| Some basic concepts | p. 1 |
| Introduction | p. 1 |
| Exponential family models | p. 4 |
| Transformation models | p. 7 |
| Cumulants | p. 11 |
| Sufficiency | p. 16 |
| Ancillary statistics | p. 19 |
| Normal distribution theory | p. 22 |
| Discussion and references | p. 23 |
| Exercises | p. 24 |
| Large-sample approximations | p. 27 |
| Introduction | p. 27 |
| Central limit theorem | p. 28 |
| Edgeworth series approximations | p. 31 |
| Saddlepoint approximation of densities | p. 37 |
| Approximation of integrals and sums | p. 40 |
| Saddlepoint approximations for distribution functions | p. 46 |
| Saddlepoint approximations for lattice variables | p. 49 |
| Saddlepoint approximations for multivariate distributions | p. 53 |
| Stochastic asymptotic expansions | p. 54 |
| Approximation of conditional distributions | p. 58 |
| Laplace approximations | p. 66 |
| Discussion and references | p. 68 |
| Exercises | p. 69 |
| Likelihood | p. 73 |
| Introduction | p. 73 |
| Some properties of the likelihood function | p. 75 |
| The likelihood principle | p. 77 |
| Regular models | p. 80 |
| Log-likelihood derivatives | p. 85 |
| Information | p. 88 |
| Methods of inference | p. 96 |
| Discussion and references | p. 100 |
| Exercises | p. 102 |
| First-order asymptotic theory | p. 105 |
| Introduction | p. 105 |
| Maximum likelihood estimates | p. 105 |
| The likelihood ratio statistic | p. 113 |
| The score and Wald statistics | p. 120 |
| Confidence regions | p. 123 |
| The profile likelihood function | p. 126 |
| Nonregular models | p. 129 |
| Discussion and references | p. 133 |
| Exercises | p. 134 |
| Higher-order asymptotic theory | p. 138 |
| Introduction | p. 138 |
| Some preliminary results | p. 138 |
| Maximum likelihood estimates | p. 141 |
| Likelihood ratio statistic | p. 154 |
| Saddlepoint approximations | p. 163 |
| Discussion and references | p. 171 |
| Exercises | p. 172 |
| Asymptotic theory and conditional inference | p. 175 |
| Introduction | p. 175 |
| Log-likelihood derivatives | p. 176 |
| Conditional distribution of maximum likelihood estimates | p. 183 |
| Stable inference | p. 196 |
| Approximation of the conditional model | p. 204 |
| Approximate ancillarity | p. 209 |
| Approximation of sample space derivatives | p. 218 |
| Discussion and references | p. 234 |
| Exercises | p. 235 |
| The signed likelihood ratio statistic | p. 238 |
| Introduction | p. 238 |
| Normalizing transformations | p. 239 |
| One-parameter models | p. 241 |
| Scalar parameter of interest in the presence of a nuisance parameter | p. 248 |
| Approximations to R* | p. 261 |
| Discussion and references | p. 274 |
| Exercises | p. 275 |
| Likelihood functions for a parameter of interest | p. 278 |
| Introduction | p. 278 |
| Conditional likelihood functions | p. 279 |
| Marginal likelihood functions | p. 298 |
| Integrated likelihood functions | p. 306 |
| Inference based on a pseudo-likelihood function | p. 309 |
| Discussion and references | p. 319 |
| Exercises | p. 320 |
| The modified profile likelihood function | p. 323 |
| Introduction | p. 323 |
| Profile likelihood | p. 323 |
| Modified profile likelihood | p. 327 |
| Calculation of the modified profile likelihood without an explicit nuisance paramter | p. 337 |
| Approximations to the modified profile likelihood | p. 340 |
| Discussion and references | p. 352 |
| Exercises | p. 352 |
| Data sets used in the examples | p. 354 |
| References | p. 362 |
| Author index | p. 374 |
| Subject index | p. 377 |
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