Package {NPFD}

Construct a Sample from Replicated Mixed Measurements

Description

Constructs a sample from paired replicated measurements by taking their scaled differences.

Usage

createSample(z1, z2)

Arguments

Details

Suppose that paired observations satisfy z_1 = x_1 + y and z_2 = x_2 + y, where the same realization of y is contained in both measurements. Then

\frac{z_1-z_2}{\sqrt{2}} = \frac{x_1-x_2}{\sqrt{2}},

so that the common component y is removed.

If x_1 and x_2 are identically distributed and independent, the resulting sample is centered at zero. If they additionally have finite variance \sigma^2, the scaled difference has variance \sigma^2.

Value

A numeric vector containing (z_1-z_2)/\sqrt{2}.

Examples

# Set seed for reproducibility
set.seed(123)

# Generate random data
x1 <- rnorm(1000)
x2 <- rnorm(1000)
y <- rgamma(1000, 10, 2)
z1 <- x1 + y
z2 <- x2 + y

# Use createSample to generate a sample
x <- createSample(z1, z2)

# Perform density estimation
f.x <- stats::density(x, adjust = 1.5)
x.x <- f.x$x
f <- dnorm(x.x)

# Plot the results
plot(NULL, xlim = range(f.x$x), ylim = c(0, max(f, f.x$y)), xlab = "x", ylab = "Density")
lines(x.x, f, col = "blue", lwd = 2)
lines(f.x, col = "orange", lwd = 2)
legend("topright", legend = c(expression(f), expression(f[x])), col = c("blue", "orange"), lwd = 2)

N-Power Fourier Deconvolution

Description

Estimates the density f_y, given vectors x and z, where f_z results from the convolution of f_x and f_y.

Usage

deconvolve(
  x = NULL,
  z,
  mode = c("empirical", "denspr"),
  dfx = 5,
  dfz = 5,
  Lx = 100,
  Lz = 100,
  Ly = 100,
  ymin = NULL,
  ymax = NULL,
  N = 1:100,
  FT.grid = seq(0, 100, 0.1),
  lambda = 1,
  eps = 10^-3,
  delta = 10^-2,
  error = c("unknown", "normal", "laplacian"),
  sigma = NULL,
  calc.error = FALSE,
  plot = FALSE,
  legend = TRUE,
  positive = FALSE
)

Arguments

Value

A list with the following components:

Author(s)

Akin Anarat akin.anarat@hhu.de

References

Anarat, A., Krutmann, J., and Schwender, H. (2026). A nonparametric statistical method for deconvolving densities in the analysis of proteomic data. BMC Bioinformatics, 27(1), 83. doi:10.1186/s12859-026-06408-0

Examples

# Deconvolution when mixed data and data from an independent experiment are provided:
set.seed(123)
x <- rnorm(1000)
y <- rgamma(1000, 10, 2)
z <- x + y

f <- function(x) dgamma(x, 10, 2)

independent.x <- rnorm(100)

fy.NPFD <- deconvolve(independent.x, z, calc.error = TRUE, plot = TRUE)
x.x <- fy.NPFD$x
fy <- f(x.x)

# Check power and error values
fy.NPFD$N
fy.NPFD$error

# Plot density functions
plot(NULL, xlim = range(y), ylim = c(0, max(fy, fy.NPFD$y)), xlab = "x", ylab = "Density")
lines(x.x, fy, col = "blue", lwd = 2)
lines(fy.NPFD, col = "orange", lwd = 2)
legend("topright", legend = c(expression(f[y]), expression(f[y]^{NPFD})),
       col = c("blue", "orange"), lwd = c(2, 2))

# For replicated mixed data:
set.seed(123)
x1 <- VGAM::rlaplace(1000, 0, 1/sqrt(2))
x2 <- VGAM::rlaplace(1000, 0, 1/sqrt(2))
y <- rgamma(1000, 10, 2)
z1 <- z <- x1 + y
z2 <- x2 + y

x <- createSample(z1, z2)

fy.NPFD <- deconvolve(x, z, mode = "denspr", calc.error = TRUE, plot = TRUE)
x.x <- fy.NPFD$x
fy <- f(x.x)

# Check power and error values
fy.NPFD$N
fy.NPFD$error

# Plot density functions
plot(NULL, xlim = range(y), ylim = c(0, max(fy, fy.NPFD$y)), xlab = "x", ylab = "Density")
lines(x.x, fy, col = "blue", lwd = 2)
lines(fy.NPFD, col = "orange", lwd = 2)
legend("topright", legend = c(expression(f[y]), expression(f[y]^{NPFD})),
       col = c("blue", "orange"), lwd = c(2, 2))

# When the distribution of x is asymmetric and the sample size is very small:
set.seed(123)
x <- rgamma(5, 4, 2)
y <- rgamma(1000, 10, 2)
z <- x + y

fy.NPFD <- deconvolve(x, z, mode = "empirical", lambda = 2)
x.x <- fy.NPFD$x
fy <- f(x.x)

# Check power value
fy.NPFD$N

# Plot density functions
plot(NULL, xlim = range(y), ylim = c(0, max(fy, fy.NPFD$y)), xlab = "x", ylab = "Density")
lines(x.x, fy, col = "blue", lwd = 2)
lines(fy.NPFD, col = "orange", lwd = 2)
legend("topright", legend = c(expression(f[y]), expression(f[y]^{NPFD})),
       col = c("blue", "orange"), lwd = c(2, 2))

Spline-Based Density Estimation

Description

Estimates a probability density by fitting a Poisson generalized linear model with natural splines to histogram counts.

Usage

densprf(
  x,
  n.interval = NULL,
  df = 5,
  knots.mode = TRUE,
  type.nclass = c("wand", "scott", "FD"),
  addx = FALSE
)

Arguments

Details

densprf is a modification of the denspr function from the siggenes package. In contrast to denspr, the function returns a function that can be evaluated at arbitrary positions.

The number of histogram intervals is either specified through n.interval or determined automatically. The Poisson regression fit is subsequently normalized to obtain a density estimate.

Value

A function that takes a numeric vector of evaluation points and returns the estimated density at these points.

Examples

# Set seed for reproducibility
set.seed(123)

# Generate random data
z <- rnorm(1000)

# Apply densprf function
f <- densprf(z)

# Define sequences for evaluation
x1 <- seq(-4, 4, 0.5)
x2 <- seq(-5, 5, 0.1)

# Evaluate the density function at specified points
f1 <- f(x1)
f2 <- f(x2)