise introduction to Bartlett and Bartlett-type corrections of statistical tests and bias correction of point estimators. The underlying idea behind both groups of corrections is to obtain higher accuracy in small samples. While the main focus is on corrections that can be analytically derived, the authors also present alternative strategies for improving estimators and tests based on bootstrap, a data resampling technique and discuss concrete applications to several important statistical models. |

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### Contents

1 | |

2 Bartlett Corrections and Bootstrap Testing Inference | 12 |

3 BartlettType Corrections | 45 |

4 Analytical and Bootstrap Bias Corrections | 69 |

Appendix ASupplementary Material | 100 |

Glossary | 106 |

### Other editions - View all

An Introduction to Bartlett Correction and Bias Reduction Gauss M. Cordeiro,Francisco Cribari-Neto No preview available - 2014 |

### Common terms and phrases

ˆθ alternative approximation Barndorff-Nielsen Bartlett and Bartlett-type Bartlett corrections Bartlett identities Bartlett-type corrections bias correction bias function bias reduction bias-corrected estimator Biometrika bootstrap replications bootstrap sample closed-form expressions corrected estimators corrected statistics covariance matrix Cribari-Neto and Ferrari critical value cumulants of log-likelihood deﬁned denotes density function diagonal Econometrics Equation error expected value exponential family Ferrari ﬁrst given GLMs heteroskedastic information matrix joint cumulants Lawley Lemonte likelihood function likelihood ratio test linear models linear regression link function log-likelihood derivatives log-likelihood function LR statistic LR test Mathematica McCullagh nonlinear regression nonlinear regression models nuisance parameters null distribution null hypothesis obtained one-parameter order O(n−1 random variable resampling respectively Royal Statistical Society score function score statistic score tests second-order bias Simulation Statistical Computation test statistic testing H0 testing inference Theta unknown parameters unmodified statistic variance Vasconcellos Wald statistic Wald test