first shot for add vcov #311

Santymax98 · 2025-10-02T19:22:15Z

Okay, let's forget about the pr I made by mistake.

In this PR, I added the vcov function for the fit API. This ensures that it's the user's decision whether to calculate it or not. I also added a function to print the values for copula measurements (again, the decision is up to the user). Here are some examples.

julia> G = GaussianCopula([1.0 0.3 0.2; 0.3 1.0 0.4; 0.2 0.4 1.0])
GaussianCopula{3, Matrix{Float64}}(Σ = [1.0 0.3 0.2; 0.3 1.0 0.4; 0.2 0.4 1.0]))

julia> U = rand(G, 300)
3×300 Matrix{Float64}:
 0.222071  0.991229  0.343356  0.447073  0.756457  0.909128  0.429314  …  0.117147  0.23917   0.886017  0.779509  0.239024   0.252678  0.0907745
 0.53644   0.790178  0.593496  0.45622   0.763848  0.166268  0.464444     0.51989   0.601099  0.965531  0.710267  0.0481338  0.156809  0.477384
 0.456802  0.832535  0.644807  0.571332  0.370216  0.255189  0.642993     0.57973   0.637748  0.894761  0.607114  0.164993   0.290189  0.67479

julia> fit(CopulaModel, GaussianCopula, U; vcov = true)
[ Info: Running the itau/irho/ibeta routine from the generic implementation
Gaussian d=3 fitted via itau
Number of observations:       300
Null Loglikelihood:        0.0000
Loglikelihood:            32.2020
LR Test (vs indep. copula): 64.40 ~ χ²(3)  =>  p = 6.727e-14
AIC: -58.404       BIC: -47.293
Converged: true   Iterations: 52   Elapsed: 3.077s
────────────────────────────────────────────────────────────────────────────────────────
Parameter          Estimate      Std.Err   z-value   Pr(>|z|)       95% Lo       95% Hi
────────────────────────────────────────────────────────────────────────────────────────
Σ_1_2              0.219403   0.00354438    61.902          0     0.212456      0.22635
Σ_1_3              0.160347   0.00349548    45.873          0     0.153496     0.167198
Σ_2_3               0.38445   0.00319102   120.479          0     0.378196     0.390704
────────────────────────────────────────────────────────────────────────────────────────

For Archimedean Copulas

julia> C = ClaytonCopula(3, 3.5)
ClaytonCopula{3, Float64}(θ = 3.5,)

julia> U = rand(C, 300)
3×300 Matrix{Float64}:
 0.994932  0.476203  0.52375   0.00110445   0.270389  0.579527  0.959464  …  0.896951  0.858705  0.223188  0.261711  0.924947  0.322537  0.552703
 0.823358  0.389963  0.492272  0.000697532  0.313849  0.905658  0.565444     0.837394  0.81539   0.198364  0.309672  0.46887   0.358373  0.705274
 0.842299  0.945494  0.534202  0.00101964   0.234375  0.495992  0.665326     0.53361   0.866946  0.266491  0.939297  0.57424   0.369273  0.742542

julia> fit(CopulaModel, ClaytonCopula, U; method=:itau, vcov = true)
Archimedean d=3 fitted via itau
Number of observations:       300
Null Loglikelihood:        0.0000
Loglikelihood:           531.8877
LR Test (vs indep. copula): 1063.78 ~ χ²(1)  =>  p = 2.467e-233
AIC: -1061.775       BIC: -1058.072
Converged: true   Iterations: 0   Elapsed: 2.401s
────────────────────────────────────────────────────────────────────────────────────────
Parameter          Estimate      Std.Err      z-value     Pr(>|z|)       95% Lo       95% Hi
────────────────────────────────────────────────────────────────────────────────────────
θ                    3.7830       1.3000       2.9101       0.0036       1.2352       6.3309
────────────────────────────────────────────────────────────────────────────────────────

