## Applied Asymptotics: Case Studies in Small-Sample StatisticsIn fields such as biology, medical sciences, sociology, and economics researchers often face the situation where the number of available observations, or the amount of available information, is sufficiently small that approximations based on the normal distribution may be unreliable. Theoretical work over the last quarter-century has led to new likelihood-based methods that lead to very accurate approximations in finite samples, but this work has had limited impact on statistical practice. This book illustrates by means of realistic examples and case studies how to use the new theory, and investigates how and when it makes a difference to the resulting inference. The treatment is oriented towards practice and comes with code in the R language (available from the web) which enables the methods to be applied in a range of situations of interest to practitioners. The analysis includes some comparisons of higher order likelihood inference with bootstrap or Bayesian methods. Author resource page: http://www.isib.cnr.it/~brazzale/AA/ |

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### Contents

Introduction | 1 |

Uncertainty and approximation | 5 |

23 Several parameters | 10 |

24 Further remarks | 14 |

Simple illustrations | 17 |

33 Top quark | 20 |

34 Astronomer data | 23 |

35 Cost data | 28 |

75 Vector parameter of interest | 121 |

76 Laplace approximation | 123 |

77 Partial likelihood | 127 |

78 Constructed exponential families | 129 |

Likelihood approximations | 134 |

83 First order theory | 138 |

84 Higher order density approximations | 140 |

85 Tail area approximations | 147 |

Discrete data | 37 |

42 Urine data | 39 |

43 Cell phone data | 46 |

44 Multiple myeloma data | 49 |

45 Speed limit data | 52 |

46 Smoking data | 55 |

Regression with continuous responses | 58 |

52 Nuclear power station data | 61 |

53 Daphnia magna data | 66 |

54 Radioimmunoassay data | 72 |

55 Leukaemia data | 78 |

56 PET film data | 81 |

Some case studies | 86 |

63 Grazing data | 91 |

64 Herbicide data | 96 |

Further topics | 108 |

73 Variance components | 111 |

74 Dependent data | 117 |

86 Tail area expressions for special cases | 155 |

87 Approximations for Bayesian inference | 161 |

88 Vector parameters of interest | 164 |

Numerical implementation | 170 |

92 Buildingblocks | 171 |

93 Pivot profiling | 174 |

94 Family objects and symbolic differentiation | 177 |

95 Other software | 182 |

Problems and further results | 185 |

Some numerical techniques | 211 |

A3 Laplace approximation | 216 |

A4 X² approximations | 217 |

219 | |

229 | |

Name index | 230 |

233 | |

### Other editions - View all

Applied Asymptotics: Case Studies in Small-Sample Statistics A. R. Brazzale,A. C. Davison,N. Reid Limited preview - 2007 |

### Common terms and phrases

analysis ancillary statistic applied Barndorff-Nielsen and Cox Bartlett correction Bayesian Bellio bibliographic notes binomial bootstrap Brazzale calculate canonical parameter censoring Chapter Code components computed confidence intervals corresponding covariates Cox and Snell data set Davison derivatives difference discussed distribution function dose exact example exponential family exponential family model expression Fisher information fitted given higher order approximations higher order asymptotics higher order inference illustrate Laplace approximation likelihood function likelihood ratio statistic linear model linear regression log likelihood function logistic regression make.V marginal likelihood matrix maximum likelihood estimate modified likelihood root nlogL nlreg package nonlinear regression normal approximation normal distribution nuisance parameters obtained P-value panel of Figure parameter of interest plot posterior profile log likelihood quantities regression model response sample space Section shows significance level simulation Skovgaard's approximation standard normal sufficient statistic Table tail area approximation tangent exponential model testing Total number values variance function variance parameters vector Wald pivot

### Popular passages

Page 227 - Tempany CM, Zhou X, Zerhouni EA, et al. Staging of prostate cancer: results of Radiology Diagnostic Oncology Group project comparison of three MR imaging techniques. Radiology 1994; 192:47-54.

Page 228 - Zhou, X.-H.. Tsao, M. and Qin, G. (2004) New intervals for the difference between two independent binomial proportions. Journal of Statistical Planning and Inference 123, 97-1 15.