README.md
In DanielBonnery/pubBonneryBreidtCoquet2016: X
Asymptotics for the maximum sample likelihood estimator under informative selection from a finite population
pubBonneryBreidtCoquet2016 is a R package that contains the source code to reproduce the simulations of "Asymptotics for the maximum sample likelihood estimator under informative selection from a finite population" by Bonnery, Breidt and Coquet
NB: no seed was used for table 1 and 2 in the paper, so results differ slightly.
Execution
devtools::install_github("DanielBonnery/pubBonneryBreidtCoquet2016")
library(pubBonneryBreidtCoquet2016)
demo(table1)
demo(table2)
demo(table3)
Output
Table 1
|Estimator |$\theta$ |$\xi$ |Conditional to (N,sampleparam.tauh1,sampleparam.tauh2) |Mean |% Relative Bias |RMSE Ratio |Empirical Variance |Asymptotic Variance |
|:---------|:--------|:-----|:------------------------------------------------------|:----|:---------------|:----------|:------------------|:-------------------|
|Naive |4 |0.1 |1e+04, 1e-02, 1e-01 |4.1 |2.39 |1.35043 |0.0181758 |NA |
|Pseudo |4 |0.1 |1e+04, 1e-02, 1e-01 |4.01 |0.311 |1.53996 |0.0309899 |NA |
|Sample |4 |0.1 |1e+04, 1e-02, 1e-01 |4.01 |0.143 |1 |0.0201916 |0.0200028 |
|Full |4 |0.1 |1e+04, 1e-02, 1e-01 |NaN |NaN |NA |NA |NA |
|Estimator |$\theta$ |$\xi$ |Conditional to (N,sampleparam.tauh1,sampleparam.tauh2) |Mean |% Relative Bias |RMSE Ratio |Empirical Variance |Asymptotic Variance |
|:---------|:--------|:-----|:------------------------------------------------------|:----|:---------------|:----------|:------------------|:-------------------|
|Naive |4 |1 |1e+04, 1e-02, 1e-01 |4.86 |21.5 |15.3729 |0.031139 |NA |
|Pseudo |4 |1 |1e+04, 1e-02, 1e-01 |4.05 |1.19 |2.13148 |0.104135 |NA |
|Sample |4 |1 |1e+04, 1e-02, 1e-01 |4.02 |0.416 |1 |0.0496496 |0.0509886 |
|Full |4 |1 |1e+04, 1e-02, 1e-01 |NaN |NaN |NA |NA |NA |
|Estimator |$\theta$ |$\xi$ |Conditional to (N,sampleparam.tauh1,sampleparam.tauh2) |Mean |% Relative Bias |RMSE Ratio |Empirical Variance |Asymptotic Variance |
|:---------|:--------|:-----|:------------------------------------------------------|:----|:---------------|:----------|:------------------|:-------------------|
|Naive |4 |2 |1e+04, 1e-02, 1e-01 |5.59 |39.7 |33.8249 |0.0567029 |NA |
|Pseudo |4 |2 |1e+04, 1e-02, 1e-01 |4.06 |1.4 |1.87451 |0.139452 |NA |
|Sample |4 |2 |1e+04, 1e-02, 1e-01 |4.02 |0.419 |1 |0.0757842 |0.0771277 |
|Full |4 |2 |1e+04, 1e-02, 1e-01 |NaN |NaN |NA |NA |NA |
Table 2
|Estimator |$\theta$ |$\xi$ |Conditional to (N,sigma,EX,SX,sampleparam.proph1,sampleparam.proph2,sampleparam.tauh1,sampleparam.tauh2) |Mean |% Relative Bias |RMSE Ratio |Empirical Variance |Asymptotic Variance |
|:---------|:-------------|:-----|:--------------------------------------------------------------------------------------------------------------|:-------------------|:---------------------|:--------------------------|:----------------------------------|:----------------------------------|
