SICM: Simulated integrated conditional moment test statistic

In gofreg: Bootstrap-Based Goodness-of-Fit Tests for Parametric Regression

Simulated integrated conditional moment test statistic

Description

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) \Sexpr[results=rd]{tools:::Rd_expr_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

• SICM$new()

• SICM$calc_stat()

• SICM$clone()

Inherited methods

• gofreg::TestStatistic$geom_ts_proc()
• gofreg::TestStatistic$get_plot_xy()
• gofreg::TestStatistic$get_value()
• gofreg::TestStatistic$plot()
• gofreg::TestStatistic$print()

---

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)
plot(ts)

# 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)
plot(ts2)

gofreg documentation built on Oct. 4, 2024, 5:10 p.m.