## Statistical InferenceAdopting a broad view of statistical inference, this text concentrates on what various techniques do, with mathematical proofs kept to a minimum. The approach is rigorous, but will be accessible to final year undergraduates. Classical approaches to point estimation, hypothesis testing andinterval estimation are all covered thoroughly, with recent developments outlined. Separate chapters are devoted to Bayesian inference, to decision theory and to non-parametric and robust inference. The increasingly important topics of computationally intensive methods and generalised linear modelsare also included. In this edition, the material on recent developments has been updated, and additional exercises are included in most chapters. |

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### Contents

Introduction | 1 |

12 Plan of the book | 3 |

13 Notation and terminology | 4 |

Properties of estimators | 7 |

23 Consistency | 8 |

24 Efficiency | 10 |

25 Sufficiency | 18 |

26 Exponential families of distributions | 27 |

66 Interval estimation | 132 |

67 Bayesian sequential procedures | 133 |

68 Exercises | 144 |

Bayesian inference | 151 |

73 Credible intervals | 154 |

74 Hypothesis testing | 158 |

75 Nuisance parameters | 164 |

76 Noninformative stopping | 168 |

27 Complete sufficient statistics | 31 |

28 Problems with MVUEs | 33 |

29 Summary | 34 |

Maximum likelihood and other methods of estimation | 40 |

33 Modifications and extensions of maximum likelihood estimation | 54 |

34 Other methods of estimation | 60 |

35 Discussion | 63 |

36 Exercises | 64 |

Hypothesis testing | 71 |

43 Pure significance tests | 77 |

44 Composite hypothesesuniformly most powerful tests | 78 |

45 Further properties of tests of hypothesis | 83 |

46 Maximum likelihood ratio tests | 84 |

47 Alternatives to and modifications of maximum likelihood ratio tests | 89 |

48 Discussion | 92 |

49 Exercises | 93 |

Interval estimation | 97 |

52 Construction of confidence sets | 98 |

53 Optimal properties of confidence sets | 106 |

54 Some problems with confidence sets | 108 |

55 Exercises | 111 |

The decisiontheory approach to inference | 114 |

62 Elements of decision theory | 115 |

63 Point estimation | 117 |

64 Loss functions and prior distributions | 122 |

65 Hypothesis testing | 128 |

77 Hierarchical models | 170 |

78 Empirical Bayes | 173 |

79 Exercises | 178 |

Nonparametric and robust inference | 185 |

82 Nonparametric hypothesis testing | 186 |

83 Nonparametric estimation | 199 |

84 Goodnessoffit tests and related techniques | 201 |

85 Semiparametric methods | 203 |

86 Robust inference | 204 |

87 Exercises | 212 |

Computationally intensive methods | 217 |

93 Permutation and randomization tests | 222 |

94 Crossvalidation | 227 |

95 Jackknife and bootstrap methods | 230 |

96 Gibbs sampling and related methodology | 244 |

97 Exercises | 256 |

Generalized linear models | 265 |

102 Specifying the model | 266 |

103 Fitting a generalized linear model using maximum likelihood | 270 |

104 Deciding if the model fits the data | 278 |

105 Model checking for glms | 287 |

106 Quasilikelihood | 295 |

107 Exercises | 305 |

Bibliography | 308 |

319 | |

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### Common terms and phrases

alternative Amer approach approximate assumption asymptotic Bayes risk Bayesian Chapter confidence coefficient confidence interval confidence set conjugate prior constant continuedl credible interval critical region defined Definition denote density deviance discussed distribution with p.d.f. efficiency equation example Exercise exponential family F(xl frequentist gamma distribution Gibbs sampling given gives Hence hypothesis testing independent inference interval estimation iterations J. R. Statist jackknife Lemma likelihood function linear models log-likelihood loss function matrix methods minimal sufficient statistic minimax MLRT MVUEs non-parametric normal distribution nuisance parameters null hypothesis observations obtained p-value permutation plot point estimation Poisson distribution possible posterior distribution Pr[X prior distribution probability problems properties quasi-likelihood r.vs random sample randomization test regression residuals result robust score test Section simulation specified standard sufficient statistic Suppose test statistic Theorem trials UMP test unbiased estimator unknown parameters usual values variance vector Wald test