## Selected Statistical Papers of Sir David Cox: Volume 2, Foundations of Statistical Inference, Theoretical Statistics, Time Series and Stochastic ProcessesSir David Cox is one of the seminal statistical thinkers of the twentieth and twenty-first centuries. In this selection of his work, Professor Cox reviews his most influential and interesting papers published before 1993. Each paper is the subject of a candid commentary written especially for this collection. In these he describes the context in which the papers arose and their subsequent influence. He also identifies avenues for future research. Organized in two volumes and grouped by theme, the papers and commentaries provide excellent coverage of many of the most significant advances in statistics in recent times. |

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### Contents

Commentaries | 3 |

Original papers | 9 |

Original papers | 13 |

F2 The choice between alternative ancillary statistics | 25 |

F3 The role of significance tests | 31 |

D3 The use of a concomitant variable in selecting an experimental design | 35 |

D4 The use of control observations as an alternative to incomplete block designs | 45 |

F4 Statistical significance tests | 47 |

Effective degrees of freedom and the likelihood ratio test | 227 |

The effect of sampling rules on likelihood statistics | 235 |

Two new tests associated with analysis of variance with A Azzalini | 253 |

Th17 Barlett adjustments to the likelihood ratio statistic and the distribution of | 263 |

Some general aspects of the theory of statistics | 277 |

Th19 Invariants and likelihood ratio statistics with P McCullagh | 287 |

Th20 Approximations to noncentral distributions with N Reid | 299 |

Th21 Parameter orthogonality and approximate conditional inference | 307 |

D5 Some systematic supersaturated designs with K H V Booth | 53 |

the case for eclecticism | 55 |

some personal views Design | 61 |

F6 Theory and general principle in statistics | 69 |

D7 A note on design when response has an exponential family distribution | 71 |

F7 Role of models in statistical analysis | 75 |

D9 Some sampling problems in technology | 80 |

some statistical aspects | 81 |

Commentaries | 95 |

D10 On sampling and the estimation of rare errors with E J Snell | 103 |

Original papers | 107 |

Statistical Methods | 111 |

Th2 Further results on tests of separate families of hypotheses | 127 |

Th3 Fiellers theorem and a generalization | 147 |

Th4 A note on the efficiency of leastsquares estimates | 153 |

Thi The continuity correction | 159 |

Th7 A note on datasplitting for the evaluation of significance levels | 171 |

Th9 A note on partially Bayes inference and the linear model | 183 |

Th11 Edgeworth and saddlepoint approximations with statistical | 191 |

Th12 Local ancillarity | 213 |

Th22 An approximation to maximum likelihood estimates in reduced models | 329 |

Commentaries | 347 |

some recent developments | 361 |

a review | 379 |

TS4 Longrange dependence nonlinearity and time irreversibility | 399 |

Commentaries | 409 |

Original papers | 417 |

SP2 On the superposition of renewal processes with W L Smith | 429 |

SP3 A use of complex probabilities in the theory of stochastic processes | 439 |

SP4 The analysis of nonMarkovian stochastic processes by the inclusion | 454 |

SP6 A low traffic approximation for queues with P Bloomfield | 469 |

SP7 A bivariate point process connected with electronic counters | 479 |

SP8 The virtual waitingtime and related processes with V Isham | 491 |

Applications | 511 |

SP9 Spatial modelling of total storm rainfall with I RodriguezIturbe | 514 |

568 | |

Acknowledgements | 587 |

Acknowledgements | 589 |

### Common terms and phrases

analysis ancillary statistic applications argument asymptotic Barndorff-Nielsen Bartlett adjustment Bayesian Biometrika calculation causal cell censoring chi-squared coefficient components conditional distribution confidence intervals consider constant corresponding covariance matrix cumulants D. R. COX defined degrees of freedom denote density derived discussion Edgeworth effect empirical equation example expansion explanatory variables exponential distribution exponential family follows formulation gamma distribution given gives Hinkley independent interpretation J. R. Statist likelihood function likelihood ratio statistic log likelihood long-range dependence Markov mathematical maximum likelihood estimates mean square error methods multivariate normal distribution Note nuisance parameters null hypothesis observed obtained orthogonal paper particular Poisson distribution Poisson process possible prior distribution probability problem procedure profile likelihood properties qualitative random variables regression saddle-point approximation sample second-order Section significance tests simple statistical inference stochastic Suppose test statistic theoretical theory tion transformation unknown parameters values variance vector zero

### Popular passages

Page 566 - The effect of skewness of the frequency distribution on the relationship between required test factors and strength variation. Selected Government Research Reports 6, 39-49. Cox, DR