UMR_CC_generic: @title Second derivative computations of least-squares...
In UMR: Unmatched Monotone Regression

Description Usage Arguments

@title Second derivative computations of least-squares Unlinked Isotonic Regression criterion ("SIR" comes from "shuffled isotonic regression" although this terminology is now outdated).

UMR_curv_generic(
  yy,
  mm,
  ww_y = rep(1/length(yy), length(yy)),
  ww_m = rep(1/length(mm), length(mm)),
  densfunc,
  BBpfunc
)

UMR_curv_generic2(
  yy,
  mm,
  ww_y = rep(1/length(yy), length(yy)),
  ww_m = rep(1/length(mm), length(mm)),
  densfunc,
  DDfunc
)

UMR_CC_generic(
  yy,
  mm,
  ww_y = rep(1/length(yy), length(yy)),
  ww_m = rep(1/length(mm), length(mm)),
  densfunc,
  DDfunc
)

`yy`	Y (response) observation vector (numeric)
`mm`	Current (unsorted) estimate/iterate at which to compute gradient. (Length is <= than the number of X observations in the problem).
`ww_y`	Weights (nonnegative, sum to 1) corresponding to yy. Same length as yy. Default is just 1/length(yy) for each value.
`ww_m`	Weights (nonnegative, sum to 1) corresponding to mm. Same length as mm.
`densfunc`	This is the error density, a function object (Balabdaoui, Doss, Durot (2021+).
`BBpfunc`	This is the function B', i.e. derivative of "B" function in the paper. @details The "CC" or "curv" functions are used to be passed in to UMRactiveSet_trust() (generally after 'currying'/substituting in for the parameter arguments). UMR_CC_generic returns a 1xlength(mm) matrix giving the C function defined in the paper. UMR_curv_generic is returning also a 1xlength(mm) matrix giving the (d^2/dtheta^2)(objective function), where "theta" is as defined in the paper. [This is mathfrakC in the paper.] These are similar quantities, the "curv" quantity is just C rescaled by the weight. See calculations in paper. The more substantive difference is that UMR_CC_generic requires a closed form for the "D" function whereas UMR_curv_generic simply uses the hessian computation (i.e., requires B', the derivative of the "B" function). (The closed form of the "D" function can be found from the closed form of the hessian, but it is not necessary.) UMR_curv_generic2 is analogous to UMR_curv_generic but the latter relies on UMR_CC_generic. UMR_CC_generic1 is analogous to UMR_CC_generic (aka CC_SIR_generic) but the former is calculated in fashion identical to UMR_curv_generic (i.e., relying on UMRhess). DDfunc_Gauss_generic is the "D" function that can be passed in (after substituting for sig) for DDfunc in various other functions to compute the "C" function (e.g., UMR_CC_generic). Note: "CC" and "DD", etc., refer to the "C" or "D" functions. Double lettering is a convention often used in the code to refer to the single letter.
`DDfunc`	This is the function "D" defined in the second derivative calculations in the paper (Balabdaoui, Doss, Durot (2021+).