Log-spline density estimator (Stone 1990, Ghosal Ch 8)
Source:R/ghlgd.R
morie_ghosal_log_density.RdLog-spline density estimator (Stone 1990, Ghosal Ch 8)
Examples
set.seed(1)
morie_ghosal_log_density(x = rnorm(50))
#> $estimate
#> [1] -0.6931484
#>
#> $theta
#> [1] 0.4995664153 -0.5890118459 -0.2282776488 -0.0006530812 0.0103234023
#>
#> $log_lik
#> [1] -68.27323
#>
#> $grid
#> [1] -3.046093818 -3.032411896 -3.018729975 -3.005048053 -2.991366132
#> [6] -2.977684211 -2.964002289 -2.950320368 -2.936638447 -2.922956525
#> [11] -2.909274604 -2.895592682 -2.881910761 -2.868228840 -2.854546918
#> [16] -2.840864997 -2.827183076 -2.813501154 -2.799819233 -2.786137311
#> [21] -2.772455390 -2.758773469 -2.745091547 -2.731409626 -2.717727705
#> [26] -2.704045783 -2.690363862 -2.676681940 -2.663000019 -2.649318098
#> [31] -2.635636176 -2.621954255 -2.608272334 -2.594590412 -2.580908491
#> [36] -2.567226569 -2.553544648 -2.539862727 -2.526180805 -2.512498884
#> [41] -2.498816963 -2.485135041 -2.471453120 -2.457771198 -2.444089277
#> [46] -2.430407356 -2.416725434 -2.403043513 -2.389361592 -2.375679670
#> [51] -2.361997749 -2.348315827 -2.334633906 -2.320951985 -2.307270063
#> [56] -2.293588142 -2.279906221 -2.266224299 -2.252542378 -2.238860456
#> [61] -2.225178535 -2.211496614 -2.197814692 -2.184132771 -2.170450850
#> [66] -2.156768928 -2.143087007 -2.129405085 -2.115723164 -2.102041243
#> [71] -2.088359321 -2.074677400 -2.060995479 -2.047313557 -2.033631636
#> [76] -2.019949714 -2.006267793 -1.992585872 -1.978903950 -1.965222029
#> [81] -1.951540108 -1.937858186 -1.924176265 -1.910494343 -1.896812422
#> [86] -1.883130501 -1.869448579 -1.855766658 -1.842084737 -1.828402815
#> [91] -1.814720894 -1.801038972 -1.787357051 -1.773675130 -1.759993208
#> [96] -1.746311287 -1.732629366 -1.718947444 -1.705265523 -1.691583601
#> [101] -1.677901680 -1.664219759 -1.650537837 -1.636855916 -1.623173995
#> [106] -1.609492073 -1.595810152 -1.582128230 -1.568446309 -1.554764388
#> [111] -1.541082466 -1.527400545 -1.513718624 -1.500036702 -1.486354781
#> [116] -1.472672859 -1.458990938 -1.445309017 -1.431627095 -1.417945174
#> [121] -1.404263253 -1.390581331 -1.376899410 -1.363217488 -1.349535567
#> [126] -1.335853646 -1.322171724 -1.308489803 -1.294807882 -1.281125960
#> [131] -1.267444039 -1.253762117 -1.240080196 -1.226398275 -1.212716353
#> [136] -1.199034432 -1.185352511 -1.171670589 -1.157988668 -1.144306746
#> [141] -1.130624825 -1.116942904 -1.103260982 -1.089579061 -1.075897140
#> [146] -1.062215218 -1.048533297 -1.034851375 -1.021169454 -1.007487533
#> [151] -0.993805611 -0.980123690 -0.966441769 -0.952759847 -0.939077926
#> [156] -0.925396004 -0.911714083 -0.898032162 -0.884350240 -0.870668319
#> [161] -0.856986398 -0.843304476 -0.829622555 -0.815940633 -0.802258712
