mcmc_h: MH Sampler of the Proposal Distribution of...

In omkarakatta/ivqr: Instrumental Variables Quantile Regression

MH Sampler of the Proposal Distribution of Coefficients/Active Bases

Description

The proposal distribution Q_beta is the asymptotic distribution of the IQR estimator limited to the finite support of possible solutions enumerated by the active basis. This MH sampler returns draws from the proposal distribution by

Usage

mcmc_h(
  iterations,
  h_opt,
  beta_D_opt,
  beta_X_opt,
  residuals_opt,
  theta,
  varcov_mat,
  Y,
  X,
  D,
  Phi,
  discard_burnin,
  manual_burnin = 1,
  unique_beta_quota = rep(0, ncol(D)),
  largest_min = rep(Inf, ncol(D)),
  smallest_max = rep(-Inf, ncol(D)),
  max_iterations = Inf,
  label_function = function(idx, total = iterations) {
     print(paste("MCMC-H IDX:",
    idx, "/", total))
 },
  label_skip = floor(iterations/5),
  label_bool = TRUE,
  always_accept = FALSE
)

Arguments

iterations	Number of iterations
residuals_opt	Residuals from IQR-QR problem
theta	Tuning parameter
varcov_mat	Variance-covariance matrix
Y, X, D, Phi	Data
discard_burnin	If TRUE, remove first few samples that have the same coefficients
unique_beta_quota	Vector of length p_D; minimum number of unique beta (defaults to 0)
largest_min	Vector of length p_D; sample from MCMC must contain beta_D below corresponding value of largest_min; defaults to Inf
smallest_max	Vector of length p_D; sample from MCMC must contain beta_D above corresponding value of smallest_max; defaults to -Inf
max_iterations	Total number of iterations before stopping the program; defaults to Inf, but set to a lower number when using largest_min or smallest_max
always_accept	If FALSE (default), sample from proposal_h. Else, sample from target_h.
initial_h	Initial active basis indices
initial_beta_D, initial_beta_X	Initial coefficients, e.g., IQR point estimate

Details

1. Proposing an active basis h_star according to Q_h, which puts more weight on indices with smaller residuals

2. Computing coefficients beta_star (see h_to_beta)

3. Computing the acceptance probability

4. Accept/Reject in the usual MH manner

Value

named list

1. beta: data frame where each row is a vector of coefficients (one row per iteration)

2. h: data frame where each row is a vector of indices in the active basis (one row per iteration)

3. record: binary vector, 1 if that iteration's proposal was accepted

4. stationary_begin: all iterations prior to this number were discarded

omkarakatta/ivqr documentation built on Aug. 20, 2022, 11:04 p.m.