The TOJ bias-corrected empirical CDF estimation
tojecdf.RdThe `tojecdf()` function enables to implement the TOJ bias-corrected estimation of the cumulative distribution function (CDF) of the heterogeneous mean, the heterogeneous autocovariance, and the heterogeneous autocorrelation. The method is developed by Okui and Yanagi (2019). For more details, see the package vignette with `vignette("panelhetero")`.
Arguments
- data
A matrix of panel data. Each row corresponds to individual time series.
- acov_order
A non-negative integer of the order of autocovariance. Default is 0.
- acor_order
A positive integer of the order of autocorrelation. Default is 1.
- R
A positive integer of the number of bootstrap repetitions. Default is 1000.
- ci
A logical whether to estimate the confidence interval. Default is TRUE.
Value
A list that contains the following elements.
- mean
A plot of the corresponding CDF
- acov
A plot of the corresponding CDF
- acor
A plot of the corresponding CDF
- mean_func
A function that returns the corresponding CDF
- acov_func
A function that returns the corresponding CDF
- acor_func
A function that returns the corresponding CDF
- mean_ci_func
A function that returns the 95 percent confidence interval for the corresponding CDF
- acov_ci_func
A function that returns the 95 percent confidence interval for the corresponding CDF
- acor_ci_func
A function that returns the 95 percent confidence interval for the corresponding CDF
- quantity
A matrix of the estimated heterogeneous quantities
- acov_order
The order of autocovariance
- acor_order
The order of autocorrelation
- N
The number of cross-sectional units
- S
The length of time series
- R
The number of bootstrap repetitions
References
Okui, R. and Yanagi, T., 2019. Panel data analysis with heterogeneous dynamics. Journal of Econometrics, 212(2), pp.451-475.
Examples
data <- panelhetero::simulation(N = 300, S = 50)
panelhetero::tojecdf(data = data, R = 50)
#> $mean
#>
#> $acov
#>
#> $acor
#>
#> $mean_func
#> function (x)
#> {
#> tojecdfest2(x = x, X = mean_est, X21 = mean_est21, X22 = mean_est22,
#> X31 = mean_est31, X32 = mean_est32, X33 = mean_est33,
#> X34 = mean_est34, X35 = mean_est35, X36 = mean_est36,
#> X37 = mean_est37, X38 = mean_est38, X39 = mean_est39)
#> }
#> <bytecode: 0x563093f95868>
#> <environment: 0x563093f1c238>
#>
#> $acov_func
#> function (x)
#> {
#> tojecdfest2(x = x, X = acov_est, X21 = acov_est21, X22 = acov_est22,
#> X31 = acov_est31, X32 = acov_est32, X33 = acov_est33,
#> X34 = acov_est34, X35 = acov_est35, X36 = acov_est36,
#> X37 = acov_est37, X38 = acov_est38, X39 = acov_est39)
#> }
#> <bytecode: 0x563093f96240>
#> <environment: 0x563093f1c238>
#>
#> $acor_func
#> function (x)
#> {
#> tojecdfest2(x = x, X = acor_est, X21 = acor_est21, X22 = acor_est22,
#> X31 = acor_est31, X32 = acor_est32, X33 = acor_est33,
#> X34 = acor_est34, X35 = acor_est35, X36 = acor_est36,
#> X37 = acor_est37, X38 = acor_est38, X39 = acor_est39)
#> }
#> <bytecode: 0x563093f96c18>
#> <environment: 0x563093f1c238>
#>
#> $mean_ci_func
