| Title: | Nonparametric Bootstrap Test for Regression Monotonicity |
|---|---|
| Description: | Implements nonparametric bootstrap tests for detecting monotonicity in regression functions from Hall, P. and Heckman, N. (2000) <doi:10.1214/aos/1016120363> Includes tools for visualizing results using Nadaraya-Watson kernel regression and supports efficient computation with 'C++'. |
| Authors: | Dylan Huynh [aut, cre] |
| Maintainer: | Dylan Huynh <[email protected]> |
| License: | GPL |
| Version: | 1.0 |
| Built: | 2025-01-17 14:17:29 UTC |
| Source: | CRAN |
Creates a scatter plot of the input vectors and , and overlays
a Nadaraya-Watson kernel regression curve using the specified bandwidth.
create_kernel_plot(X, Y, bandwidth = bw.nrd(X) * (length(X)^-0.1))create_kernel_plot(X, Y, bandwidth = bw.nrd(X) * (length(X)^-0.1))
X |
Vector of x values. |
Y |
Vector of y values. |
bandwidth |
Kernel bandwidth used for the Nadaraya-Watson estimator.
Default is calculated as
|
A ggplot object containing the scatter plot with the kernel regression curve.
Nadaraya, E. A. (1964). On estimating regression. Theory of Probability and Its Applications, 9(1), 141–142.
Watson, G. S. (1964). Smooth estimates of regression functions. Sankhyā: The Indian Journal of Statistics, Series A, 359-372.
# Example 1: Basic plot on quadratic function seed <- 42 set.seed(seed) X <- runif(500) Y <- X ^ 2 + rnorm(500, sd = 0.1) plot <- create_kernel_plot(X, Y, bandwidth = bw.nrd(X) * (length(X) ^ -0.1))# Example 1: Basic plot on quadratic function seed <- 42 set.seed(seed) X <- runif(500) Y <- X ^ 2 + rnorm(500, sd = 0.1) plot <- create_kernel_plot(X, Y, bandwidth = bw.nrd(X) * (length(X) ^ -0.1))
Performs a monotonicity test between the vectors and
as described in Hall and Heckman (2000).
This function uses a bootstrap approach to test for monotonicity
in a nonparametric regression setting.
monotonicity_test( X, Y, bandwidth = bw.nrd(X) * (length(X)^-0.1), boot_num = 200, m = floor(0.05 * length(X)), ncores = 1, negative = FALSE, seed = NULL )monotonicity_test( X, Y, bandwidth = bw.nrd(X) * (length(X)^-0.1), boot_num = 200, m = floor(0.05 * length(X)), ncores = 1, negative = FALSE, seed = NULL )
X |
Numeric vector of predictor variable values. Must not contain missing or infinite values. |
Y |
Numeric vector of response variable values. Must not contain missing or infinite values. |
bandwidth |
Numeric value for the kernel bandwidth used in the
Nadaraya-Watson estimator. Default is calculated as
|
boot_num |
Integer specifying the number of bootstrap samples.
Default is |
m |
Integer parameter used in the calculation of the test statistic.
Corresponds to the minimum window size to calculate the test
statistic over or a "smoothing" parameter. Lower values increase
the sensitivity of the test to local deviations from monotonicity.
Default is |
ncores |
Integer specifying the number of cores to use for parallel
processing. Default is |
negative |
Logical value indicating whether to test for a monotonic
decreasing (negative) relationship. Default is |
seed |
Optional integer for setting the random seed. If NULL (default), the global random state is used. |
The test evaluates the following hypotheses:
: The regression function is monotonic
Non-decreasing if negative = FALSE
Non-increasing if negative = TRUE
: The regression function is not monotonic
A list with the following components:
pThe p-value of the test. A small p-value (e.g., < 0.05) suggests evidence against the null hypothesis of monotonicity.
distThe distribution of test statistic under the null from
bootstrap samples. The length of dist is equal
to boot_num.
statThe test statistic calculated from the original data.
plotA ggplot object with a scatter plot where the points of the
"critical interval" are highlighted. This critical interval
is the interval where is greatest.
intervalNumeric vector containing the indices of the "critical interval".
The first index indicates where the interval starts, and
the second indicates where it ends in the sorted X vector.
For large datasets (e.g., ) this function may require
significant computation time due to having to compute the statistic
for every possible interval. Consider reducing boot_num, using
a subset of the data, or using parallel processing with ncores
to improve performance.
In addition to this, a minimum of 300 observations is recommended for kernel estimates to be reliable.
Hall, P., & Heckman, N. E. (2000). Testing for monotonicity of a regression mean by calibrating for linear functions. The Annals of Statistics, 28(1), 20–39.
# Example 1: Usage on monotonic increasing function # Generate sample data seed <- 42 set.seed(seed) X <- runif(500) Y <- 4 * X + rnorm(500, sd = 1) result <- monotonicity_test(X, Y, boot_num = 25, seed = seed) print(result$p) print(result$stat) print(result$dist) print(result$interval) # Example 2: Usage on non-monotonic function seed <- 42 set.seed(seed) X <- runif(500) Y <- (X - 0.5) ^ 2 + rnorm(500, sd = 0.5) result <- monotonicity_test(X, Y, boot_num = 25, seed = seed) print(result$p) print(result$stat) print(result$dist) print(result$interval)# Example 1: Usage on monotonic increasing function # Generate sample data seed <- 42 set.seed(seed) X <- runif(500) Y <- 4 * X + rnorm(500, sd = 1) result <- monotonicity_test(X, Y, boot_num = 25, seed = seed) print(result$p) print(result$stat) print(result$dist) print(result$interval) # Example 2: Usage on non-monotonic function seed <- 42 set.seed(seed) X <- runif(500) Y <- (X - 0.5) ^ 2 + rnorm(500, sd = 0.5) result <- monotonicity_test(X, Y, boot_num = 25, seed = seed) print(result$p) print(result$stat) print(result$dist) print(result$interval)