|Naive |0.5, 1.0, 2.0 |2 |5.000000e+03, 1.000000e-01, 1.000000e+00, 1.000000e+00, 7.000000e-01, 3.000000e-01, 1.428571e-02, 1.333333e-01 |2.270, 0.788, 1.770 |354.0, -21.2, -11.4 |93.64490, 3.20856, 6.60702 |0.03503440, 0.01488560, 0.00829343 |NA |
|Pseudo |0.5, 1.0, 2.0 |2 |5.000000e+03, 1.000000e-01, 1.000000e+00, 1.000000e+00, 7.000000e-01, 3.000000e-01, 1.428571e-02, 1.333333e-01 |0.506, 1.010, 1.980 |1.110, 0.764, -1.150 |2.04428, 1.91212, 1.92925 |0.0692524, 0.0355714, 0.0170555 |NA |
|Sample |0.5, 1.0, 2.0 |2 |5.000000e+03, 1.000000e-01, 1.000000e+00, 1.000000e+00, 7.000000e-01, 3.000000e-01, 1.428571e-02, 1.333333e-01 |0.513, 0.994, 1.990 |2.590, -0.571, -0.465 |1, 1, 1 |0.03372290, 0.01860110, 0.00902876 |0.03207760, 0.01771640, 0.00892672 |
|Full |0.5, 1.0, 2.0 |2 |5.000000e+03, 1.000000e-01, 1.000000e+00, 1.000000e+00, 7.000000e-01, 3.000000e-01, 1.428571e-02, 1.333333e-01 |NaN, NaN, NaN |NaN, NaN, NaN |NA, NA, NA |NA, NA, NA |NA |
|Estimator |$\theta$ |$\xi$ |Conditional to (N,sigma,EX,SX,sampleparam.proph1,sampleparam.proph2,sampleparam.tauh1,sampleparam.tauh2) |Mean |% Relative Bias |RMSE Ratio |Empirical Variance |Asymptotic Variance |
|:---------|:-------------|:-----|:--------------------------------------------------------------------------------------------------------------|:-------------------|:------------------------|:--------------------------|:----------------------------------|:-------------------------------|
|Naive |0.5, 1.0, 2.0 |2 |5.000000e+03, 1.000000e+00, 1.000000e+00, 1.000000e+00, 7.000000e-01, 3.000000e-01, 1.428571e-02, 1.333333e-01 |2.22, 0.80, 1.78 |344.0, -20.0, -10.8 |68.18110, 2.93315, 4.96587 |0.03629040, 0.01526960, 0.00786459 |NA |
|Pseudo |0.5, 1.0, 2.0 |2 |5.000000e+03, 1.000000e+00, 1.000000e+00, 1.000000e+00, 7.000000e-01, 3.000000e-01, 1.428571e-02, 1.333333e-01 |0.509, 1.000, 1.980 |1.7900, -0.0283, -1.0800 |1.64742, 1.89880, 1.54051 |0.0722261, 0.0359059, 0.0163376 |NA |
|Sample |0.5, 1.0, 2.0 |2 |5.000000e+03, 1.000000e+00, 1.000000e+00, 1.000000e+00, 7.000000e-01, 3.000000e-01, 1.428571e-02, 1.333333e-01 |0.514, 0.996, 1.990 |2.830, -0.361, -0.532 |1, 1, 1 |0.0436903, 0.0188967, 0.0107968 |0.0421493, 0.0177310, 0.0113943 |
|Full |0.5, 1.0, 2.0 |2 |5.000000e+03, 1.000000e+00, 1.000000e+00, 1.000000e+00, 7.000000e-01, 3.000000e-01, 1.428571e-02, 1.333333e-01 |NaN, NaN, NaN |NaN, NaN, NaN |NA, NA, NA |NA, NA, NA |NA |
|Estimator |$\theta$ |$\xi$ |Conditional to (N,sigma,EX,SX,sampleparam.proph1,sampleparam.proph2,sampleparam.tauh1,sampleparam.tauh2) |Mean |% Relative Bias |RMSE Ratio |Empirical Variance |Asymptotic Variance |
|:---------|:-------------|:-----|:--------------------------------------------------------------------------------------------------------------|:-------------------|:--------------------|:----------------------------|:----------------------------------|:----------------------------------|
|Naive |0.5, 1.0, 2.0 |2 |5.000000e+03, 1.000000e+01, 1.000000e+00, 1.000000e+00, 7.000000e-01, 3.000000e-01, 1.428571e-02, 1.333333e-01 |1.140, 0.967, 1.960 |129.00, -3.28, -1.84 |8.694410, 0.995954, 1.050590 |0.03690170, 0.01580060, 0.00764552 |NA |
