select_h {QuadratiK}

Select the value of the kernel tuning parameter

Description

This function computes the kernel bandwidth of the Gaussian kernel for the normality, two-sample and k-sample kernel-based quadratic distance (KBQD) tests.

Usage

select_h(
  x,
  y = NULL,
  alternative = NULL,
  method = "subsampling",
  b = 0.8,
  B = 100,
  delta_dim = 1,
  delta = NULL,
  h_values = NULL,
  Nrep = 50,
  n_cores = 2,
  Quantile = 0.95,
  power.plot = TRUE
)

Arguments

x

Data set of observations from X.

y

Numeric matrix or vector of data values. Depending on the input y, the selection of h is performed for the corresponding test.

• if y = NULL, the function performs the tests for normality o n x

• if y is a data matrix, with same dimensions of x, the function performs the two-sample test between x and y.

• if y if a numeric or factor vector, indicating the group memberships for each observation, the function performs the k-sample test.

alternative

Family of alternative chosen for selecting h, between "location", "scale" and "skewness".

method

The method used for critical value estimation ("subsampling", "bootstrap", or "permutation").

b

The size of the subsamples used in the subsampling algorithm .

B

The number of iterations to use for critical value estimation, B = 150 as default.

delta_dim

Vector of coefficient of alternative with respect to each dimension

delta

Vector of parameter values indicating chosen alternatives

h_values

Values of the tuning parameter used for the selection

Nrep

Number of bootstrap/permutation/subsampling replications.

n_cores

Number of cores used to parallel the h selection algorithm (default:2).

Quantile

The quantile to use for critical value estimation, 0.95 is the default value.

power.plot

Logical. If TRUE, it is displayed the plot of power for values in h_values and delta.

Details

The function performs the selection of the optimal value for the tuning parameter h of the normal kernel function, for normality test, the two-sample and k-sample KBQD tests. It performs a small simulation study, generating sample according to the family of alternative specified, for the chosen values of h_values and delta.

Value

A list with the following attributes:

• h_sel the selected value of tuning parameter h;

• power matrix of power values computed for the considered values of delta and h_values;

• power.plot power plots (if power.plot is TRUE).

References

Markatou, M., Saraceno, G., Chen, Y. (2023). “Two- and k-Sample Tests Based on Quadratic Distances.” Manuscript, (Department of Biostatistics, University at Buffalo)

Examples

# Select the value of h using the mid-power algorithm

x <- matrix(rnorm(100),ncol=2)
y <- matrix(rnorm(100),ncol=2)
h_sel <- select_h(x,y,"skewness")
h_sel