Sequential Tests of Statistical Hypotheses.

By R. Khan, B. K. Ghosh. 1972

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Citations in the corpus

Counterfactual reasoning and learning systems: the example of computational advertising (2012, background): “…it is relatively easy to construct convergent sequential design algorithms, reaching the optimal learning performance is notoriously difficult (Wald, 1945) because the selection of parameter θt involves a trade-off between exploitation, that is, the maximization of the immediate reward Y θt ,…”
On the Complexity of Best-Arm Identification in Multi-Armed Bandit Models (2014, background): “) I It is known since Wald (1945 that among the sequential tests such that type and type II error probabilities are both smaller than δ , the Sequential Probability Ratio Test (SPRT) minimizes the expected number of required samples, and is such that E ν [ τ ] = 2 σ 2 / ( µ 1 − µ 2 ) 2 log(1 /δ ).”
Rough Sets: Selected Methods and Applications in Management and Engineering (2012, methodology): “Soft computing is a consortium of methodologies that works synergistically and provides flexible information processing capability for handling real life ambiguous situations [9].”
Time-uniform Chernoff bounds via nonnegative supermartingales (2018, methodology): “Then Ville’s inequality gives a sequential test with valid type I error, equivalent to an open-ended sequential probability ratio test (SPRT, Wald, 1945), in which we stop when the likelihood ratio exceeds an upper threshold, but not when it drops below any lower threshold.”
Uppaal SMC tutorial (2015, methodology): “The above test can be solved by using Wald’s sequential hypothesis testing [40].”
Item Response Theory—A Statistical Framework for Educational and Psychological Measurement (2021, unknown): “…experimental design problem in the literature of sequential analysis, where the former dates back to Wald’s pioneer works on sequential testing (Wald, 1945; Wald and Wolfowitz, 1948) and the latter dates back to Chernoﬀ’s seminal works on sequential experimental design (Chernoﬀ, 1959, 1972).”
Optimal Design of a CUSUM Chart for a Mean Shift of Unknown Size (2010, methodology): “The second line of the above equation can be justified by Wald’s equation (Wald (1945)).”
Uniform, nonparametric, non-asymptotic confidence sequences (2018, methodology): “…mixtures yield closed-form or efficiently computable curved boundaries; this approach is known as the method of mixtures, one of the most widely-studied techniques for constructing uniform bounds (Ville, 1939; Wald, 1945; Darling and Robbins, 1968; Robbins, 1970; Robbins and Siegmund, 1969, 1970).”
crowdsourcing : rating annotators and obtaining cost-effective labels (2010, unknown): “In this case, the stopping criterion is equivalent to Wald’s stopping rule for accepting or rejecting the null hypothesis in the Sequential Probability Ratio Test (SPRT) [13].”
When power analyses based on pilot data are biased: Inaccurate effect size estimators and follow-up bias (2018, methodology): “For a frequentist introduction of sequential analysis, see Lakens (2014), for a Bayesian introduction, see Schönbrodt, Wagenmakers, Zehetleitner, and Perugini (2017), for the mathematical background, see Wald (1945), and Siegmund (2013).”
Spontaneous Dynamics of Asymmetric Random Recurrent Spiking Neural Networks (2004, background): “It leads that : We are now able to retrieve the variance of X t ( second Wald’s identity ) : More generally the moment generating function can be recursively computed :”
Martingales in Sequential Analysis and Time Series, 1945-1985 ∗ (2009, methodology): “Alternative approaches that were used subsequently include analytic methods based on the strong Markov property and the fluctuation theory of random walks; see Ghosh (1970), Siegmund (1985) and Woodroofe (1982).”
Learning in Nonstationary Environments: A Survey (2015, background): “Examples of SHTs are the sequential probability ratio test [60] and the repeated significance test [61].”
Kullback–Leibler upper confidence bounds for optimal sequential allocation (2012, background): “…bandit was probably coined in the late 1960s [Gittins (1979)], the origin of the problem can be traced back to fundamental questions about optimal stopping policies in the context of clinical trials [see Thompson (1933, 1935)] raised since the 1930s; see also Wald (1945), Robbins (1952).”