#> function (x)
#> {
#> args <- lapply(as.list(match.call())[-1L], eval, parent.frame())
#> names <- if (is.null(names(args)))
#> character(length(args))
#> else names(args)
#> dovec <- names %in% vectorize.args
#> do.call("mapply", c(FUN = FUN, args[dovec], MoreArgs = list(args[!dovec]),
#> SIMPLIFY = SIMPLIFY, USE.NAMES = USE.NAMES))
#> }
#> <environment: 0x563094f3f188>
#>
#> $acov_ci_func
#> function (x)
#> {
#> args <- lapply(as.list(match.call())[-1L], eval, parent.frame())
#> names <- if (is.null(names(args)))
#> character(length(args))
#> else names(args)
#> dovec <- names %in% vectorize.args
#> do.call("mapply", c(FUN = FUN, args[dovec], MoreArgs = list(args[!dovec]),
#> SIMPLIFY = SIMPLIFY, USE.NAMES = USE.NAMES))
#> }
#> <environment: 0x563096829338>
#>
#> $acor_ci_func
#> function (x)
#> {
#> args <- lapply(as.list(match.call())[-1L], eval, parent.frame())
#> names <- if (is.null(names(args)))
#> character(length(args))
#> else names(args)
#> dovec <- names %in% vectorize.args
#> do.call("mapply", c(FUN = FUN, args[dovec], MoreArgs = list(args[!dovec]),
#> SIMPLIFY = SIMPLIFY, USE.NAMES = USE.NAMES))
#> }
#> <environment: 0x56309606c828>
#>
#> $quantity
#> mean autocovariance autocorrelation
#> [1,] -0.9262876406 0.34939475 0.175608385
#> [2,] 0.6763047731 1.39351890 0.496323392
#> [3,] 2.1526114807 0.23782987 0.310848296
#> [4,] -0.5321177959 0.28972250 0.159517560
#> [5,] 0.9536379941 0.25264020 0.555010191
#> [6,] -0.3712116519 0.41950023 0.270310077
#> [7,] -0.8118713916 0.14972202 0.241391904
#> [8,] 0.7144362126 0.35440253 0.126982452
#> [9,] -0.7158457846 0.39985078 0.307067717
#> [10,] 1.8074632502 0.85973909 0.096610271
#> [11,] 0.3243361785 0.15470235 0.137868715
#> [12,] 0.1074939205 0.20132438 0.555798468
#> [13,] -1.2326732823 0.79423391 -0.137612763
#> [14,] 0.0499597515 0.52088670 0.293977746
#> [15,] 0.1270539232 0.21610127 0.354471217
#> [16,] -0.3885392174 0.16682043 0.461837618
#> [17,] 0.7492399312 0.32251245 0.060451914
#> [18,] 0.7594942040 0.33946285 0.402508676
#> [19,] 0.6519905139 0.78401784 0.292622213
#> [20,] 0.3076956367 0.17135224 0.597366701
#> [21,] -1.8881869825 0.29260038 0.369363623
#> [22,] 1.0753792189 0.56739576 0.237122943
#> [23,] 1.1709788465 0.58522289 0.006751810
#> [24,] -1.0154256472 0.37252289 0.284925747
#> [25,] -1.0575506194 0.28289278 0.324137036
#> [26,] 0.8856601236 0.31764815 0.112962216
#> [27,] -0.5376299292 0.40305814 0.260151872
#> [28,] 0.8123313039 0.16010656 0.136267896
#> [29,] 1.3164499429 0.33939818 0.065318628
#> [30,] 0.1371489578 0.26391485 0.077726996
#> [31,] -1.1824409583 0.27249165 0.355412407
#> [32,] -0.0192766907 0.27515882 0.186488969
#> [33,] -0.7360687398 0.29342458 0.338976601
#> [34,] 0.6773015509 0.26791042 0.062184934
#> [35,] -1.1225597134 0.38431777 0.243253099
#> [36,] -0.3274688119 0.26067337 0.455926835
#> [37,] 1.5884320388 0.24180951 0.050367810
#> [38,] 1.0100830064 0.23639331 0.438169935
#> [39,] -0.7236553852 0.04267870 0.897230235
#> [40,] -0.9997598697 0.21450285 0.149043221
