asm.fit {asm}

Fit a linear regression model via antitonic score matching

Description

Performs linear regression via M-estimation with respect to a data-driven convex loss function

Usage

asm.fit(
  X,
  Y,
  betapilot = "OLS",
  alt_iter = 1,
  intercept.selection = "mean",
  k = 3000,
  max_iter = 65,
  kernel_pts = 2^15,
  bw = "nrd0",
  kernel = "gaussian",
  verbose = FALSE,
  ...
)

Arguments

X

design matrix

Y

response vector

betapilot

initial estimate of the regression coefficients: can be "LAD", "OLS" or a vector of coefficients

alt_iter

number of iterations of the alternating procedure: when alt_iter == 1, this function is equivalent to asm_regression

intercept.selection

mean or median of the residuals if intercept.selection == "median", then the standard error of the intercept estimate is set to NA

k

the density quantile function is evaluated at (0, 1/k, 2/k, ..., 1)

max_iter

maximum number of iterations for the damped Newton–Raphson algorithm when minimizing the convex loss function

kernel_pts

number of points at which the kernel density estimate is evaluated, i.e. the parameter "n" in density()

bw

bandwidth for kernel density estimation i.e. the parameter "bw" in density()

kernel

kernel for kernel density estimation i.e. the parameter "kernel" in density()

verbose

logical; if TRUE, print optimization progress

...

additional arguments to ensure compatibility with generic functions

Value

asm class object containing the following components:

betahat:

vector of estimated coefficients

std_errs:

vector of standard errors of the estimated coefficients

fitted.values:

fitted values

residuals:

residuals

zvals:

z-values

sig_vals:

p-values

info_asm:

antitonic information

I_mat:

estimated antitonic information matrix

Cov_mat:

asymptotic covariance matrix of the estimated coefficients

psi:

estimated antitonic score function

Examples

n <- 1000 ; d <- 2
X <- matrix(rnorm(n * d), n, d)
Y <- X %*% c(2, 3) + rnorm(n) # no intercept!
asm.fit(X,Y)