Conditional Kolmogorov test statistic for the marginal distribution of Y under random censorship

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 defined by $$\tilde{\alpha}_n^{KM}(t) = \sqrt{n} \left( \hat{F}^{KM}_n(t) - \frac{1}{n} \sum_{i=1}^n F(t|\hat{\vartheta}_n, X_i) \right), \quad -\infty \le t \le \infty.$$

Super class

gofreg::TestStatistic -> CondKolmY_RCM

Methods

Public methods

• CondKolmY_RCM$calc_stat()

• CondKolmY_RCM$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_RCM$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_RCM$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))
c <- rnorm(n, mean(y)*1.2, sd(y)*0.5)
data <- dplyr::tibble(x = x, z = pmin(y,c), delta = as.numeric(y <= c))

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

# Print value of test statistic and plot corresponding process
ts <- CondKolmY_RCM$new()
ts$calc_stat(data, model)
print(ts)
#> Test statistic with value 0.8832506
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, loglik = loglik_xzd)

# Print value of test statistic and plot corresponding process
ts2 <- CondKolmY_RCM$new()
ts2$calc_stat(data, model2)
print(ts2)
#> Test statistic with value 4.557321
plot(ts2)