Copulas with more than 2 params... with fallback to avoid errors

julia> B = BB1Copula(2, 1.5, 3.2)
BB1Copula{2, Float64}(θ = 1.5, δ = 3.2)

julia> U = rand(B, 300)
2×300 Matrix{Float64}:
 0.0868505  0.369871  0.0876678  0.192073  0.902674  0.411426  0.0638137  …  0.742172  0.583333  0.532168  0.0187803  0.0129811  0.554113  0.950487
 0.150734   0.595093  0.139971   0.145485  0.892565  0.263838  0.105728      0.884073  0.539801  0.551795  0.010793   0.0161772  0.713115  0.93326

julia> fit(CopulaModel, BB1Copula, U; vcov = true)
┌ Warning: vcov(hessian) failed (NaN/Inf). Falling back to jackknife.
└ @ Copulas ~/Desktop/Repositorios/Copulas.jl/src/Fitting.jl:490
Archimedean d=2 fitted via mle
Number of observations:       300
Null Loglikelihood:        0.0000
Loglikelihood:           409.2012
LR Test (vs indep. copula): 818.40 ~ χ²(2)  =>  p = 1.933e-178
AIC: -814.402       BIC: -806.995
Converged: true   Iterations: 9   Elapsed: 3.916s
────────────────────────────────────────────────────────────────────────────────────────
Parameter          Estimate      Std.Err      z-value     Pr(>|z|)       95% Lo       95% Hi
────────────────────────────────────────────────────────────────────────────────────────
θ                    1.2132       0.0117     103.3044       0.0000       1.1902       1.2362
δ                    3.5206       0.0154     228.2639       0.0000       3.4903       3.5508
────────────────────────────────────────────────────────────────────────────────────────

For SklarDist

julia> X₁, X₂, X₃ = Gamma(2,3), Pareto(), LogNormal(0,1)
(Gamma{Float64}(α=2.0, θ=3.0), Pareto{Float64}(α=1.0, θ=1.0), LogNormal{Float64}(μ=0.0, σ=1.0))

julia> C = ClaytonCopula(3, 1.7)
ClaytonCopula{3, Float64}(θ = 1.7,)

julia> D = SklarDist(C,(X₁,X₂,X₃))
SklarDist{ClaytonCopula{3, Float64}, Tuple{Gamma{Float64}, Pareto{Float64}, LogNormal{Float64}}}(
C: ClaytonCopula{3, Float64}(θ = 1.7,)
m: (Gamma{Float64}(α=2.0, θ=3.0), Pareto{Float64}(α=1.0, θ=1.0), LogNormal{Float64}(μ=0.0, σ=1.0))
)


julia> x = rand(D,1000)
3×1000 Matrix{Float64}:
 2.05448  2.3674   13.5994    4.19579  13.6778   1.47767   2.26288   1.96553   …  7.10346   7.15242  12.8446  2.50478  6.31336   6.18693  7.3298
 1.21988  1.55024   4.87178   1.84246   1.27558  1.02665   1.41345   1.69677      1.42585   4.57979   2.8184  1.88363  3.5216    2.29623  1.2645
 3.6093   2.01363   0.702068  1.43357   1.13343  0.788215  0.409093  0.613827     0.544334  1.70939   1.2616  1.52514  0.653832  1.03131  0.334373

julia> fit(CopulaModel,
           SklarDist{ClaytonCopula,Tuple{Gamma,Pareto,LogNormal}},
           x; copula_method=:mle, sklar_method=:ifm,
           copula_kwargs=(vcov=true,), derived_measures=true)
SklarDist{Copula=Archimedean d=3, Margins=(Gamma, Pareto, LogNormal)} fitted via mle
Number of observations:      1000
Null Loglikelihood:    -6176.8206
Loglikelihood:         -5423.4946
LR Test (vs indep. copula): 1506.65 ~ χ²(1)  =>  p = 0
AIC: 10860.989       BIC: 10895.343
Converged: true   Iterations: 4   Elapsed: 3.540s
──────────────────────────────────────────────────────────
[ Copula ]
──────────────────────────────────────────────────────────
Family: Archimedean d=3
────────────────────────────────────────────────────────────────────────────────────────
Param            Estimate      Std.Err   z-value   Pr(>|z|)       95% Lo       95% Hi
────────────────────────────────────────────────────────────────────────────────────────
θ                  1.5829       0.0075   212.179          0       1.5683       1.5975
────────────────────────────────────────────────────────────────────────────────────────
[ Copula Derived measures ]
Kendall τ(θ)   = 0.4418
Spearman ρ(θ)  = 0.6149
Blomqvist β(θ) = 0.1550
Gini γ(θ)      = 0.5124
Upper λᵤ(θ)    = 0.0000
Lower λₗ(θ)    = 0.4995
Entropy ι(θ)   = -0.7601
──────────────────────────────────────────────────────────
[ Marginals ]
──────────────────────────────────────────────────────────
Margin Dist         Param       Estimate      Std.Err       95% CI
#1     Gamma        α             1.9651            —            —
       Gamma        θ             3.0329            —            —
#2     Pareto       α             0.9651            —            —
       Pareto       θ             1.0003            —            —
#3     LogNormal    μ             0.0115            —            —
       LogNormal    σ             1.0008            —            —

