test.gaplin {regsubseq}

Detect and Test Almost Gap-Linear Subsequnces.

Description

test.gaplin.t find the most almost gap-linear length k+1 subsequence of a given sequence and compute the almost gap-linearity test statistic for this subsequence. test.gaplin.p compute the p-value corresponding to a computed test statistic. test.gaplin compute the test statistics and the p-values for subsequences of all lengths.

Usage

test.gaplin(Tn);
test.gaplin.t(Tn, k);
test.gaplin.p(t, n, k);

Arguments

Tn

A sequence of numbers. Currently, only support sequence of length less than 50.

k

The length of the subsequences for which we want to test for almost gap-linearity.

n

The length of the sequence for which we want to test for subsequence almost gap-linearity.

t

Test statistic computed for a length k+1 subsequence of a length n+1 sequence.

Details

Almost gap-linear means the spacings of a subsequence are almost in proportion to the spacings of the corresponding indicies. For example, for Tn=c(11, 14, (.), 20), the subs sequence (11, 14, 20) is gap-linear, since the spacings (3, 6) is in proportion with the spacings of hte corresponding indicies (1, 2). Equivalently, almost gap-linearity can measured by the distance between the standardized spacings of the subsequnce and the standardized spacings of the corresponding indicies. See Di and Perlman (2007) for more details.

Value

test.gaplin.t returns the most gap-linear length k+1 subsequence of the input sequence and corresponding almost gap-linearity test statistic. test.gaplin.p returns the p-value corresponding to the input test statistic t. test.lin has no return value, instead, a table containing the most almost gap-linear subsequences, corresponding test staistics and p-values will be outputed.

Author(s)

Yanming Di

References

Di and Perlman, 2007

See Also

test.lin.

Examples

  ## A sequence representing arrival times of events.
  Tn = c(13, 21, 24, 33, 40, 55, 59, 63, 72, 85, 87);

  ## Test for almost linearity.
  t = test.gaplin.t(Tn, 4);
  print(t$sub);
  p = test.gaplin.p(t$t, 10, 4);
  print(p);
  test.gaplin(Tn);