Journal of Probability and Statistics / 2016 / Article / Tab 2

Research Article

Estimating the Proportion of True Null Hypotheses in Multiple Testing Problems

Table 2

Monte Carlo empirical estimates with standard deviations (in parentheses) by the new innovative approach along with existing estimators. The Monte Carlo size is 1,000 in each case. Denote for the new estimator, for Storey’s estimator, for Storey’s estimator with , for the convex method estimator, and for the average method estimator.

Estimates of

2000.250.2350.300.5000.3140.430
(0.016)(0.021)(0.035)(0.022)(0.03)
0.50.4890.6130.6600.5840.626
(0.035)(0.043)(0.047)(0.041)(0.044)
0.750.780.7170.790.6850.773
(0.055)(0.051)(0.056)(0.048)(0.054)

5000.250.2490.340.5280.330.491
(0.011)(0.015)(0.024)(0.014)(0.022)
0.50.520.6460.7200.6230.704
(0.023)(0.028)(0.032)(0.027)(0.031)
0.750.720.8060.8600.7850.819
(0.032)(0.036)(0.038)(0.035)(0.035)

10000.250.2420.3930.4820.3490.394
(0.005)(0.012)(0.015)(0.011)(0.013)
0.50.510.610.660.610.63
(0.016)(0.019)(0.021)(0.019)(0.019)
0.750.720.670.860.790.81
(0.023)(0.021)(0.027)(0.025)(0.026)

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