In this last case, I had trouble getting the marginal vcov...

lrnv · 2025-10-02T19:44:04Z

This looks great, although I think it would be better (more generic) if everything happened in the outer level, without having to go inside the different methods, so that we get vcov whatever the fitting method. I will take a look tomorrow to see what I can do.

codecov · 2025-10-02T19:48:49Z

Codecov Report

❌ Patch coverage is 70.33639% with 194 lines in your changes missing coverage. Please review.
✅ Project coverage is 78.55%. Comparing base (29108e3) to head (fc12c12).
⚠️ Report is 3 commits behind head on main.

Files with missing lines	Patch %	Lines
src/show.jl	0.00%	129 Missing ⚠️
src/Fitting.jl	84.00%	32 Missing ⚠️
src/utils.jl	58.82%	7 Missing ⚠️
src/WilliamsonTransforms.jl	84.61%	6 Missing ⚠️
src/Generator.jl	86.20%	4 Missing ⚠️
src/MiscellaneousCopulas/FGMCopula.jl	91.11%	4 Missing ⚠️
src/ExtremeValueCopula.jl	83.33%	2 Missing ⚠️
src/Generator/BB2Generator.jl	88.88%	2 Missing ⚠️
src/MiscellaneousCopulas/IndependentCopula.jl	0.00%	2 Missing ⚠️
src/MiscellaneousCopulas/MCopula.jl	0.00%	2 Missing ⚠️
... and 4 more

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@@            Coverage Diff             @@
##             main     #311      +/-   ##
==========================================
+ Coverage   74.50%   78.55%   +4.04%     
==========================================
  Files          84       85       +1     
  Lines        4837     4994     +157     
==========================================
+ Hits         3604     3923     +319     
+ Misses       1233     1071     -162

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Santymax98 · 2025-10-02T19:49:11Z

I understand, but sometimes one technique is used for MLE and another for moment methods, finally the safe fallback to light Jackknife because I think a bootstrap would be too heavy

lrnv · 2025-10-03T09:47:12Z

So if one technique is for MLE and the other one for moment methods, then we could simply dipatch on the method, or even add a new argument vcov_method to decide what we'll do, whihc could have a smart default behavior:

If the method is MLE, dispatch by defautl to the MLE hessian
If the method is moment-matching, dispatch to the correct code
Else dispatch to jacknife by default.

Let me look at your code and try to do that.

lrnv

@Santymax So I think i have it working now :

julia> U = rand(GaussianCopula([1.0 0.3 0.2; 0.3 1.0 0.4; 0.2 0.4 1.0]), 300);
julia> fit(CopulaModel, GaussianCopula, U)
────────────────────────────────────────────────────────────────────────────────
[ CopulaModel: Gaussian d=3 ]
────────────────────────────────────────────────────────────────────────────────
Method:                mle
Number of observations: 300
────────────────────────────────────────────────────────────────────────────────
[ Fit metrics ]
────────────────────────────────────────────────────────────────────────────────
Null Loglikelihood:          0.0000
Loglikelihood:              50.4789
LR (vs indep.):        100.96 ~ χ²(3)  ⇒  p = <1e-16
AIC:                   -94.958
BIC:                   -83.847
Converged:             true
Iterations:            0
Elapsed:               0.000s
────────────────────────────────────────────────────────────────────────────────
[ Parameters ]
────────────────────────────────────────────────────────────────────────────────
Parameter    Estimate   Std.Err   z-value    p-val     95% Lo     95% Hi
Σ₁₂            0.2793    0.0538     5.196 2.038e-07     0.1740     0.3847
Σ₁₃            0.2057    0.0569     3.615 0.0003009     0.0942     0.3173
Σ₂₃            0.4754    0.0435    10.924   <1e-16     0.3901     0.5607


