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I want to estimate nonparametric estimates for an independent variable by using lokern package at R.

I have the below data which have 2 variables:

x: independent variable

y: dependent variable

data_test<-structure(list(y = c(0.875261480116371, 0.13319865469368, 0.00127171595390059, 
                     0.120784784396633, 0.396145484602405, 0.0145083415906443, 0.126972404606687, 
                     0.158633863426125, 0.307832433458906, 3.42112531824949, 0.0340520045576305, 
                     0.0577209021937775, 0.0296622168402153, 0.519694575795073, 0.598147976985479, 
                     0.0130977584533862, 0.158721871619698, 0.0345042704092106, 0.828465740122911, 
                     0.288698762072103, 0.00612936654816416, 0.660590833311049, 0.744003852280185, 
                     0.0218624098840227, 0.0643524619734905, 0.106603465426499, 0.996560657600869, 
                     0.122380988335843, 0.533105113544206, 0.0275922420213573, 0.107316738492487, 
                     0.560308948944375, 0.143056108849691, 0.0161973817777236, 0.131817444834554, 
                     1.0931449919045, 0.676905541419034, 0.0264930182311347, 0.0219841874288544, 
                     0.488998767576592, 0.0347315975270806, 0.0411243463454958, 0.239393381406891, 
                     0.518050404977722, 0.0446311348629937, 1.06966798067092, 0.181537821115414, 
                     0.0313727396250001, 0.0216034647860423, 0.0276009215712176, 0.363985328271051, 
                     0.360296428331267, 0.0668551459074575, 0.0096603143441187, 0.0105876830440506, 
                     0.417186148227153, 0.553820116962763, 0.0411408340216935, 0.171913862343572, 
                     0.0514348158606772, 0.389026902873765, 0.185058082651845, 0.0369879163899647, 
                     1.08104328029981, 0.00746768318488792, 0.605457684587019, 0.0144968484938537, 
                     0.00602213252556212, 0.0866902221106011, 2.86731502732902, 0.0410085953665955, 
                     0.013626354236944, 0.000188405910625031, 0.0585839444657251, 
                     0.238292013239626, 0.0792612023923057, 0.108649755268567, 0.00461453622722967, 
                     0.171731805762336, 0.375266208662383, 0.15081802592681, 0.0993654895544528, 
                     1.04912058404724, 0.00688994906597782, 0.00131255129276553, 0.0299156532828988, 
                     1.65913122506183, 1.2779796600082, 0.0635807935616347, 0.0350137919082677, 
                     2.88472754915262, 0.451804325441365, 0.170435290928851, 0.153848212504272, 
                     0.190051111767901, 0.0250402432610551, 1.27823234596823, 0.325244428486599, 
                     2.55249481518541, 0.652738453178641), x = c(0.157051206555181, 
                                                                 93.5554103254521, 36.4963908754934, -3.56611266493445, 34.7541054260692, 
                                                                 -62.9400893391807, 12.0450577377795, -35.6331874250237, -39.828866846312, 
                                                                 55.4826489507221, -184.96284270765, 18.45318524202, 24.0251747535325, 
                                                                 -17.2227224445543, 72.0898450404128, 77.3400269579394, 11.4445438761823, 
                                                                 -39.8399136067962, 18.5753251409526, -91.0200933927729, -53.7306953307048, 
                                                                 7.82902710952271, -81.2767391884694, 86.2556579176221, -14.7859426091212, 
                                                                 25.3677870484381, -32.6501861291018, 99.8278847617673, 34.9829942023039, 
                                                                 73.0140475212959, -16.6109126845448, -32.7592335826843, 74.8537874088129, 
                                                                 -37.8227588694546, 12.7268934849489, 36.3066722290206, -104.553574396311, 
                                                                 82.2742694540057, -16.276676021576, -14.8270655993876, -69.9284468279249, 
                                                                 -18.6364153009855, 20.2791386270462, -48.9278429329243, 71.9757184735048, 
                                                                 21.1260821883741, 103.424754322692, 42.6072553816148, 17.7123515166677, 
                                                                 14.698117153582, -16.6135250838639, -60.331196596044, 60.0246972779761, 
                                                                 -25.8563620618713, 9.82868981305174, -10.2896467597535, -64.5899487712409, 
                                                                 74.419091432425, -20.2832034012612, -41.4624965895172, 22.6792451066338, 
                                                                 62.3720212013179, 43.0183777764626, -19.2322428203173, -103.973231184753, 
                                                                 8.64157577348479, -77.8111614478938, 12.0402859159796, 7.7602400256449, 
                                                                 -29.4432033091852, 169.331480455615, 20.2505790945828, 11.6731976068873, 
                                                                 -1.37261032571168, -24.2041204066012, -48.8151629352629, 28.1533661206446, 
                                                                 32.9620623245219, 6.79303777939566, -41.4405364060766, 61.2589755596993, 
                                                                 -38.8352965646988, 31.5222920414193, 102.426587566278, -8.30057170680298, 
                                                                 3.62291497659761, -17.2961421371642, -128.80726784859, -113.047762472691, 
                                                                 25.2152322142063, -18.7119726133478, -169.84485712416, -67.2163912629475, 
                                                                 41.2838092875223, -39.2234894552068, -43.5948519630358, 15.8241092201283, 
                                                                 113.058937991131, 57.0302050221283, -159.765290823302)), class = "data.frame", row.names = c(NA, 
                                                                                                                                                              -100L))