|Pseudo |0.5, 1.0, 2.0 |2 |5.000000e+03, 1.000000e+01, 1.000000e+00, 1.000000e+00, 7.000000e-01, 3.000000e-01, 1.428571e-02, 1.333333e-01 |0.506, 0.998, 1.970 |1.24, -0.23, -1.32 |1.67253, 2.36019, 2.29071 |0.0866027, 0.0399814, 0.0189159 |NA |
|Sample |0.5, 1.0, 2.0 |2 |5.000000e+03, 1.000000e+01, 1.000000e+00, 1.000000e+00, 7.000000e-01, 3.000000e-01, 1.428571e-02, 1.333333e-01 |0.501, 1.000, 1.990 |0.103, 0.153, -0.502 |1, 1, 1 |0.05180200, 0.01693980, 0.00845887 |0.05181540, 0.01628270, 0.00887132 |
|Full |0.5, 1.0, 2.0 |2 |5.000000e+03, 1.000000e+01, 1.000000e+00, 1.000000e+00, 7.000000e-01, 3.000000e-01, 1.428571e-02, 1.333333e-01 |NaN, NaN, NaN |NaN, NaN, NaN |NA, NA, NA |NA, NA, NA |NA |
Table 3
|Selection |Estimator |Mean |% Relative Bias |RMSE Ratio |Empirical Variance |Average Estimated Variance |Variance Ratio |
|:------------|:---------|:------|:---------------|:----------|:------------------|:--------------------------|:--------------|
|Unstratified |Naive |36.949 |-7.286 |20.995 |0.188 |0.186 |0.989 |
|Unstratified |Pseudo |39.805 |-0.122 |1.106 |0.452 |0.419 |0.926 |
|Unstratified |Sample |39.827 |-0.065 |1 |0.41 |0.388 |0.945 |
|Stratified |Naive |36.932 |-7.328 |113.911 |0.006 |0.188 |30.271 |
|Stratified |Pseudo |39.858 |0.013 |2.448 |0.184 |0.169 |0.923 |
|Stratified |Sample |39.848 |-0.012 |1 |0.075 |0.066 |0.886 |
DanielBonnery/pubBonneryBreidtCoquet2016 documentation built on May 6, 2019, 1:35 p.m.
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Asymptotics for the maximum sample likelihood estimator under informative selection from a finite population
pubBonneryBreidtCoquet2016 is a R package that contains the source code to reproduce the simulations of "Asymptotics for the maximum sample likelihood estimator under informative selection from a finite population" by Bonnery, Breidt and Coquet
NB: no seed was used for table 1 and 2 in the paper, so results differ slightly.
Execution
devtools::install_github("DanielBonnery/pubBonneryBreidtCoquet2016")
library(pubBonneryBreidtCoquet2016)
demo(table1)
demo(table2)
demo(table3)
Output
Table 1
|Estimator |$\theta$ |$\xi$ |Conditional to (N,sampleparam.tauh1,sampleparam.tauh2) |Mean |% Relative Bias |RMSE Ratio |Empirical Variance |Asymptotic Variance | |:---------|:--------|:-----|:------------------------------------------------------|:----|:---------------|:----------|:------------------|:-------------------| |Naive |4 |0.1 |1e+04, 1e-02, 1e-01 |4.1 |2.39 |1.35043 |0.0181758 |NA | |Pseudo |4 |0.1 |1e+04, 1e-02, 1e-01 |4.01 |0.311 |1.53996 |0.0309899 |NA | |Sample |4 |0.1 |1e+04, 1e-02, 1e-01 |4.01 |0.143 |1 |0.0201916 |0.0200028 | |Full |4 |0.1 |1e+04, 1e-02, 1e-01 |NaN |NaN |NA |NA |NA |