julia>

ulia> U = rand(ClaytonCopula(3, 3.5), 300);
julia> fit(CopulaModel, ClaytonCopula, U; method=:itau)
────────────────────────────────────────────────────────────────────────────────
[ CopulaModel: Archimedean d=3 ]
────────────────────────────────────────────────────────────────────────────────
Method:                itau
Number of observations: 300
────────────────────────────────────────────────────────────────────────────────
[ Fit metrics ]
────────────────────────────────────────────────────────────────────────────────
Null Loglikelihood:          0.0000
Loglikelihood:             456.7272
LR (vs indep.):        913.45 ~ χ²(1)  ⇒  p = <1e-16
AIC:                   -911.454
BIC:                   -907.751
Converged:             true
Iterations:            0
Elapsed:               1.165s
────────────────────────────────────────────────────────────────────────────────
[ Parameters ]
────────────────────────────────────────────────────────────────────────────────
Parameter    Estimate   Std.Err   z-value    p-val     95% Lo     95% Hi
θ              3.5488    0.0000 3548815.824   <1e-16     3.5488     3.5488


julia>

julia> U = rand(BB1Copula(2, 1.5, 3.2), 300);
julia> fit(CopulaModel, BB1Copula, U)
────────────────────────────────────────────────────────────────────────────────
[ CopulaModel: Archimedean d=2 ]
────────────────────────────────────────────────────────────────────────────────
Method:                mle
Number of observations: 300
────────────────────────────────────────────────────────────────────────────────
[ Fit metrics ]
────────────────────────────────────────────────────────────────────────────────
Null Loglikelihood:          0.0000
Loglikelihood:             376.9690
LR (vs indep.):        753.94 ~ χ²(2)  ⇒  p = <1e-16
AIC:                   -749.938
BIC:                   -742.530
Converged:             true
Iterations:            8
Elapsed:               2.469s
────────────────────────────────────────────────────────────────────────────────
[ Parameters ]
────────────────────────────────────────────────────────────────────────────────
Parameter    Estimate   Std.Err   z-value    p-val     95% Lo     95% Hi
θ              1.5194    0.2542     5.978 2.259e-09     1.0213     2.0176
δ              2.9502    0.2617    11.275   <1e-16     2.4373     3.4630


julia>

julia> x = rand(SklarDist(ClaytonCopula(3, 1.7),(Gamma(2,3), Pareto(), LogNormal(0,1))),1000);
julia> fit(CopulaModel, SklarDist{ClaytonCopula,Tuple{Gamma,Pareto,LogNormal}}, x)
────────────────────────────────────────────────────────────────────────────────
[ CopulaModel: SklarDist (Copula=Archimedean d=3, Margins=(Gamma, Pareto, LogNormal)) ]
────────────────────────────────────────────────────────────────────────────────
Copula:                Archimedean d=3
Margins:               (Gamma, Pareto, LogNormal)
Methods:               copula=mle, sklar=ifm
Number of observations: 1000
────────────────────────────────────────────────────────────────────────────────
[ Fit metrics ]
────────────────────────────────────────────────────────────────────────────────
Null Loglikelihood:      -6062.1153
Loglikelihood:                 -Inf
LR (vs indep.):        -Inf ~ χ²(1)  ⇒  p = 1
AIC:                   Inf
BIC:                   Inf
Converged:             true
Iterations:            1
Elapsed:               3.258s
────────────────────────────────────────────────────────────────────────────────
[ Dependence metrics ]
────────────────────────────────────────────────────────────────────────────────
Kendall τ:             0.4290
Spearman ρ:            0.5995
Blomqvist β:           0.1464
────────────────────────────────────────────────────────────────────────────────
[ Copula parameters ] (vcov=hessian)
────────────────────────────────────────────────────────────────────────────────
Parameter    Estimate   Std.Err   z-value    p-val     95% Lo     95% Hi
θ              1.5026    0.0515    29.184   <1e-16     1.4017     1.6035
────────────────────────────────────────────────────────────────────────────────
[ Marginals ]
────────────────────────────────────────────────────────────────────────────────
Margin Dist       Param    Estimate   Std.Err 95% CI
#1     Gamma      α          2.1972    0.0918 [2.0173, 2.3770]
                  θ          2.7371    0.1284 [2.4855, 2.9887]
#2     Pareto     α          0.9967    0.5524 [-0.0859, 2.0794]
                  θ          1.0016    0.5560 [-0.0881, 2.0914]
#3     LogNormal  μ         -0.0028    0.0313 [-0.0641, 0.0585]
                  σ          0.9886    0.0221 [0.9452, 1.0319]


julia>

Now by default everything is computed, and i have tried to make the output better-looking. Also I have fixed the marginal vcov.

