setup.softinfo: Set up softinfo for exponential epi-splines.

In episplineDensity: Density Estimation with Soft Information by Exponential Epi-splines

Description

The softinfo prescribes constraints imposed on the density estimate.

Usage

setup.softinfo(N = 10, order = 2, warn = FALSE, ...)

Arguments

N	Integer giving number of interior mesh points (knots) for the splines. Default 10.
order	Integer giving the order for the polynomial splines. Default 2, and only 2 is permitted right now.
warn	Logical: emit warnings when contradictory conditions are imposed? Currently ignored. It is easy to generate contradictory conditions and the code only tests for a few combinations.
...	A set of named arguments describing the possible values of soft information. The current possibilities are: M Numeric : number of points in each segment at which Fisher and other constraints are imposed unimodal Logical: if TRUE, require that the density be unimodal. unimodaluppertail, unimodallowertail Numeric. Impose unimodality only on the lower or upper floor (N * unimodallowertail) or floor (N * unimodaluppertail) segments. monotone Character: describes what sort of monotonicty is required. Possible values "nondecreasing" or "nonincreasing". lowerboundsk, upperboundsk Numeric, length N+1. Bounds on epiparameters s[0] through s[N]. See expepi for details. Default: -1000 for lower, +1000 for upper. lowerboundak0, upperboundak0, lowerboundakp, upperboundakp Numeric, length N. Lower and upper bounds on the linear coefficients (ak0) and quadratic coefficients (akp) of the splines. continuous, continuousDiff, lsc, usc Logicals. When TRUE, require continuity, continuous differentiability, or that the density be lower semi-continuous (lsc) or upper semi-continuous (usc). pointwiseFisherLower, pointwiseFisherUpper Numeric, length 1. Lower and upper bound on the value of slope/value at every point in every segment. lowerdensityvalue, upperdensityvalue Numeric vectors of length N giving lower and upper bounds on the density estimate inside segments. lowerdensityvalueEndpt, upperdensityvalueEndpt Numeric vectors of length N + 1 giving lower and upper bounds on the density estimate at segment end points. lowerdensityvalueSpecific Two-column numeric matrix. Each row has an x value and a density value and the density estimate is constrained to be at least lowerdensityvalueSpecific[j,2] at x = lowerdensityvalueSpecific[j,1] for each row j. KLDivergenceUpper, KLDivergenceLower, KLDensity, KLDensityParams Upper and lower bounds on the KL divergence of the density estimate from the density whose name is given as an R density function in KLDensity, e.g. dnorm, and whose parameters are given as a list in DLDensityParams, e.g. list (mean = 0, sd = 1) upperbound1moment, upperbound2moment Numeric; upper bounds on the first or second (non-central) moment of the estimate

Value

List with any specified values, plus any defaults (notably M = 5).

Author(s)

Sam Buttrey, after Matlab code by Royset and Wets.

See Also

expepi

episplineDensity documentation built on May 1, 2019, 7:28 p.m.