Conditional Kolmogorov test statistic for the marginal distribution of Y

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 Kremling & Dikta (2024) https://arxiv.org/abs/2409.20262 and defined by $$\tilde{\alpha}_n(t) = \frac{1}{\sqrt{n}} \sum_{i=1}^n \left( I_{\{Y_i \le t\}} - F(t|\hat{\vartheta}_n, X_i) \right), \quad -\infty \le t \le \infty.$$

Super class

gofreg::TestStatistic -> CondKolmY

Methods

Public methods

• CondKolmY$calc_stat()

• CondKolmY$clone()

Inherited methods

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

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Method calc_stat()

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

Usage

CondKolmY$calc_stat(data, model)

Arguments

data

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

model

ParamRegrModel to test for, already fitted to the data

Returns

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

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Method clone()

The objects of this class are cloneable with this method.

Usage

CondKolmY$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 <- CondKolmY$new()
ts$calc_stat(data, model)
print(ts)
#> Test statistic with value 0.5057936
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 <- CondKolmY$new()
ts2$calc_stat(data, model2)
print(ts2)
#> Test statistic with value 4.151777
plot(ts2)