#> [41,] -0.4485029475 0.26380921 0.425152716
#> [42,] -0.3714713887 0.26473287 0.394740351
#> [43,] -0.2914812007 0.19220330 0.449505800
#> [44,] -0.8013376381 0.18815155 0.094440065
#> [45,] 1.2374131685 0.29802090 0.184289207
#> [46,] 1.5944563630 0.34642636 0.384026458
#> [47,] -0.0018701215 0.39763437 0.338641956
#> [48,] -0.2519835218 0.09746520 0.307358163
#> [49,] -1.0729906889 0.23842549 0.370140897
#> [50,] 0.4217091069 0.32343430 0.316953814
#> [51,] -0.5165932762 0.03482342 0.589742731
#> [52,] 0.1948331167 0.52053452 0.633705804
#> [53,] -0.9981687255 0.32594182 0.080288290
#> [54,] -0.4361260471 0.87083289 0.185870339
#> [55,] -0.1817442934 0.18222120 0.469976638
#> [56,] -0.7270635807 0.10288853 0.492439968
#> [57,] -0.0458704124 0.16640302 0.178370157
#> [58,] 0.7010152680 0.18295837 0.606570325
#> [59,] -1.8485941287 0.18740246 0.302806786
#> [60,] -1.4477913683 0.54915278 0.034814061
#> [61,] -0.0267450182 0.48487892 0.003589912
#> [62,] -0.0936822138 0.33403642 0.165917732
#> [63,] -1.3319617495 0.07810282 0.566706149
#> [64,] -1.7657162167 0.54211421 0.026852846
#> [65,] 0.4760780565 0.37763692 0.127069376
#> [66,] -0.7417764871 0.44800834 0.101037646
#> [67,] 1.3958519255 0.15833040 -0.013673017
#> [68,] -0.2343373024 0.45741260 0.030210529
#> [69,] -0.2407424045 0.30009382 0.246988569
#> [70,] -0.5661422285 1.27441913 -0.059547626
#> [71,] -0.4814230680 0.27017040 0.782000070
#> [72,] -0.4397049129 0.41333385 0.066250806
#> [73,] -1.3267840267 0.55251275 0.464255674
#> [74,] 0.1904150870 0.35389574 0.414981866
#> [75,] 0.3279284170 1.23755652 0.434182913
#> [76,] -0.1450008855 0.40745223 0.244145985
#> [77,] 0.0818424784 0.52411871 0.071677603
#> [78,] 0.9449225027 0.47586979 0.156948850
#> [79,] 1.7780741885 0.36372488 0.179285730
#> [80,] -1.1774964864 0.23342971 0.174335562
#> [81,] 1.5241672955 0.14956032 -0.024865697
#> [82,] 0.1099181492 0.31581846 0.290902426
#> [83,] -1.1605477310 0.13345320 0.235882147
#> [84,] 1.2854430994 0.66482067 0.284130832
#> [85,] -0.0943346259 0.07531572 0.583282542
#> [86,] -1.0502126363 0.15955808 0.303496292
#> [87,] -0.1816898624 0.17121516 0.191738455
#> [88,] 1.0264616838 0.30944498 0.016018233
#> [89,] 0.0844908308 0.24057059 0.480298218
#> [90,] 1.4919736922 0.22106549 0.196087292
#> [91,] -0.7645942627 0.46253296 0.029357343
#> [92,] 0.6526195157 0.53222689 -0.080292224
#> [93,] 0.9774169592 0.34667264 0.341474094
#> [94,] -1.2379232424 0.31280104 0.157470676
#> [95,] 1.0248784461 0.34759156 0.328961082
#> [96,] -0.3090776506 0.25841957 0.299462548
#> [97,] 0.6630567165 0.37382460 0.489653996
#> [98,] -2.4875160376 0.75254711 0.171478605
#> [99,] -0.3622386033 0.21842478 0.463963412
#> [100,] 1.9959130476 0.30262456 0.298184694
#> [101,] -0.8651478142 0.64216417 0.355170147
#> [102,] 0.5268520509 0.22865363 0.131422862
#> [103,] 0.0333422495 0.18596112 -0.060741564
#> [104,] -1.3292843218 0.87100802 0.275688655
#> [105,] -1.0588720046 0.21649738 0.432269609
#> [106,] -2.5509932929 0.20903085 0.335967237
#> [107,] 0.1045999018 0.33606924 0.008873681
