Univariate_Score_function: Graphical plots to assess the univarite noramality assumption...

In PlotNormTest: Graphical Univariate/Multivariate Assessments for Normality Assumption

Graphical plots to assess the univarite noramality assumption of data.

Description

Score function of a univariate normal distribution is a straight line. A non-linear graph of score function estimator shows evidence of non-normality.

Outliers are detected using the 2-sigma bands method.

Usage

cox(x, P = NULL, lambda = 0.5, x.dist = NULL)

score_plot1D(x, P = NULL, lambda = 0.5, x.dist = NULL, ori.index = NULL)

Arguments

x	univariate data.
P	vector of weight.
lambda	smoothing parameter, default is 0.5.
x.dist	the minimum distance between two data points in vector x.
ori.index	original index of vector x, default is NULL when index is just the order.

Details

To avoid the singularity of coefficient matrices in spline method, points with distance less than x.dist are merged and weight of the representative points is updated by the summation of weight of discarded points.

Under null hypothesis, a unbiased estimator score function of a given data point x_k is

\hat{\psi}(x_k) = \dfrac{n - 4}{n - 2} \dfrac{x_k - \bar{X}_{-k}}{S_{-k}^2}

and if a_{k} is the estimate score from function cox at the point x_k, then

a_k\in \hat{\psi}(x_k) \pm 2 \sqrt{\hat{\text{Var}}(\hat{\psi}(x_k))}.

Hence points outside the 2-sigma bands are outliers.

Value

cox returns the estimate of score function.

• x: The updated univariate data if merging happens.

• a: Score value estimated at x.

• P: Updated weight (if merging happens).

• slt: Index of merged data point (is NULL if x.dist = NULL).

score_plot1D returns score functions together with 2-sigma bands for outlier detection.

• plot: plot of estimate score function and its band.

• outlier: index of outliers.

References

\insertRef

ref:sp_estimatePlotNormTest

Examples

set.seed(1)
x <- rnorm(100, 2, 4)
re <- cox(sort(x))
plot(re$x, re$a, xlab = "x", ylab = "Estimated Score",
 main = "Estimator of score function")
abline(0, 1)

set.seed(1)
x <- rnorm(100, 2, 4)
score_plot1D(sort(x))

PlotNormTest documentation built on April 12, 2025, 9:14 a.m.