#> [166] -0.788576791 -0.774894869 -0.761212948 -0.747531027 -0.733849105
#> [171] -0.720167184 -0.706485262 -0.692803341 -0.679121420 -0.665439498
#> [176] -0.651757577 -0.638075656 -0.624393734 -0.610711813 -0.597029891
#> [181] -0.583347970 -0.569666049 -0.555984127 -0.542302206 -0.528620285
#> [186] -0.514938363 -0.501256442 -0.487574520 -0.473892599 -0.460210678
#> [191] -0.446528756 -0.432846835 -0.419164914 -0.405482992 -0.391801071
#> [196] -0.378119149 -0.364437228 -0.350755307 -0.337073385 -0.323391464
#> [201] -0.309709543 -0.296027621 -0.282345700 -0.268663778 -0.254981857
#> [206] -0.241299936 -0.227618014 -0.213936093 -0.200254172 -0.186572250
#> [211] -0.172890329 -0.159208407 -0.145526486 -0.131844565 -0.118162643
#> [216] -0.104480722 -0.090798801 -0.077116879 -0.063434958 -0.049753036
#> [221] -0.036071115 -0.022389194 -0.008707272 0.004974649 0.018656570
#> [226] 0.032338492 0.046020413 0.059702335 0.073384256 0.087066177
#> [231] 0.100748099 0.114430020 0.128111941 0.141793863 0.155475784
#> [236] 0.169157706 0.182839627 0.196521548 0.210203470 0.223885391
#> [241] 0.237567312 0.251249234 0.264931155 0.278613077 0.292294998
#> [246] 0.305976919 0.319658841 0.333340762 0.347022683 0.360704605
#> [251] 0.374386526 0.388068448 0.401750369 0.415432290 0.429114212
#> [256] 0.442796133 0.456478055 0.470159976 0.483841897 0.497523819
#> [261] 0.511205740 0.524887661 0.538569583 0.552251504 0.565933426
#> [266] 0.579615347 0.593297268 0.606979190 0.620661111 0.634343032
#> [271] 0.648024954 0.661706875 0.675388797 0.689070718 0.702752639
#> [276] 0.716434561 0.730116482 0.743798403 0.757480325 0.771162246
#> [281] 0.784844168 0.798526089 0.812208010 0.825889932 0.839571853
#> [286] 0.853253774 0.866935696 0.880617617 0.894299539 0.907981460
#> [291] 0.921663381 0.935345303 0.949027224 0.962709145 0.976391067
#> [296] 0.990072988 1.003754910 1.017436831 1.031118752 1.044800674
#> [301] 1.058482595 1.072164516 1.085846438 1.099528359 1.113210281
#> [306] 1.126892202 1.140574123 1.154256045 1.167937966 1.181619887
#> [311] 1.195301809 1.208983730 1.222665652 1.236347573 1.250029494
#> [316] 1.263711416 1.277393337 1.291075258 1.304757180 1.318439101
#> [321] 1.332121023 1.345802944 1.359484865 1.373166787 1.386848708
#> [326] 1.400530629 1.414212551 1.427894472 1.441576394 1.455258315
#> [331] 1.468940236 1.482622158 1.496304079 1.509986000 1.523667922
#> [336] 1.537349843 1.551031765 1.564713686 1.578395607 1.592077529
#> [341] 1.605759450 1.619441371 1.633123293 1.646805214 1.660487136
#> [346] 1.674169057 1.687850978 1.701532900 1.715214821 1.728896742
#> [351] 1.742578664 1.756260585 1.769942507 1.783624428 1.797306349
#> [356] 1.810988271 1.824670192 1.838352113 1.852034035 1.865715956
#> [361] 1.879397878 1.893079799 1.906761720 1.920443642 1.934125563
