Nonparametric

Nonparametric — selected nonparametric routines

Synopsis

#include <libgretl.h>

int                 spearman_rho                        (const int *list,
                                                         const DATASET *dset,
                                                         gretlopt opt,
                                                         PRN *prn);
int                 kendall_tau                         (const int *list,
                                                         const DATASET *dset,
                                                         gretlopt opt,
                                                         PRN *prn);
double              lockes_test                         (const double *x,
                                                         int t1,
                                                         int t2);
int                 runs_test                           (int v,
                                                         const DATASET *dset,
                                                         gretlopt opt,
                                                         PRN *prn);
int                 diff_test                           (const int *list,
                                                         const DATASET *dset,
                                                         gretlopt opt,
                                                         PRN *prn);
int                 sort_pairs_by_x                     (gretl_matrix *x,
                                                         gretl_matrix *y,
                                                         int **order,
                                                         char **labels);
gretl_matrix *      loess_fit                           (const gretl_matrix *x,
                                                         const gretl_matrix *y,
                                                         int d,
                                                         double q,
                                                         gretlopt opt,
                                                         int *err);

Description

Includes various nonparametric tests: rank correlation, runs (randomness), and differences between series. Also "loess" regression a la William Cleveland.

Details

spearman_rho ()

int                 spearman_rho                        (const int *list,
                                                         const DATASET *dset,
                                                         gretlopt opt,
                                                         PRN *prn);

Calculates and prints Spearman's rank correlation coefficient for the two variables specified in the list.

list :

list of (two) variables to process.

dset :

dataset struct.

opt :

if includes OPT_V, print both the "raw" and the ranked data.

prn :

gretl printing struct.

Returns :

0 on successful completion, 1 on error.

kendall_tau ()

int                 kendall_tau                         (const int *list,
                                                         const DATASET *dset,
                                                         gretlopt opt,
                                                         PRN *prn);

Calculates and prints Kendall's rank correlation tau statistic for the two variables specified in list.

list :

list of (two) variables to process.

dset :

dataset struct.

opt :

if includes OPT_V, print both the "raw" and the ranked data.

prn :

gretl printing struct.

Returns :

0 on successful completion, 1 on error.

lockes_test ()

double              lockes_test                         (const double *x,
                                                         int t1,
                                                         int t2);

Performs Charles Locke's nonparametric test for whether an empirical distribution (namely, that of x over the range t1 to t2) is gamma. See C. Locke, "A Test for the Composite Hypothesis that a Population has a Gamma Distribution," Commun. Statis.-Theor. Meth. A5(4), 351-364 (1976). Also see Shapiro and Chen, Journal of Quality Technology 33(1), Jan 2001.

x :

data series.

t1 :

start of sample range.

t2 :

end of sample range.

Returns :

the z value for test, or NADBL on error.

runs_test ()

int                 runs_test                           (int v,
                                                         const DATASET *dset,
                                                         gretlopt opt,
                                                         PRN *prn);

Performs, and prints the results of, the runs test for randomness for the variable specified by v. The normal approximation is that given in Gary Smith, Statistical Reasoning, 2e, p. 674.

v :

ID number of the variable to process.

dset :

dataset struct.

opt :

OPT_D to use first difference of variable, OPT_E to assume positive and negative are equiprobable.

prn :

gretl printing struct.

Returns :

0 on successful completion, non-zero on error.

diff_test ()

int                 diff_test                           (const int *list,
                                                         const DATASET *dset,
                                                         gretlopt opt,
                                                         PRN *prn);

Performs, and prints the results of, a non-parametric test for a difference between two variables or groups. The specific test performed depends on opt.

list :

list containing 2 variables.

dset :

dataset struct.

opt :

OPT_G, sign test; OPT_R, rank sum; OPT_I, signed rank; OPT_V, verbose (for rank tests).

prn :

gretl printing struct.

Returns :

0 on successful completion, non-zero on error.

sort_pairs_by_x ()

int                 sort_pairs_by_x                     (gretl_matrix *x,
                                                         gretl_matrix *y,
                                                         int **order,
                                                         char **labels);

Orders the elements of x and y by increasing value of x. Optionally, returns in order an array of integers representing the order in which the original observations appear in the sorted vectors. Also optionally sorts an accomanying array of observation labels.

x :

data vector by which to sort.

y :

data vector.

order :

location to receive sort order, or NULL.

labels :

array of strings to be sorted along with the data, or NULL.

Returns :

0 on successful completion, non-zero on error.

loess_fit ()

gretl_matrix *      loess_fit                           (const gretl_matrix *x,
                                                         const gretl_matrix *y,
                                                         int d,
                                                         double q,
                                                         gretlopt opt,
                                                         int *err);

Computes loess estimates based on William Cleveland, "Robust Locally Weighted Regression and Smoothing Scatterplots", Journal of the American Statistical Association, Vol. 74 (1979), pp. 829-836. Typically one expects that d = 1 and q is in the neighborhood of 0.5.

The x,y pairs must be pre-sorted by increasing value of x; an error is flagged if this is not the case. See also sort_pairs_by_x().

x :

x-axis variable (must be pre-sorted).

y :

response variable.

d :

order for polynomial fit (0 <= d <= 2).

q :

bandwidth (0 < q <= 1).

opt :

give OPT_R for robust variant (with re-weighting based on the first-stage residuals).

err :

location to receive error code.

Returns :

allocated vector containing the loess fitted values, or NULL on failure.