MEP: Marked empirical process test statistic for a given GLM

MEPR Documentation

Marked empirical process test statistic for a given GLM

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 Dikta & Scheer (2021) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/978-3-030-73480-0")} and defined by

\bar{R}^1_n(u) = \frac{1}{\sqrt{n}} \sum_{i=1}^n \left( Y_i - m(X_i, \hat{\beta}_n) \right) I_{\{\hat{\beta}_n X_i \le u\}}, \quad -\infty \le u \le \infty.

Super class

gofreg::TestStatistic -> MEP

Methods

Public methods

Inherited methods

Method calc_stat()

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

Usage
MEP$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
MEP$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 <- MEP$new()
ts$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 <- MEP$new()
ts2$calc_stat(data, model2)
print(ts2)
plot(ts2)

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