scholarly journals PERFORMANCE ANALYSIS AND ROBUSTNESS EVALUATION OF A SEQUENTIAL PROBABILITY RATIO TEST FOR NON-IDENTICALLY DISTRIBUTED OBSERVATIONS

2018 ◽  
Vol 54 (2) ◽  
pp. 179-192
Author(s):  
A. Yu. Kharin ◽  
Ton That Tu
Keyword(s):  
Time Series ◽  
Numerical Approach ◽  
Sequential Probability Ratio Test ◽  
Sequential Test ◽  
Ratio Test ◽  
Probability Ratio ◽  
Test Characteristics ◽  
Sequential Probability ◽  
Recursive Calculation ◽  
Likelihood Ratio Statistics

In this article the problem of a sequential test for the model of independent non-identically distributed observations is considered. Based on recursive calculation a new numerical approach to approximate test characteristics for a sequential probability ratio test (SPRT) and a truncated SPRT (TSPRT) is constructed. The problem of robustness evaluation is also studied when the contamination is presented by the distortion of the distributions of all increments of the log-likelihood ratio statistics. The two-side truncated functions are proposed to be used for constructing the robustified SPRT. An algorithm to choose the thresholds of these truncated functions is indicated. The results are applied for a sequential test on parameters of time series with trend. Some kinds of the contaminated models of time series with trend are used to study the robustness of the truncated SPRT. Numerical examples confirming the theoretical results mentioned above are given.

scholarly journals Sequential probability ratio test for many simple hypotheses on parameters of time series with trend

2019 ◽  
pp. 35-45
Author(s):  
Ton That Tu ◽  
Yu. Kharin
Keyword(s):  
Time Series ◽  
Statistical Tests ◽  
Sufficient Conditions ◽  
Sequential Probability Ratio Test ◽  
Sequential Test ◽  
Stopping Times ◽  
Ratio Test ◽  
Probability Ratio ◽  
Sequential Probability ◽  
Finite Moments

The problem of sequential test for many simple hypotheses on parameters of time series with trend is considered. Two approaches, including M-ary sequential probability ratio test and matrix sequential probability ratio test are used for constructing the sequential test. The sufficient conditions of finite terminations of the test and the existence of finite moments of their stopping times are given. The upper bounds for the average numbers of observations are obtained. With the thresholds chosen suitably, these tests can belong to some specified classes of statistical tests. Numerical examples are presented.

scholarly journals The VPRT: A Sequential Testing Procedure Dominating the SPRT

1993 ◽  
Vol 9 (3) ◽  
pp. 431-450 ◽  
Author(s):  
Noel Cressie ◽  
Peter B. Morgan
Keyword(s):  
Sample Size ◽  
Decision Problem ◽  
Sequential Analysis ◽  
Testing Procedure ◽  
Sequential Probability Ratio Test ◽  
Ratio Test ◽  
Sequential Decision ◽  
Probability Ratio ◽  
Sampling Cost ◽  
Sequential Probability

Under more general assumptions than those usually made in the sequential analysis literature, a variable-sample-size-sequential probability ratio test (VPRT) of two simple hypotheses is found that maximizes the expected net gain over all sequential decision procedures. In contrast, Wald and Wolfowitz [25] developed the sequential probability ratio test (SPRT) to minimize expected sample size, but their assumptions on the parameters of the decision problem were restrictive. In this article we show that the expected net-gain-maximizing VPRT also minimizes the expected (with respect to both data and prior) total sampling cost and that, under slightly more general conditions than those imposed by Wald and Wolfowitz, it reduces to the one-observation-at-a-time sequential probability ratio test (SPRT). The ways in which the size and power of the VPRT depend upon the parameters of the decision problem are also examined.

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