I using lokern package at R to obtain nonparametric estimates for y.

Then I have the below simple code:

  library(lokern)
  model_np<-lokerns(y~x, data=data_test)

After executing the below code for getting estimates of y:

> predict(model_np,data_test$x)
$x
  [1]    0.1570512   93.5554103   36.4963909   -3.5661127   34.7541054  -62.9400893   12.0450577  -35.6331874  -39.8288668   55.4826490 -184.9628427   18.4531852   24.0251748
 [14]  -17.2227224   72.0898450   77.3400270   11.4445439  -39.8399136   18.5753251  -91.0200934  -53.7306953    7.8290271  -81.2767392   86.2556579  -14.7859426   25.3677870
 [27]  -32.6501861   99.8278848   34.9829942   73.0140475  -16.6109127  -32.7592336   74.8537874  -37.8227589   12.7268935   36.3066722 -104.5535744   82.2742695  -16.2766760
 [40]  -14.8270656  -69.9284468  -18.6364153   20.2791386  -48.9278429   71.9757185   21.1260822  103.4247543   42.6072554   17.7123515   14.6981172  -16.6135251  -60.3311966
 [53]   60.0246973  -25.8563621    9.8286898  -10.2896468  -64.5899488   74.4190914  -20.2832034  -41.4624966   22.6792451   62.3720212   43.0183778  -19.2322428 -103.9732312
 [66]    8.6415758  -77.8111614   12.0402859    7.7602400  -29.4432033  169.3314805   20.2505791   11.6731976   -1.3726103  -24.2041204  -48.8151629   28.1533661   32.9620623
 [79]    6.7930378  -41.4405364   61.2589756  -38.8352966   31.5222920  102.4265876   -8.3005717    3.6229150  -17.2961421 -128.8072678 -113.0477625   25.2152322  -18.7119726
 [92] -169.8448571  -67.2163913   41.2838093  -39.2234895  -43.5948520   15.8241092  113.0589380   57.0302050 -159.7652908

