sqrt(n)(beta_post - beta0) tends to N(0, I_beta^(-1)) with the
information taken from the PARTIAL likelihood. That the infinite
dimensional baseline hazard costs nothing asymptotically – the
partial likelihood is already efficient for beta – is the reason the
Cox model is the standard example of semiparametric BvM. Exponential
baseline and a binary covariate here, so the truth is known.
Usage
Ghosalcoxbvmsp(beta0 = 0.8, n = 600, seed = 42)
Arguments
- beta0
True log hazard ratio.
- n
Sample size.
- seed
Seed for the deterministic draws.
Value
List with estimate (the partial-likelihood maximiser),
error, method.
Details
Formula: -log PL(b) = sum over the event ordering of
[log(sum_{j in risk set} exp(b z_j)) - b z_i]; minimised on a grid.
References
Ghosal & van der Vaart (2017), Fundamentals of
Nonparametric Bayesian Inference, CUP, section 12.3.3.
Examples
Ghosalcoxbvmsp()
#> $estimate
#> [1] 0.76
#>
#> $error
#> [1] 0.04
#>
#> $method
#> [1] "Cox partial-likelihood BvM (GvdV 2017 sec. 12.3.3)"
#>
#> attr(,"class")
#> [1] "morie_rich_result" "list"
