Test of independence in presence of heteroscedastic treatments

Description

NPtest_indept performs the test of independence between the response variable and a single covariate when there is potentially heteroscedastic treatment effects present (see Wang, Tolos and Wang (2010)).

Usage

NPtest_indept(dat, k = 7)

Arguments

Value

A list containing the following variables:

Asys_var: the asymptotic variance for the test statistics

Tstat: the test statistic

pvalue: the p-value of the test under H0: independence between X and Y.

References

Haiyan Wang, Siti Tolos, and Suojin Wang (2010). A Distribution Free Nonparametric Test to Detect Dependence Between a Response Variable and Covariate in Presence of Heteroscedastic Treatment Effects. The Canadian Journal of Statistics. 38(3), 408433. Doi:10.1002/cjs.10068

Examples

n=64;  X=runif(n); trt=gl(2, n/2)
e=rnorm(n, 0, 0.1)
Y=ifelse(trt==1, 4*(X-0.5)^2+e, 2*X+e)
dat=data.frame(X, Y, trt)
NPtest_indept(dat, k=7)

Image structural similarity measure PSSIM based on hypothesis test

Description

PSSIM_snow computes image structural similarity PSSIM of Wang, Maldonado and Silwal (2011) using parallel programming.

Usage

PSSIM_snow(
  A,
  A1,
  nprocess = min(8, parallel::detectCores()),
  b = 64,
  a = 2,
  vs = 32,
  wavecoeff = FALSE,
  cs = 2,
  dyn = FALSE
)

Arguments

Value

: Image structural similarity based on PSSIM. The value is in [0,1] with values close to 0 meaning the two images are different and values close to 1 meaning the two iamges are similar.

References

Haiyan Wang, Diego Maldonado, and Sharad Silwal (2011). A Nonparametric-Test-Based Structural Similarity Measure for Digital Images. Computational Statistics and Data Analysis. 55: 2925-2936. Doi:10.1016/j.csda.2011.04.021

Examples

  A=miniimagematrix$A
  B=miniimagematrix$B
  # see it with image(A, axes=FALSE, col  = gray((0:255)/256) )
  PSSIM_snow(A, B, nprocess=2)

Nearest neighbor augmentatation based on ranks

Description

The function makepseudo performs the nearest neighbor augmentation based on the rank of covariate values according to the scheme discribed on page 410-411 of Wang, Tolos and Wang (2010)

Usage

makepseudo(N, n, k, a, alltrt)

Arguments

Value

A list containing the following: psudo: a 3-d array of the dimension (k, a, N) that stores the augmented observations based on k-nearest neighbor rule in Wang, Tolos and Wang (2010). index: a 3-d array of the dimension (k, a, N) that stores the index of which observation was used for augmentation.

References

Haiyan Wang, Siti Tolos, and Suojin Wang (2010). A Distribution Free Nonparametric Test to Detect Dependence Between a Response Variable and Covariate in Presence of Heteroscedastic Treatment Effects. The Canadian Journal of Statistics. 38(3), 408433. Doi:10.1002/cjs.10068

Examples

 a=2; n=c(7,9); N=sum(n);  X=runif(N);
 trt=c(rep(1,n[1]), rep(2, n[2])); e=rnorm(N, 0, 0.1)
 Y=ifelse(trt==1, 4*(X-0.5)^2+e, 2*X+e)
 ranksuse=unlist(tapply(X, trt, rank) )
 alltrt=rbind(Y, X, ranksuse )
 aug=makepseudo(N,n, k=3, a, alltrt)

Index in one vector mapped to treatment and observation index

Description

Function mapindex() maps the 1-d index r=1,...,N to 2-d index i=1, ...a, j=1, ..., ni. Generally the covariate values from all treatments are stored together in one vector and r=1,...,N enumerates the values. For any integer between 1 and N, mapindex tells which treatment the rth value belongs to, and which observation in the identified treatment.

Usage

mapindex(r, n)

Arguments

Value

the 2-d index, where the first gives which treatment the value belongs to and the second gives which observation in that treatment.

Examples

r=5; n=c(7, 8); mapindex(r, n)
r=7; n=c(7, 8); mapindex(r, n)
r=9; n=c(7, 8); mapindex(r, n)

Mini-image data matrice for example

Description

The matrices are grayscale images in matrix format.

Usage

data(miniimagematrix)

Format

A list with two grayscale image matrices

A

A matrix for one image

B

A matrix for a second image

Examples

 
data(miniimagematrix)
miniimagematrix$A

Starting and ending position in a vector

Description

Function trt_position() gives the starting and ending index of covariate values in the i1th group if all the covariate values from all treatment groups are together in a vector. E.g., covariate values in group 1 start from 1st value to the n1 th value; those in group 2 start from n1+1 and end at (n1+n2)th value. This function is for retrieving the position of an observations when the covariate values from all treatments are stored together in one vector.

Usage

trt_position(i1, n)

Arguments

Examples

i = 2; n=c(7, 8); trt_position(i, n)