|Estimator |$\theta$ |$\xi$ |Conditional to (N,sampleparam.tauh1,sampleparam.tauh2) |Mean |% Relative Bias |RMSE Ratio |Empirical Variance |Asymptotic Variance | |:---------|:--------|:-----|:------------------------------------------------------|:----|:---------------|:----------|:------------------|:-------------------| |Naive |4 |1 |1e+04, 1e-02, 1e-01 |4.86 |21.5 |15.3729 |0.031139 |NA | |Pseudo |4 |1 |1e+04, 1e-02, 1e-01 |4.05 |1.19 |2.13148 |0.104135 |NA | |Sample |4 |1 |1e+04, 1e-02, 1e-01 |4.02 |0.416 |1 |0.0496496 |0.0509886 | |Full |4 |1 |1e+04, 1e-02, 1e-01 |NaN |NaN |NA |NA |NA |
|Estimator |$\theta$ |$\xi$ |Conditional to (N,sampleparam.tauh1,sampleparam.tauh2) |Mean |% Relative Bias |RMSE Ratio |Empirical Variance |Asymptotic Variance | |:---------|:--------|:-----|:------------------------------------------------------|:----|:---------------|:----------|:------------------|:-------------------| |Naive |4 |2 |1e+04, 1e-02, 1e-01 |5.59 |39.7 |33.8249 |0.0567029 |NA | |Pseudo |4 |2 |1e+04, 1e-02, 1e-01 |4.06 |1.4 |1.87451 |0.139452 |NA | |Sample |4 |2 |1e+04, 1e-02, 1e-01 |4.02 |0.419 |1 |0.0757842 |0.0771277 | |Full |4 |2 |1e+04, 1e-02, 1e-01 |NaN |NaN |NA |NA |NA |
Table 2
|Estimator |$\theta$ |$\xi$ |Conditional to (N,sigma,EX,SX,sampleparam.proph1,sampleparam.proph2,sampleparam.tauh1,sampleparam.tauh2) |Mean |% Relative Bias |RMSE Ratio |Empirical Variance |Asymptotic Variance | |:---------|:-------------|:-----|:--------------------------------------------------------------------------------------------------------------|:-------------------|:---------------------|:--------------------------|:----------------------------------|:----------------------------------| |Naive |0.5, 1.0, 2.0 |2 |5.000000e+03, 1.000000e-01, 1.000000e+00, 1.000000e+00, 7.000000e-01, 3.000000e-01, 1.428571e-02, 1.333333e-01 |2.270, 0.788, 1.770 |354.0, -21.2, -11.4 |93.64490, 3.20856, 6.60702 |0.03503440, 0.01488560, 0.00829343 |NA | |Pseudo |0.5, 1.0, 2.0 |2 |5.000000e+03, 1.000000e-01, 1.000000e+00, 1.000000e+00, 7.000000e-01, 3.000000e-01, 1.428571e-02, 1.333333e-01 |0.506, 1.010, 1.980 |1.110, 0.764, -1.150 |2.04428, 1.91212, 1.92925 |0.0692524, 0.0355714, 0.0170555 |NA | |Sample |0.5, 1.0, 2.0 |2 |5.000000e+03, 1.000000e-01, 1.000000e+00, 1.000000e+00, 7.000000e-01, 3.000000e-01, 1.428571e-02, 1.333333e-01 |0.513, 0.994, 1.990 |2.590, -0.571, -0.465 |1, 1, 1 |0.03372290, 0.01860110, 0.00902876 |0.03207760, 0.01771640, 0.00892672 | |Full |0.5, 1.0, 2.0 |2 |5.000000e+03, 1.000000e-01, 1.000000e+00, 1.000000e+00, 7.000000e-01, 3.000000e-01, 1.428571e-02, 1.333333e-01 |NaN, NaN, NaN |NaN, NaN, NaN |NA, NA, NA |NA, NA, NA |NA |
|Estimator |$\theta$ |$\xi$ |Conditional to (N,sigma,EX,SX,sampleparam.proph1,sampleparam.proph2,sampleparam.tauh1,sampleparam.tauh2) |Mean |% Relative Bias |RMSE Ratio |Empirical Variance |Asymptotic Variance | |:---------|:-------------|:-----|:--------------------------------------------------------------------------------------------------------------|:-------------------|:------------------------|:--------------------------|:----------------------------------|:-------------------------------| |Naive |0.5, 1.0, 2.0 |2 |5.000000e+03, 1.000000e+00, 1.000000e+00, 1.000000e+00, 7.000000e-01, 