#> [108,] 0.3558491847 0.76326406 0.016810986
#> [109,] -0.9676579932 0.55007069 -0.058978131
#> [110,] -0.9441831189 0.47227979 0.099185438
#> [111,] 0.9404319795 0.22279069 0.223295566
#> [112,] -0.7688126336 0.22129979 0.280343595
#> [113,] 0.8440086676 0.29178557 -0.019156741
#> [114,] 0.6958518521 0.47730889 0.179948931
#> [115,] 0.3161501435 0.36555652 0.484311190
#> [116,] -0.7453987351 0.65666055 0.128865641
#> [117,] 0.5790067807 0.31432488 0.103444808
#> [118,] 0.0162995659 0.45467432 0.081457716
#> [119,] 1.2423398958 0.51714053 0.378895659
#> [120,] -1.7174198837 0.31277616 0.368548522
#> [121,] -0.7959449843 0.15805277 0.355426368
#> [122,] 0.0259122396 0.29401016 -0.091015406
#> [123,] 0.0841761839 0.68560096 0.055054025
#> [124,] -1.4666713020 0.44351451 0.081412036
#> [125,] -1.4641149380 0.17822861 0.555464624
#> [126,] 0.5519367916 0.57047840 -0.020155539
#> [127,] 0.4022648426 0.20673746 0.144312984
#> [128,] 1.2625437569 0.11152978 0.161461765
#> [129,] -0.1035825952 0.73318728 0.330155761
#> [130,] 0.5618760998 0.66890439 0.148266403
#> [131,] 0.2930950756 0.54943181 -0.136983998
#> [132,] 2.2698527771 0.20976323 -0.055958444
#> [133,] 0.1354894807 0.47662374 0.382801162
#> [134,] -0.5899333295 0.36832266 0.226654459
#> [135,] -2.0987309521 0.34138519 0.130499426
#> [136,] -0.1747866569 0.28035603 0.453040676
#> [137,] 0.9645061760 0.38385924 0.124359865
#> [138,] 0.5693808152 0.55538883 0.383101408
#> [139,] 0.1512246716 0.72584621 0.085489070
#> [140,] 1.5562646744 0.38002220 0.373305667
#> [141,] 0.2739045908 0.54909105 0.395949528
#> [142,] 0.3687534238 0.25399458 0.278176948
#> [143,] -0.3143135554 0.28373239 0.301857735
#> [144,] -0.9453876484 0.55959724 -0.089355110
#> [145,] 0.0288090892 0.25864412 0.504311174
#> [146,] 0.1635059466 0.11623414 0.390892515
#> [147,] 1.4775696431 0.30289440 0.301320775
#> [148,] -0.4318483321 0.15748257 0.062205526
#> [149,] 1.2513965795 0.56343861 0.358623966
#> [150,] 1.2342144498 0.28617146 0.250161805
#> [151,] -0.3256371311 0.27829933 0.014153946
#> [152,] -0.4597414432 0.32932992 0.540835265
#> [153,] 1.0628720999 0.48894754 0.604712172
#> [154,] -0.0585986583 0.21084362 0.617232903
#> [155,] -0.5134099239 0.31140947 0.493111234
#> [156,] 0.7535236061 0.38231972 -0.087220382
#> [157,] 0.0463121540 0.33676393 0.211591210
#> [158,] 0.9483691509 0.20047318 0.432762146
#> [159,] -0.4573830265 0.86312181 0.165759284
#> [160,] 0.9772943114 0.06849904 0.653481503
#> [161,] -1.5490702117 0.64065109 0.202715191
#> [162,] 1.2279704497 0.26100090 -0.049240714
#> [163,] -0.0750990635 0.32156600 0.205064718
#> [164,] -0.3357700599 0.30465261 0.370108872
#> [165,] 2.4659184795 0.43145489 0.285351956
#> [166,] -1.1471613096 0.22320227 0.396981832
#> [167,] 0.3320420041 0.26185449 0.366223981
#> [168,] -0.7397034764 0.92763428 0.223206088
#> [169,] -0.0019597700 0.45130520 0.101513891
#> [170,] 1.2456731032 0.47011026 0.278819635
#> [171,] -1.8942634846 0.27734651 0.357787094
#> [172,] 1.8324795828 0.23017158 0.155907824
