bias_AND_scaledvar: Estimators of Bias and Scaled Variance

Description Usage Arguments Details Value References Examples

Description

“Workhorse” function for vectorized (in σ) computation of both the bias estimator and the scaled variance estimator of eq. (2.3) in Srihera & Stute (2011), and for the analogous computation of the bias and scaled variance estimator for the rank transformation method in the paragraph after eq. (6) in Eichner & Stute (2013).

Usage

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bias_AND_scaledvar(sigma, Ai, Bj, h, K, fnx, ticker = FALSE)

Arguments

sigma

Numeric vector (σ_1, …, σ_s) with s ≥ 1.

Ai

Numeric vector expecting (x_0 - X_1, …, x_0 - X_n) / h, where (usually) x_0 is the point at which the density is to be estimated for the data X_1, …, X_n with h = n^{-1/5}.

Bj

Numeric vector expecting (-J(1/n), …, -J(n/n)) in case of the rank transformation method, but (\hat{θ} - X_1, …, \hat{θ} - X_n) in case of the non-robust Srihera-Stute-method. (Note that this the same as argument Bj of adaptive_fnhat!)

h

Numeric scalar, where (usually) h = n^{-1/5}.

K

Kernel function with vectorized in- & output.

fnx

f_n(x_0) = mean(K(Ai))/h, where here typically h = n^{-1/5}.

ticker

Logical; determines if a 'ticker' documents the iteration progress through sigma. Defaults to FALSE.

Details

Pre-computed f_n(x_0) is expected for efficiency reasons (and is currently prepared in function adaptive_fnhat).

Value

A list with components BiasHat and VarHat.scaled, both numeric vectors of same length as sigma.

References

Srihera & Stute (2011) and Eichner & Stute (2013): see kader.

Examples

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require(stats)

set.seed(2017);     n <- 100;     Xdata <- sort(rnorm(n))
x0 <- 1;      Sigma <- seq(0.01, 10, length = 21)

h <- n^(-1/5)
Ai <- (x0 - Xdata)/h
fnx0 <- mean(dnorm(Ai)) / h   # Parzen-Rosenblatt estimator at x0.

 # non-robust method:
Bj <- mean(Xdata) - Xdata
# # rank transformation-based method (requires sorted data):
# Bj <- -J_admissible(1:n / n)   # rank trafo

kader:::bias_AND_scaledvar(sigma = Sigma, Ai = Ai, Bj = Bj, h = h,
  K = dnorm, fnx = fnx0, ticker = TRUE)

kader documentation built on May 1, 2019, 10:13 p.m.