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# Sequential probability ratio test

About: Sequential probability ratio test is a(n) research topic. Over the lifetime, 1248 publication(s) have been published within this topic receiving 22355 citation(s).

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Abstract: By a sequential test of a statistical hypothesis is meant any statistical test procedure which gives a specific rule, at any stage of the experiment (at the n-th trial for each integral value of n), for making one of the following three decisions: (1) to accept the hypothesis being tested (null hypothesis), (2) to reject the null hypothesis, (3) to continue the experiment by making an additional observation. Thus, such a test procedure is carried out sequentially. On the basis of the first trial, one of the three decisions mentioned above is made. If the first or the second decision is made, the process is terminated. If the third decision is made, a second trial is performed. Again on the basis of the first two trials one of the three decisions is made and if the third decision is reached a third trial is performed, etc. This process is continued until either the first or the second decision is made.

1,455 citations

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15 Sep 1999Abstract: INTRODUCTION About This Book Why Sequential Methods A Short History of Sequential and Group Sequential Methods Chapter Organization: A Roadmap Bibliography and Notes TWO-SIDED TESTS: INTRODUCTION Two-Sided Tests for Comparing Two Treatments with Normal Response of Known Variance A Fixed Sample Test Group Sequential Tests Pocock's Test O'Brien and Fleming's Test Properties of Pocock and O'Brien and Fleming Tests Other Tests Conclusions TWO-SIDED TESTS: GENERAL APPLICATIONS A Unified Formulation Applying the Tests with Equal Group Sizes Applying the Tests with Unequal Increments in Information Normal Linear Models Other Parametric Models Binary Data: Group Sequential Tests for Proportions The Group Sequential Log-Rank Test for Survival Data Group Sequential t-Tests ONE-SIDED TESTS Introduction The Power Family of One-Sided Group Sequential Tests Adapting Power Family Tests to Unequal Increments in Information Group Sequential One-Sided t-Tests Whitehead's Triangular Test TWO-SIDED TESTS WITH EARLY STOPPING UNDER THE NULL HYPOTHESIS Introduction The Power Family of Two-Sided, Inner Wedge Tests Whitehead's Double Triangular Test EQUIVALENCE TESTS Introduction One-Sided Tests of Equivalence Two-Sided Tests of Equivalence: Application to Comparative Bioavailability Studies Individual Bioequivalence: A One-Sided Test for Proportions Bibliography and Notes FLEXIBLE MONITORING: THE ERROR SPENDING APPROACH Unpredictable Information Sequences Two-Sided Tests One-Sided Tests Data Dependent Timing of Analyses Computations for Error Spending Tests ANALYSIS FOLLOWING A SEQUENTIAL TEST Introduction Distribution Theory Point Estimation P-Values Confidence intervals REPEATED CONFIDENCE INTERVALS Introduction Example: Difference of Normal Means Derived Tests: Use of RCIs to Aid Early Stopping Decisions Repeated P-Values Discussion STOCHASTIC CURTAILMENT Introduction Conditional Power Approach Predictive Power Approach A Parameter-Free Approach A Case Study with Survival Data Bibliography and Notes GENERAL GROUP SEQUENTIAL DISTRIBUTION THEORY Introduction A Standard Joint Distribution for Successive Estimates of a Parameter Vector Normal Linear Models Normal Linear Models with Unknown Variance: Group Sequential t-Tests Example: An Exact One-Sample Group Sequential t-Test General Parametric Models: Generalized Linear Models Connection with Survival Analysis BINARY DATA A Single Bernoulli Probability Two Bernoulli Probabilities The Odds Ratio and Multiple 2 x 2 Tables Case-Control and Matched Pair Analysis Logistic Regression: Adjusting for Covariates Bibliography and Notes SURVIVAL DATA Introduction The Log Rank Test The Stratified Log-Rank Test Group Sequential Methods for Survival Data with Covariates Repeated Confidence Intervals for a Hazard Ratio Example: A Clinical Trial for Carcinoma of the Oropharynx Survival Probabilities and Quantiles Bibliography and Notes INTERNAL PILOT STUDIES: SAMPLE SIZE RE-ESTIMATION The Role of an Internal Pilot Phase Sample Size Re-estimation for a Fixed Sample Test Sample Size Re-estimation in Group Sequential Tests MULTIPLE ENDPOINTS Introduction The Bonferroni Procedure A Group Sequential Hotelling Test A Group Sequential Version of O'Brien's Test Tests Based on other Global Statistics Tests Based on Marginal Criteria Bibliography and Notes MULTI-ARMED TRIALS Introduction Global Tests Monitoring Pairwise Comparisons Bibliography and Notes ADAPTIVE TREATMENT ASSIGNMENT A Multi-Stage Adaptive Design A Multi-Stage Adaptive Design with Time Trends Validity of Adaptive Multi-Stage Procedures Bibliography and Notes BAYESIAN APPROACHES The Bayesian Paradigm Stopping Rules Choice of Prior Distribution Discussion NUMERICAL COMPUTATIONS FOR GROUP SEQUENTIAL TESTS Introduction The Basic Calculation Error Probabilities and Sample Size Distributions Tests Defined by Error Spending Functions Analysis Following a Group Sequential Test Further Applications of Numerical Computation Computer Software

1,104 citations

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13 Apr 2008TL;DR: This work proposes a new data fusion technique that uses a variable number of samples, and introduces a reputation-based mechanism to the Sequential Probability Ratio Test (SPRT), which is evaluated by comparing it with a variety of data fusion techniques under various network operating conditions.

Abstract: Distributed spectrum sensing (DSS) enables a Cognitive Radio (CR) network to reliably detect licensed users and avoid causing interference to licensed communications. The data fusion technique is a key component of DSS. We discuss the Byzantine failure problem in the context of data fusion, which may be caused by either malfunctioning sensing terminals or Spectrum Sensing Data Falsification (SSDF) attacks. In either case, incorrect spectrum sensing data will be reported to a data collector which can lead to the distortion of data fusion outputs. We investigate various data fusion techniques, focusing on their robustness against Byzantine failures. In contrast to existing data fusion techniques that use a fixed number of samples, we propose a new technique that uses a variable number of samples. The proposed technique, which we call Weighted Sequential Probability Ratio Test (WSPRT), introduces a reputation-based mechanism to the Sequential Probability Ratio Test (SPRT). We evaluate WSPRT by comparing it with a variety of data fusion techniques under various network operating conditions. Our simulation results indicate that WSPRT is the most robust against the Byzantine failure problem among the data fusion techniques that were considered.

551 citations

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01 Jan 1987

Abstract: Randomly Stopped Sequences Random Walks The Sequential Probability Ratio Test Nonlinear Renewal Theory Local Limit Theorems Open-Ended Tests Repeated Significance Tests Multiparameter Problems Estimation Following Sequential Testing Sequential Estimation.

500 citations

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Abstract: This paper considers the problem of testing statistical hypotheses in linear regression models with inequality constraints on the regression coefficients. The Kuhn-Tucker multiplier test statistic is defined and its relationships with the likelihood ratio test and the Wald test are examined. It is shown, in particular, that these relationships are the same as in the equality constrained case. It is emphasized, however, that their common asymptotic distribution is a mixture of chi-square distributions under the null hypothesis.

470 citations