#> [173,] -0.7999225300 0.12420137 0.194657263
#> [174,] 1.2228300595 0.17326470 0.247411673
#> [175,] -1.0309544441 0.49336782 0.135096518
#> [176,] 0.3183935148 0.54516398 0.369595111
#> [177,] 0.0563599022 0.29936856 0.434919265
#> [178,] -0.9065551192 0.38781215 -0.110343295
#> [179,] 1.2979967575 0.28148103 0.028430264
#> [180,] 1.0791584082 0.42209643 0.324169834
#> [181,] 1.2017339224 0.15949960 0.330895297
#> [182,] 0.1185586240 0.22434554 -0.010986766
#> [183,] 0.3648377548 0.25977611 0.617700162
#> [184,] 0.0748076479 0.25983640 0.021114088
#> [185,] -0.5337043324 0.23021568 0.409802195
#> [186,] -0.6537981762 0.31137134 0.102923917
#> [187,] 0.7812010520 0.53188030 -0.285751951
#> [188,] -0.3429014733 0.12022577 0.214461944
#> [189,] 1.0518359556 0.54103129 0.062334573
#> [190,] -1.5086616565 0.59464454 0.499303343
#> [191,] -0.3578514898 0.16235730 0.579216745
#> [192,] -2.0060984077 0.17903068 0.565536389
#> [193,] -0.1031194713 0.30902965 -0.012729927
#> [194,] -1.0008826617 0.26592410 -0.053305678
#> [195,] 0.3187296362 0.81100028 0.360144186
#> [196,] 1.0656950073 0.30501281 -0.089092846
#> [197,] -0.1333788984 0.27702375 0.112592867
#> [198,] 1.6689328395 0.16300573 0.207919955
#> [199,] -1.2748718286 0.14812634 0.367688910
#> [200,] -1.2800300587 0.01728024 0.832944825
#> [201,] 0.3658085895 0.27663372 0.282774009
#> [202,] 0.4367922969 0.30023928 0.480741965
#> [203,] -1.6988556271 0.42481819 -0.176622570
#> [204,] 0.0286379931 0.17996801 0.283398209
#> [205,] -1.3331250035 0.70758198 0.079336598
#> [206,] -0.4263091363 0.29924819 0.382781704
#> [207,] -1.4071750277 0.16096377 0.332487544
#> [208,] 1.2568542614 0.22463430 0.215421942
#> [209,] 0.2683114263 0.60500705 0.220398341
#> [210,] -0.6127582764 0.33804593 -0.190069685
#> [211,] -0.7244384166 0.19660963 0.394854968
#> [212,] -1.5772039898 0.16743123 0.315150992
#> [213,] -1.4033421970 0.02643180 0.320280441
#> [214,] -0.6722801163 0.34773113 0.466214485
#> [215,] -1.4695235421 0.77664344 0.070733936
#> [216,] 0.4490242631 0.24177386 0.195167596
#> [217,] -0.9390078397 0.33450180 0.409354266
#> [218,] -0.5381434848 0.31296590 0.200397287
#> [219,] 0.6989781293 0.47099901 -0.005887686
#> [220,] 1.2174099695 0.72801732 -0.033016586
#> [221,] -0.1173895208 0.42433062 0.110477727
#> [222,] -1.1951328200 0.62706932 -0.026326161
#> [223,] -0.3732926348 0.35126745 0.345039915
#> [224,] 0.8508219351 0.27615474 0.060417213
#> [225,] 0.0204326469 0.60354049 -0.131362423
#> [226,] 0.3494133194 0.20644389 0.097752285
#> [227,] 0.4901154979 0.17025763 0.403546889
#> [228,] 1.5621669861 0.26371075 0.050605124
#> [229,] 0.0840483019 0.19772963 0.183947552
#> [230,] 0.0219745611 0.08087418 0.588294183
#> [231,] 0.3216248767 0.33156821 0.147882742
#> [232,] -1.7055511791 0.41893370 0.139463793
#> [233,] 1.9172158728 0.40447393 0.294745737
#> [234,] 1.0960813555 0.48741823 0.037399294
#> [235,] -2.7937488619 0.38723779 0.153671579
#> [236,] 0.4724844843 0.08991652 0.324365113
#> [237,] -0.0007278013 0.18491455 0.220482201