#> [366] 1.947807484 1.961489406 1.975171327 1.988853249 2.002535170
#> [371] 2.016217091 2.029899013 2.043580934 2.057262855 2.070944777
#> [376] 2.084626698 2.098308620 2.111990541 2.125672462 2.139354384
#> [381] 2.153036305 2.166718226 2.180400148 2.194082069 2.207763991
#> [386] 2.221445912 2.235127833 2.248809755 2.262491676 2.276173597
#> [391] 2.289855519 2.303537440 2.317219362 2.330901283 2.344583204
#> [396] 2.358265126 2.371947047 2.385628968 2.399310890 2.412992811
#> [401] 2.426674733
#>
#> $log_density
#> [1] -6.7956446 -6.6998562 -6.6060110 -6.5140759 -6.4240181 -6.3358050
#> [7] -6.2494045 -6.1647847 -6.0819142 -6.0007618 -5.9212967 -5.8434883
#> [13] -5.7673066 -5.6927217 -5.6197041 -5.5482246 -5.4782543 -5.4097647
#> [19] -5.3427277 -5.2771153 -5.2128999 -5.1500543 -5.0885516 -5.0283651
#> [25] -4.9694684 -4.9118357 -4.8554411 -4.8002594 -4.7462653 -4.6934342
#> [31] -4.6417416 -4.5911633 -4.5416753 -4.4932543 -4.4458768 -4.3995198
#> [37] -4.3541608 -4.3097773 -4.2663471 -4.2238485 -4.1822600 -4.1415603
#> [43] -4.1017285 -4.0627439 -4.0245860 -3.9872349 -3.9506706 -3.9148736
#> [49] -3.8798247 -3.8455048 -3.8118952 -3.7789775 -3.7467334 -3.7151452
#> [55] -3.6841950 -3.6538655 -3.6241397 -3.5950006 -3.5664316 -3.5384165
#> [61] -3.5109392 -3.4839837 -3.4575347 -3.4315766 -3.4060946 -3.3810738
#> [67] -3.3564996 -3.3323577 -3.3086341 -3.2853149 -3.2623865 -3.2398357
#> [73] -3.2176493 -3.1958146 -3.1743187 -3.1531495 -3.1322947 -3.1117424
#> [79] -3.0914809 -3.0714989 -3.0517849 -3.0323282 -3.0131178 -2.9941433
#> [85] -2.9753943 -2.9568607 -2.9385327 -2.9204005 -2.9024547 -2.8846861
#> [91] -2.8670856 -2.8496445 -2.8323541 -2.8152060 -2.7981921 -2.7813044
#> [97] -2.7645351 -2.7478767 -2.7313217 -2.7148630 -2.6984937 -2.6822069
#> [103] -2.6659961 -2.6498549 -2.6337771 -2.6177567 -2.6017879 -2.5858650
#> [109] -2.5699827 -2.5541357 -2.5383189 -2.5225274 -2.5067565 -2.4910018
#> [115] -2.4752587 -2.4595233 -2.4437914 -2.4280593 -2.4123233 -2.3965799
#> [121] -2.3808257 -2.3650578 -2.3492730 -2.3334686 -2.3176418 -2.3017903
#> [127] -2.2859116 -2.2700036 -2.2540643 -2.2380918 -2.2220844 -2.2060405
#> [133] -2.1899587 -2.1738378 -2.1576767 -2.1414743 -2.1252300 -2.1089429
#> [139] -2.0926125 -2.0762386 -2.0598207 -2.0433588 -2.0268529 -2.0103031
#> [145] -1.9937098 -1.9770733 -1.9603942 -1.9436732 -1.9269110 -1.9101086
#> [151] -1.8932671 -1.8763875 -1.8594712 -1.8425196 -1.8255342 -1.8085167
#> [157] -1.7914689 -1.7743925 -1.7572896 -1.7401623 -1.7230127 -1.7058432
#> [163] -1.6886563 -1.6714543 -1.6542400 -1.6370161 -1.6197854 -1.6025507
#> [169] -1.5853152 -1.5680820 -1.5508542 -1.5336351 -1.5164282 -1.4992369
#> [175] -1.4820648 -1.4649156 -1.4477929 -1.4307007 -1.4136427 -1.3966231
#> [181] -1.3796458 -1.3627150 -1.3458350 -1.3290099 -1.3122443 -1.2955424