3.000000e-01, 1.428571e-02, 1.333333e-01 |2.22, 0.80, 1.78 |344.0, -20.0, -10.8 |68.18110, 2.93315, 4.96587 |0.03629040, 0.01526960, 0.00786459 |NA | |Pseudo |0.5, 1.0, 2.0 |2 |5.000000e+03, 1.000000e+00, 1.000000e+00, 1.000000e+00, 7.000000e-01, 3.000000e-01, 1.428571e-02, 1.333333e-01 |0.509, 1.000, 1.980 |1.7900, -0.0283, -1.0800 |1.64742, 1.89880, 1.54051 |0.0722261, 0.0359059, 0.0163376 |NA | |Sample |0.5, 1.0, 2.0 |2 |5.000000e+03, 1.000000e+00, 1.000000e+00, 1.000000e+00, 7.000000e-01, 3.000000e-01, 1.428571e-02, 1.333333e-01 |0.514, 0.996, 1.990 |2.830, -0.361, -0.532 |1, 1, 1 |0.0436903, 0.0188967, 0.0107968 |0.0421493, 0.0177310, 0.0113943 | |Full |0.5, 1.0, 2.0 |2 |5.000000e+03, 1.000000e+00, 1.000000e+00, 1.000000e+00, 7.000000e-01, 3.000000e-01, 1.428571e-02, 1.333333e-01 |NaN, NaN, NaN |NaN, NaN, NaN |NA, NA, NA |NA, NA, NA |NA |
|Estimator |$\theta$ |$\xi$ |Conditional to (N,sigma,EX,SX,sampleparam.proph1,sampleparam.proph2,sampleparam.tauh1,sampleparam.tauh2) |Mean |% Relative Bias |RMSE Ratio |Empirical Variance |Asymptotic Variance | |:---------|:-------------|:-----|:--------------------------------------------------------------------------------------------------------------|:-------------------|:--------------------|:----------------------------|:----------------------------------|:----------------------------------| |Naive |0.5, 1.0, 2.0 |2 |5.000000e+03, 1.000000e+01, 1.000000e+00, 1.000000e+00, 7.000000e-01, 3.000000e-01, 1.428571e-02, 1.333333e-01 |1.140, 0.967, 1.960 |129.00, -3.28, -1.84 |8.694410, 0.995954, 1.050590 |0.03690170, 0.01580060, 0.00764552 |NA | |Pseudo |0.5, 1.0, 2.0 |2 |5.000000e+03, 1.000000e+01, 1.000000e+00, 1.000000e+00, 7.000000e-01, 3.000000e-01, 1.428571e-02, 1.333333e-01 |0.506, 0.998, 1.970 |1.24, -0.23, -1.32 |1.67253, 2.36019, 2.29071 |0.0866027, 0.0399814, 0.0189159 |NA | |Sample |0.5, 1.0, 2.0 |2 |5.000000e+03, 1.000000e+01, 1.000000e+00, 1.000000e+00, 7.000000e-01, 3.000000e-01, 1.428571e-02, 1.333333e-01 |0.501, 1.000, 1.990 |0.103, 0.153, -0.502 |1, 1, 1 |0.05180200, 0.01693980, 0.00845887 |0.05181540, 0.01628270, 0.00887132 | |Full |0.5, 1.0, 2.0 |2 |5.000000e+03, 1.000000e+01, 1.000000e+00, 1.000000e+00, 7.000000e-01, 3.000000e-01, 1.428571e-02, 1.333333e-01 |NaN, NaN, NaN |NaN, NaN, NaN |NA, NA, NA |NA, NA, NA |NA |
Table 3
|Selection |Estimator |Mean |% Relative Bias |RMSE Ratio |Empirical Variance |Average Estimated Variance |Variance Ratio | |:------------|:---------|:------|:---------------|:----------|:------------------|:--------------------------|:--------------| |Unstratified |Naive |36.949 |-7.286 |20.995 |0.188 |0.186 |0.989 | |Unstratified |Pseudo |39.805 |-0.122 |1.106 |0.452 |0.419 |0.926 | |Unstratified |Sample |39.827 |-0.065 |1 |0.41 |0.388 |0.945 | |Stratified |Naive |36.932 |-7.328 |113.911 |0.006 |0.188 |30.271 | |Stratified |Pseudo |39.858 |0.013 |2.448 |0.184 |0.169 |0.923 | |Stratified |Sample |39.848 |-0.012 |1 |0.075 |0.066 |0.886 |
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