$y
  [1] 0.36009101 0.32846545 0.68153382 0.38608090 0.66311088 0.29850071 0.29482348 0.39911713 0.37939114 0.69109190 0.20305681 0.33928391 0.47218019 0.43021110 0.51132988 0.45387648
 [17] 0.29602706 0.37935451 0.34154393 0.31747282 0.34292331 0.30097045 0.25197283 0.37870979 0.42909551 0.50262694 0.41085661 0.28147848 0.66571168 0.50020514 0.43004120 0.41047623
 [33] 0.47934204 0.38850477 0.29338361 0.67971227 0.47394636 0.40898355 0.42994694 0.42913529 0.26796969 0.43009166 0.37838300 0.35720021 0.51272056 0.39929755 0.25286335 0.72536260
 [49] 0.32675933 0.29689589 0.43004358 0.31165451 0.65366386 0.42507672 0.29829339 0.42021518 0.29158235 0.48410922 0.42917560 0.37334202 0.43945155 0.63039245 0.72679567 0.42969163
 [65] 0.46593919 0.29918173 0.24064245 0.29483343 0.30118668 0.42028865 0.06706009 0.37770963 0.29558649 0.37134149 0.42644011 0.35747902 0.56081171 0.64072744 0.30540376 0.37341155
 [81] 0.64169987 0.38367882 0.61990595 0.26089882 0.41260902 0.33069992 0.43023107 0.72733479 0.58602504 0.49925112 0.43004441 0.40246554 0.28114869 0.71925867 0.38195198 0.36833077
 [97] 0.30465860 0.18813435 0.67963988 0.55540036

For example, for the value of x 0.157051, the estimated y value is 0.2626652.

Then, instead of using x as vector, I try to get estimates just only one input(x). 

   > predict(model_np,0.1570512)
$x
[1] 0.1570512

$y
[1] 0.2626652

For x=0.1570512 , I get estimate y=0.36009101 for the first one. But for the second one , I get y= 0.2626652. They are different from each other.

How can this be? Am I doing something wrong? Or is this something with versions of loaded packages? Are you getting the same results? Or is this a bug of the package? Or do i interpret result wrongly?

I will be very glad for any help. Thanks a lot.

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  • $\begingroup$ You are not going crazy. lokern is all over the place internally as it behaves differently if we are asking for an x point it has already seen. It internally uses a spline interpolation if we are querying points we have not trained upon. That internal and conditional interpolation messes things spectacularly. Try: predict(model_np, x = data_test$x[1]) and then try: predict(model_np, x = data_test$x[1]+ 1e-16). $\endgroup$
    – usεr11852
    Commented May 27, 2020 at 14:26
  • $\begingroup$ I think that is a little bit hard for me to understand. According to my understanding, it uses different algortihms for trained data and untrained data. And, that changes results dramatically. I am not sure, if I interpret your comment truly. So, do you have any suggestion to avoid from this problem? Or is there any other package that avoids of that pronblem(bandwith selection should be a plug-in method) Thanks a lot. $\endgroup$
    – oercim
    Commented May 27, 2020 at 14:47
  • $\begingroup$ Sorry, I was writing this very quickly. Actually what is even "funnier" is that predict(model_np, x = data_test$x[1]) and predict(model_np, x = c(0.123, data_test$x[1])) will given different results for data_test$x[1] because in the later case the interpolator will kick in. Really, just use any other option, np::npreg, stas::ksmooth, something... $\endgroup$
    – usεr11852
    Commented May 27, 2020 at 14:48
  • $\begingroup$ Yes, your understanding is correct, if we only try to predict on data we have trained upon, we will not use an internal interpolation step. If we try to predict and some of x are not already see, the estimates from the kernel regression will go through a spline smooth. And that's why we get the difference. $\endgroup$
    – usεr11852
    Commented May 27, 2020 at 14:52
  • $\begingroup$ Ok. Thanks a lot for the explanations and giving your time. I will search for other options. $\endgroup$
    – oercim
    Commented May 27, 2020 at 14:56

1 Answer 1

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First, should it be model_lok<-lokerns(y~x, data=data_test) instead of model_np<-lokerns(y~x, data=data_test)?

I ran the example but get a different result I think the difference here might be (i) the decimal different between your input and (ii) the seed for random number used in R.

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2
  • $\begingroup$ You are right about the code. I edited it. I dont think the problem is about the decimals. I tried the same digits also. It may be because of random seed number. Is there a way to fix random number seed? Thanks a lot. $\endgroup$
    – oercim
    Commented May 27, 2020 at 14:22
  • $\begingroup$ You are right that "the decimal different between your input" play a role but that is not the real reason why we have differences. $\endgroup$
    – usεr11852
    Commented May 27, 2020 at 14:47

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