#> [187] -1.2789089 -1.2623482 -1.2458651 -1.2294642 -1.2131504 -1.1969283
#> [193] -1.1808030 -1.1647794 -1.1488625 -1.1330574 -1.1173691 -1.1018029
#> [199] -1.0863640 -1.0710577 -1.0558893 -1.0408641 -1.0259876 -1.0112653
#> [205] -0.9967027 -0.9823052 -0.9680786 -0.9540284 -0.9401603 -0.9264800
#> [211] -0.9129932 -0.8997057 -0.8866234 -0.8737519 -0.8610972 -0.8486652
#> [217] -0.8364618 -0.8244928 -0.8127644 -0.8012823 -0.7900527 -0.7790815
#> [223] -0.7683747 -0.7579384 -0.7477787 -0.7379016 -0.7283132 -0.7190196
#> [229] -0.7100268 -0.7013410 -0.6929683 -0.6849147 -0.6771864 -0.6697895
#> [235] -0.6627300 -0.6560142 -0.6496480 -0.6436375 -0.6379889 -0.6327082
#> [241] -0.6278015 -0.6232747 -0.6191341 -0.6153854 -0.6120349 -0.6090884
#> [247] -0.6065519 -0.6044314 -0.6027328 -0.6014619 -0.6006247 -0.6002269
#> [253] -0.6002744 -0.6007730 -0.6017285 -0.6031464 -0.6050327 -0.6073927
#> [259] -0.6102323 -0.6135569 -0.6173721 -0.6216833 -0.6264961 -0.6318158
#> [265] -0.6376477 -0.6439972 -0.6508695 -0.6582698 -0.6662032 -0.6746750
#> [271] -0.6836900 -0.6932533 -0.7033698 -0.7140444 -0.7252818 -0.7370869
#> [277] -0.7494642 -0.7624184 -0.7759540 -0.7900755 -0.8047873 -0.8200938
#> [283] -0.8359991 -0.8525074 -0.8696230 -0.8873497 -0.9056915 -0.9246523
#> [289] -0.9442359 -0.9644459 -0.9852860 -1.0067598 -1.0288705 -1.0516216
#> [295] -1.0750164 -1.0990580 -1.1237494 -1.1490937 -1.1750936 -1.2017521
#> [301] -1.2290716 -1.2570549 -1.2857044 -1.3150225 -1.3450113 -1.3756731
#> [307] -1.4070099 -1.4390236 -1.4717160 -1.5050888 -1.5391437 -1.5738821
#> [313] -1.6093053 -1.6454145 -1.6822109 -1.7196955 -1.7578691 -1.7967324
#> [319] -1.8362861 -1.8765306 -1.9174663 -1.9590934 -2.0014120 -2.0444220
#> [325] -2.0881233 -2.1325154 -2.1775980 -2.2233705 -2.2698320 -2.3169817
#> [331] -2.3648186 -2.4133414 -2.4625489 -2.5124395 -2.5630116 -2.6142635
#> [337] -2.6661931 -2.7187984 -2.7720771 -2.8260268 -2.8806450 -2.9359289
#> [343] -2.9918755 -3.0484819 -3.1057448 -3.1636607 -3.2222262 -3.2814375
#> [349] -3.3412907 -3.4017816 -3.4629061 -3.5246596 -3.5870376 -3.6500353
#> [355] -3.7136477 -3.7778697 -3.8426958 -3.9081205 -3.9741383 -4.0407430
#> [361] -4.1079287 -4.1756890 -4.2440175 -4.3129075 -4.3823521 -4.4523443
#> [367] -4.5228767 -4.5939419 -4.6655323 -4.7376399 -4.8102567 -4.8833744
#> [373] -4.9569845 -5.0310782 -5.1056467 -5.1806808 -5.2561712 -5.3321084
#> [379] -5.4084825 -5.4852835 -5.5625013 -5.6401254 -5.7181451 -5.7965496
#> [385] -5.8753277 -5.9544681 -6.0339592 -6.1137893 -6.1939463 -6.2744178
#> [391] -6.3551916 -6.4362547 -6.5175942 -6.5991970 -6.6810495 -6.7631380
#> [397] -6.8454487 -6.9279672 -7.0106793 -7.0935701 -7.1766248
#>
#> $K
#> [1] 5
#>
#> $n
#> [1] 50
#>
#> $method
#> [1] "Log-spline density (Stone 1990)"
#>