constructSequentialTest {CVST}

Construct and Handle Sequential Tests.

Description

These functions handle the construction and calculation with sequential tests as introduced by Wald (1947). getCVSTTest constructs a special sequential test as introduced in Krueger (2011). testSequence test a sequence of 0/1 whether it is distributed according to H0 or H1.

Usage

constructSequentialTest(piH0 = 0.5, piH1 = 0.9, beta, alpha)
getCVSTTest(steps, beta = 0.1, alpha = 0.01)
testSequence(st, s)
plotSequence(st, s)

Arguments

piH0

Probability of the binomial distribution for H0.

piH1

Probability of the binomial distribution for H1.

beta

Significance level for H0.

alpha

Significance level for H1.

steps

Number of steps the CVST procedure should be executed.

st

A sequential test of type CVST.sequentialTest.

s

A sequence of 0/1 values.

Value

constructSequentialTest and getCVSTTest return a CVST.sequentialTest with the specified properties. testSequence returns 1, if H1 can be expected, -1 if H0 can be accepted, and 0 if the test needs more data for a decission. plotSequence gives a graphical impression of the this testing procedure.

Author(s)

Tammo Krueger <[e-mail]>

References

Abraham Wald. Sequential Analysis. Wiley, 1947.

Tammo Krueger, Danny Panknin, and Mikio Braun. Fast cross-validation via sequential testing. Journal of Machine Learning Research 16 (2015) 1103-1155. URL https://jmlr.org/papers/volume16/krueger15a/krueger15a.pdf.

See Also

fastCV

Examples

st = getCVSTTest(10)
s = rbinom(10,1, .5)
plotSequence(st, s)
testSequence(st, s)