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Simulated integrated conditional moment test statistic

Source: R/SICM.R
SICM.Rd

This class inherits from TestStatistic and implements a function to calculate the test statistic (and x-y-values that can be used to plot the underlying process).

The process underlying the test statistic is given in Bierens & Wang (2012) doi:10.1017/S0266466611000168 and defined by $$\hat{T}_n^{(s)}(c) = \frac{1}{(2c)^{p+1}} \int_{[-c,c]^p} \int_{-c}^c \left|\frac{1}{\sqrt{n}} \sum_{j=1}^n \Big(\exp(i \tau Y_j) - \exp(i \tau \tilde{Y}_j)\Big) \exp(i \xi^T X_j)\right|^2 d\tau d\xi $$

Super class

gofreg::TestStatistic -> SICM

Methods

Public methods

Inherited methods

Method new()

Initialize an instance of class SICM.

Usage

SICM$new(
  c,
  transx = function(values) {
     tvals <- atan(scale(values))
     tvals[,
    apply(values, 2, sd) == 0] <- 0
     return(tvals)
 },
  transy = function(values, data) {
     array(atan(scale(values, center = mean(data$y),
    scale = sd(data$y))))
 }
)

Arguments

c

chosen value for integral boundaries (see Bierens & Wang (2012))

transx

function(values) used to transform x-values to be standardized and bounded; default is standardization by subtracting the mean and dividing by the standard deviation and then applying arctan

transy

function(values, data) used to transform y-values to be standardized and bounded (same method is used for simulated y-values); default is standardization by subtracting the mean and dividing by the standard deviation and then applying arctan

Returns

a new instance of the class

Method calc_stat()

Calculate the value of the test statistic for given data and a model to test for.

Usage

SICM$calc_stat(data, model)

Arguments

data

data.frame() with columns x and y containing the data

model

ParamRegrModel to test for

Returns

The modified object (self), allowing for method chaining.

Method clone()

The objects of this class are cloneable with this method.

Usage

SICM$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

# Create an example dataset
n <- 100
x <- cbind(runif(n), rbinom(n, 1, 0.5))
model <- NormalGLM$new()
y <- model$sample_yx(x, params=list(beta=c(2,3), sd=1))
data <- dplyr::tibble(x = x, y = y)

# Fit the correct model
model$fit(data, params_init=list(beta=c(1,1), sd=3), inplace = TRUE)

# Print value of test statistic and plot corresponding process
ts <- SICM$new(c = 5)
ts$calc_stat(data, model)
print(ts)
#> Test statistic with value 0.4004599
plot(ts)
#> `geom_line()`: Each group consists of only one observation.
#> ℹ Do you need to adjust the group aesthetic?


# Fit a wrong model
model2 <- NormalGLM$new(linkinv = function(u) {u+10})
model2$fit(data, params_init=list(beta=c(1,1), sd=3), inplace = TRUE)

# Print value of test statistic and plot corresponding process
ts2 <- SICM$new(c = 5)
ts2$calc_stat(data, model2)
print(ts2)
#> Test statistic with value 10.79171
plot(ts2)
#> `geom_line()`: Each group consists of only one observation.
#> ℹ Do you need to adjust the group aesthetic?