asm.fit function

Fit a linear regression model via antitonic score matching

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

asm.fit(
  X,
  Y,
  betapilot = "LAD",
  alt_iter = 2,
  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

Returns

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)