Principles of Statistical Inference

By D. R. Cox. 2006

593 citations recorded by the source corpus.

Preface 1. Preliminaries 2. Some concepts and simple applications 3. Significance tests 4. More complicated situations 5. Some interpretational issues 6. Asymptotic theory 7. Further aspects of maximum likelihood 8. Additional objectives 9. Randomization-based analysis Appendix A. A brief history Appendix B. A personal view References Author index Index.

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Citations in the corpus

Software Intensive Science (2014, background): “Indeed, it is more than difficult to imagine a modern scientific discipline in which CSIT could not play some role in characterizing the distribution of error (Good 1983; Cox 2006; Mayo and Spanos 2011).”
Detection of Item Preknowledge Using Likelihood Ratio Test and Score Test (2017, methodology): “…alternative hypothesis in our case is one sided as discussed earlier, it is more appropriate to use the signed score statistic (Cox & Hinkley, 1974, Cox, 2006, p. 104), which, in our context, is given by: Rs ¼ ffiffiffi R p if ŷs ŷ s; ffiffiffi R p if ŷs < ŷ s ( ð5Þ A large value of Rs (that…”
Inflated beta distributions (2007, background): “Hence, the parameters are separable (Pace & Salvan, 1997, p. 128) and maximum likelihood inference for (µ, φ) can be performed separately from that for α, as if the value of α were known, and vice-versa.”
The Bayesian New Statistics: Hypothesis testing, estimation, meta-analysis, and power analysis from a Bayesian perspective (2017, unknown): “The most general definition of a confidence interval, which applies to all models and situations, is the following (e.g., Cox, 2006, p. 40): The 95 % confidence interval of a parameter contains all the values of the parameter that would not be rejected by p .05.”
Final Collapse of the Neyman-Pearson Decision Theoretic Framework and Rise of the neoFisherian (2009, background): “Indeed, Cox (2006a: 43, 195) has noted that " the differences between Fisher and Neyman … were not nearly as great as the asperity of the arguments between them might suggest … [and in] actual practice … Neyman … often reported p-values whereas some of Fisher's use of tests … was much more…”
Sustaining the Internet with Hyperbolic Mapping (2010, unknown): “In statistical inference [24], this goal is equivalent to maximising the likelihood that the observed data, i.e., the Internet topology, has been produced by the model.”
Rejecting or Accepting Parameter Values in Bayesian Estimation (2018, unknown): “…decision rule follows naturally from the meanings of the confidence interval and ROPE: The confidence interval is the range of parameter values that are not rejected (e.g., Cox, 2006), and if all the unrejected values fall within the ROPE, then they are all practically equivalent to the null value.”
Testing environmental and genetic effects in the presence of spatial autocorrelation (2014, background): “…however, all inferences are conditional on the realized values of the design matrix X, that is the set of xis for all positions (Davison 2003, p. 648; Cox 2006, p. 46), and therefore the GLMM analysis makes no assumption whether the elements of X are conceived as correlated random variables or not.”
LOPSIDED REASONING ON LOPSIDED TESTS AND MULTIPLE COMPARISONS (2012, background): “…Publishing Association Inc. hypothesis-testing and the completely unnecessary fixing of α-levels for the conduct and interpretation of significance tests or assessments (e.g. Cox 1958, 2006, pp. 36, 70, 162, 198; Eysenck 1960; Altman 1991, p. 168; Christensen 2005; Hurlbert & Lombardi 2009).”
A Kenward-Roger approximation and parametric bootstrap methods for tests in linear mixed models: The R Package pbkrtest (2014, methodology): “The idea behind adjusting the LR test statistic by a Bartlett type correction as in TB = T E∗T /d is to obtain a a statistic whose distribution becomes closer to a χ2d distribution (cfr. Cox 2006, p. 130).”
PROBABILITY DISTRIBUTIONS WITH SUMMARY GRAPH STRUCTURE (2010, methodology): “Such smooth models are curved exponential families (see Cox (2006), Section 6.8) so that they have desirable properties regarding estimation and asymptotic properties of tests.”