#> [238,] 0.4285246743 0.21715556 0.367507041
#> [239,] -1.7782603364 0.46562788 0.203174307
#> [240,] -0.0826892621 0.34825127 0.112741347
#> [241,] 0.2039490610 0.62633242 0.144782428
#> [242,] -0.3833633955 0.13104109 0.414247415
#> [243,] -1.1063839112 0.19989802 0.417428643
#> [244,] -0.6010860078 0.28501154 0.213212137
#> [245,] -0.0433248205 0.21200870 0.271170495
#> [246,] 1.3920380488 0.19030770 0.499629925
#> [247,] -0.5462715611 0.20695822 0.303345353
#> [248,] 1.1509389143 0.22554267 0.824439031
#> [249,] -0.8729517978 0.26411481 0.404132986
#> [250,] 0.1363991102 0.41503758 -0.172980483
#> [251,] -1.4691152421 0.14919317 0.115168126
#> [252,] -0.3268303938 0.43863920 0.163164617
#> [253,] 0.6966470108 0.19125281 0.536399638
#> [254,] -0.6113589150 1.38027479 0.308922000
#> [255,] -0.8500891116 0.14487611 0.262248628
#> [256,] -0.6392116967 0.22726628 0.383114244
#> [257,] -0.2639417163 0.22185419 0.295118756
#> [258,] -0.6724657725 0.34960304 0.121138113
#> [259,] 1.3803811288 0.12974934 0.388751145
#> [260,] 1.0360568022 0.33338103 0.185184378
#> [261,] -0.5184057421 0.75793957 -0.152382991
#> [262,] 0.4226212485 0.13089832 0.245613855
#> [263,] 1.4087937623 0.49827429 0.348304675
#> [264,] -0.0047323996 0.40412962 0.447954706
#> [265,] -0.0113267160 0.18927138 0.609037569
#> [266,] 0.8526045155 0.29555096 0.333546033
#> [267,] 0.4262779125 0.53534169 0.241617322
#> [268,] -0.7303363619 0.59045043 0.138801981
#> [269,] 0.1854035272 1.07265036 0.177682034
#> [270,] 2.0067188764 0.18934085 0.350339466
#> [271,] 0.9704035278 0.23544612 0.309659568
#> [272,] 0.1261205995 0.21011327 0.357809028
#> [273,] 0.0795196358 0.49764667 -0.251295305
#> [274,] 0.1805632412 0.26525646 -0.024646876
#> [275,] 0.6793295926 0.98801476 0.128810518
#> [276,] -0.1214725225 0.41197426 0.094837181
#> [277,] 2.0254155512 0.55183397 0.182255400
#> [278,] 0.9961292352 0.19097195 0.202812586
#> [279,] -0.1893219774 0.19569833 0.278550065
#> [280,] 0.4533913799 0.41783680 0.153929999
#> [281,] -0.9318309609 0.20628593 0.069982834
#> [282,] 0.0813970810 0.25437928 -0.039271734
#> [283,] 0.3745327645 0.49543924 -0.092071263
#> [284,] 0.4411927314 0.28878086 0.179243709
#> [285,] -0.5904404686 0.25144024 0.589833347
#> [286,] 0.1713338986 0.23836997 0.216793223
#> [287,] -1.7994285719 0.34298694 0.355497161
#> [288,] -1.6750288305 0.23549500 0.603057791
#> [289,] 0.3004892597 0.32496583 0.517222257
#> [290,] -0.1188241950 0.26730139 0.343614799
#> [291,] 1.9813748793 0.16681295 0.247054618
#> [292,] 0.7525154042 0.32682287 0.027103186
#> [293,] -0.4222142087 0.16137883 0.189022517
#> [294,] -0.5592799816 0.22357827 0.321143588
#> [295,] 1.3124071411 0.72089443 -0.011273085
#> [296,] 0.9173614959 0.24903731 0.503800826
#> [297,] -0.2172807431 0.10527823 0.354925561
#> [298,] 0.7562787111 0.15926410 0.131209110
#> [299,] -0.0247364563 0.27770896 0.621668782
#> [300,] -1.4103920714 0.32317262 0.170914835
#>
#> $acov_order
#> [1] 0
#>
#> $acor_order
#> [1] 1
#>
#> $N
#> [1] 300
#>
#> $S
#> [1] 50
#>
#> $R
#> [1] 50
#>