getHistory.NPVI: Returns History of TMLE Procedure

In tmle.npvi: Targeted Learning of a NP Importance of a Continuous Exposure

Description

Returns the 'history' of the TMLE procedure.

Usage

## S3 method for class 'NPVI'
getHistory(this, ...)

Arguments

this	An object of class TMLE.NPVI.
...	Not used.

Value

Returns a numeric matrix which encapsulates a summary of the TMLE procedure. If k successive updates were performed, then the matrix has either k+1 rows (if cleverCovTheta was set to FALSE in the call to tmle.npvi) or 2k+1 rows (otherwise). The matrix has 14 columns:

• "eps", values of the unique fluctuation parameter (if cleverCovTheta was set to FALSE in the call to tmle.npvi), or values of the parameter involved in the fluctuation of the joint distribution of (X,W) during each update (otherwise).

• "lli", increases in likelihood yielded by each update (if cleverCovTheta was set to FALSE in the call to tmle.npvi), or increases in likelihood yielded by the fluctuation of the joint distribution of (X,W) during each update (otherwise).

• "mic1", empirical means of the first component of the efficient influence curve at each step of the TMLE procedure.

• "epsT", values of the fluctuation parameter involved in the fluctuation of the conditional distribution of Y given (X,W) during each update (if cleverCovTheta was set to TRUE in the call to tmle.npvi), or NA (otherwise).

• "lliT", successive increases in likelihood yielded by the fluctuation of the conditional distribution of Y given (X,W) during each update (if cleverCovTheta was set to TRUE in the call to tmle.npvi), or NA (otherwise).

• "mic2", empirical means of the second component of the efficient influence curve at each step of the TMLE procedure.

• "psi", increasingly targeted estimators Ψ(P_n^k) of the parameter of interest. The last one is the TMLE. Their computation involves simulation of B iid copies of (X,W) under P_n^k.

• "psi.sd", estimated standard deviations of the increasingly targeted estimators of the parameter of interest. The last one corresponds to the TMLE. The computation involves the same B iid copies of (X,W) as above.

• "psiPn", same as "psi" except that the *observed* (X_i,W_i) are used instead of simulated copies drawn from P_n^k. Of course, "psi" must be favored.

• "psiPn.sd", same as "psi.sd" except that the *observed* (X_i,W_i) are used instead of simulated copies drawn from P_n^k. Of course, "psi.sd" must be favored.

• "mic", empirical means of the efficient influence curve at each step of the TMLE procedure. This column is the sum of the "mic1" and "mic2" columns.

• "div", total variation distances between each pair of successive distributions constructed in the course of the TMLE procedure.

• "sic", estimated standard deviations of the efficient influence curve at each step of the TMLE procedure.

• "phi", non-parametric substitution estimator of φ=Φ(P) where

  Φ(P) = E_P[f(X)Y] / E_P[f(X)^2],

  with P the distribution of the random vector (W,X,Y). The alternative parameter φ should be interpreted as the counterpart of ψ which neglects W.

• "sicAlt", estimated standard deviations of the efficient influence curve of Ψ - Φ at each step of the TMLE procedure.

Author(s)

Antoine Chambaz, Pierre Neuvial

See Also

tmle.npvi

Examples

FALSE

tmle.npvi documentation built on May 1, 2019, 6:50 p.m.