However this require a few tests: there are now many possibilities (fitting method for the copula, for the sklar, vcov method, etc...) and thus we need to test all of them. I will now review once more the code to try to simplify it again, if you could propose :

1° tests that corresponds to these new functionalities
2° Proper documentation of what the show() methods outputs

That would be nice :)

…s.jl into pr/Santymax98/311

lrnv · 2025-10-07T20:09:32Z

@Santymax98 Okay this is correctly merged now ! Do not forget to ]resolve because the packages dependencies changed. I will look at the tests now.

lrnv · 2025-10-07T20:49:43Z

@Santymax98 : Regarding specific methods for the BBCops generator derivatives, I have simply commented out your code for the moment, since it is not the main question of this PR. Once this one is merged, if you want to test this idea again please in another pull-request. This is already a very messy pull-request no need to add more.

Let's see what the tests say

Santymax98 · 2025-10-07T23:53:14Z

I completely agree. It's not essential, and perhaps we can run some benchmarks to see if it's better or not at the appropriate time. For my part, everything's fine.

lrnv · 2025-10-08T00:00:12Z

Okay. In the mean time, i would like to validate the dependence metrics to be certain that they work on every model we have. I will therefore push a nex tests into the generics and we'll see :)

It will probably fail on a lot of cases, but thats good we have to fix them

Santymax98 · 2025-10-08T00:06:39Z

I think the same and maybe polish the tail estimators and theorical tails...

lrnv · 2025-10-08T12:24:00Z

@Santymax98 Okay I think we are good to merge now. The only missing thing is correct documentation of the fitting interface and the vcov things. I was going to do it, but if you could do it that would be nice.

I will rather concentrate myself on 1) producing benchmarks so that we can see where are the problematic points and 2) make the testing framework a bit faster, 45minutes is painfully slow...

first shot for add vcov

f4670ae

lrnv added 13 commits October 3, 2025 12:55

first shot

dd51a7c

clear up archimedean too

62bf463

clear up archimedans.

2f419cd

refactor -- first pass

e857df6

simplified entropy and lower gaussian burden

3aef744

clear out gaussian and elliptical

3ae5c59

add godambe_pairwise

ad339fe

clear up EVC

62b4a5e

Refactor and simplify the code

c56e565

clear out global diff

1f38f66

debugging...

985ab30

working!

1b7c079

enhance show function

c9b734a

lrnv reviewed Oct 4, 2025

View reviewed changes

Santymax98 and others added 11 commits October 4, 2025 12:38

first shot for add vcov

c9c3ac9

first shot

9aef2c7

clear up archimedean too

375819d

clear up archimedans.

a3cd77c

refactor -- first pass

d4f071f

simplified entropy and lower gaussian burden

a440c85

clear out gaussian and elliptical

76d6bb0

add godambe_pairwise

de38b3b

clear up EVC

a7fc773

Refactor and simplify the code

e4cf3d8

clear out global diff

eb0a251

lrnv and others added 14 commits October 7, 2025 21:32

delete simlink

b9ddb58

fixed mle evd

1ac52f9

Robust hessian _vcov

95ec113

frank is very slow

d283ed8

fix a few things around

45d5df8

trying vcov with bootstrap

2c882fa

try to implement kth derivatives for BBx

d5ebb35

relaxing tolerance

47ae6d7

stable bivariate bbx for archimax

a103a75

tolerance fixing...

48a15d2

restore removed changes sorry

7a81250

Merge branch 'add_vcov_clean' of https://github.com/santymax98/copula…

c11cbe2

…s.jl into pr/Santymax98/311

fix a few Val{} still there

95d40c5

small changes

236e131

lrnv added 4 commits October 7, 2025 22:13

one first merging error

7965bfc

Try to disable upper generator for BBs to see if it works.

d1d13d0

typo

fcb4c7e

test everything now

d617ae2

no vcov for tEV

0d27a2a

new dependence metrics tests

3d28092

lrnv added 2 commits October 8, 2025 11:37

back to previous tests

2844def

avoid inverting zeros in sklardist

fc12c12

lrnv merged commit 0463930 into lrnv:main Oct 8, 2025
5 checks passed

lrnv referenced this pull request Oct 9, 2025

Bump version from 0.1.32 to 0.1.33 (#320)

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