test.lin {regsubseq}

Detect and Test Almost Linear Subsequences.

Description

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

Usage

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

Arguments

Tn

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

k

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

n

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

t

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

Details

Almost-linear means the spacings of the sequence are almost equal, or the distance between the standardized spacings as a vector and (1/k, ..., 1/k) is too small. The p-value is computed by comparing the test statistic to a procomputed test statistic quantile table. See Di and Perlman (2007) for more details.

Value

test.lin.t returns the most linear length k+1 subsequence of the input sequence and corresponding almost-linearity test statistic. test.lin.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 linear subsequences, corresponding test staistics and p-values will be outputed.

Author(s)

Yanming Di

References

Di and Perlman, 2007

See Also

test.gaplin.

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.lin.t(Tn, 4);
  print(t$sub);
  p = test.lin.p(t$t, 10, 4);
  print(p);
  test.lin(Tn);