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134 npscoefbwexplanatory data, where dependent data is a univariate response, and parametricexplanatory data and nonparametric explanatory data are both series of variablesspecified by name, separated by the separation character ’+’. For example, y1 ~ x1 + x2 |z1 specifies that the bandwidth object for the smooth coefficient model with response y1, linearparametric regressors x1 and x2, and nonparametric regressor (that is, the slope-changing variable)z1 is to be estimated. See below for further examples. In the case where the nonparametric (slopechanging)variable is not specified, it is assumed to be the same as the parametric variable.A variety of kernels may be specified by the user. Kernels implemented for continuous datatypesinclude the second, fourth, sixth, and eighth order Gaussian and Epanechnikov kernels, and theuniform kernel. Unordered discrete datatypes use a variation on Aitchison and Aitken’s (1976)kernel, while ordered datatypes use a variation of the Wang and van Ryzin (1981) kernel.Valueif bwtype is set to fixed, an object containing bandwidths (or scale factors if bwscaling =TRUE) is returned. If it is set to generalized_nn or adaptive_nn, then instead the kthnearest neighbors are returned for the continuous variables while the discrete kernel bandwidths arereturned for the discrete variables. Bandwidths are stored in a vector under the component namebw. Backfitted bandwidths are stored under the component name bw.fitted.The functions predict, summary, and plot support objects of this class.Usage IssuesIf you are using data of mixed types, then it is advisable to use the data.frame function toconstruct your input data and not cbind, since cbind will typically not work as intended onmixed data types and will coerce the data to the same type.Caution: multivariate data-driven bandwidth selection methods are, by their nature, computationallyintensive. Virtually all methods require dropping the ith observation from the data set, computing anobject, repeating this for all observations in the sample, then averaging each of these leave-one-outestimates for a given value of the bandwidth vector, and only then repeating this a large number oftimes in order to conduct multivariate numerical minimization/maximization. Furthermore, due tothe potential for local minima/maxima, restarting this procedure a large number of times may oftenbe necessary. This can be frustrating for users possessing large datasets. For exploratory purposes,you may wish to override the default search tolerances, say, setting optim.reltol=.1 and conductmultistarting (the default is to restart min(5,ncol(zdat)) times). Once the procedure terminates, youcan restart search with default tolerances using those bandwidths obtained from the less rigoroussearch (i.e., set bws=bw on subsequent calls to this routine where bw is the initial bandwidthobject). A version of this package using the Rmpi wrapper is under development that allows one todeploy this software in a clustered computing environment to facilitate computation involving largedatasets.Support for backfitted bandwidths is experimental and is limited in functionality. The code does notsupport asymptotic standard errors or out of sample estimates with backfitting.Author(s)Tristen Hayfield 〈hayfield@phys.ethz.ch〉, Jeffrey S. Racine 〈racinej@mcmaster.ca〉
npscoefbw 135ReferencesAitchison, J. and C.G.G. Aitken (1976), “Multivariate binary discrimination by the kernel method,”Biometrika, 63, 413-420.Cai Z. (2007), “Trending time-varying coefficient time series models with serially correlated errors,”Journal of Econometrics, 136, 163-188.Hastie, T. and R. Tibshirani (1993), “Varying-coefficient models,” Journal of the Royal StatisticalSociety, B 55, 757-796.Li, Q. and J.S. Racine (2007), Nonparametric Econometrics: Theory and Practice, Princeton UniversityPress.Li, Q. and J.S. Racine (2007), “Smooth varying-coefficient nonparametric models for qualitativeand quantitative data,” manuscript.Pagan, A. and A. Ullah (1999), Nonparametric Econometrics, Cambridge University Press.Racine, J.S. and D. Ouyang and Q. Li (2007), “Nonparametric multilevel models: a smoothingapproach,” manuscript.Wang, M.C. and J. van Ryzin (1981), “A class of smooth estimators for discrete distributions,”Biometrika, 68, 301-309.See Alsonpregbw, npregExamples# EXAMPLE 1 (INTERFACE=FORMULA): For this example, we compute a# smooth coefficient model with differing X and Z datan
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The np PackageFebruary 16, 2008Vers
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Italy 3Examplesdata("cps71")attach(
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wage1 5Examplesdata("oecdpanel")att
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gradients 7## S3 method for class '
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np 9A variety of bandwidth methods
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npcmstest 11npcmstestKernel Consist
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npcmstest 13ReferencesAitchison, J.
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npcdens 15npcdensKernel Conditional
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npcdens 17Valuenpcdens returns a co
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npcdens 19# Gaussian kernel (defaul
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npcdens 21# (1993) (see their descr
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npcdensbw 23fit
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npcdensbw 25na.actionxdatydatbwspro
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npcdensbw 27data. The approach is b
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npconmode 29# depending on the spee
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npconmode 31tydatexdateydata one (1
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npconmode 33lwt,family=binomial(lin
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npudens 35npudensKernel Density and
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npudens 37Author(s)Tristen Hayfield
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npudens 39# EXAMPLE 1 (INTERFACE=DA
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npudensbw 41library("datasets")data
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npudensbw 43bwsa bandwidth specific
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npudensbw 45fvalobjective function
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npudensbw 47# previous examples.bw
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npudensbw 49# previous examples.bw
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npksum 51Argumentsformuladatanewdat
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npksum 53Usage IssuesIf you are usi
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npksum 55# the bandwidth object its
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npksum 57ss
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npplot 59plot.behavior = c("plot","
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npplot 61xtrim = 0.0,neval = 50,com
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npplot 63xdatydatzdatxqyqzqxtrimytr
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npplot 65DetailsValuenpplot is a ge
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npplot 67year.seq
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npplot 69# npplot(). When npplot()
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npplreg 71## S3 method for class 'c
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npplreg 73residR2MSEMAEMAPECORRSIGN
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npplreg 75# Plot the regression sur
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npplregbw 77and dependent data), an
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npplregbw 79Detailsnpplregbw implem
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npplregbw 81x2
Page 83 and 84: npqcmstest 83npqcmstestKernel Consi
Page 85 and 86: npqcmstest 85Author(s)Tristen Hayfi
Page 87 and 88: npqreg 87ftol = 1.19209e-07,tol = 1
Page 89 and 90: npqreg 89Li, Q. and J.S. Racine (20
Page 91 and 92: npreg 91Usagenpreg(bws, ...)## S3 m
Page 93 and 94: npreg 93residR2MSEMAEMAPECORRSIGNif
Page 95 and 96: npreg 95summary(model)# Use npplot(
Page 97 and 98: npreg 97# - this may take a few min
Page 99 and 100: npreg 99# then a noisy samplen
Page 101 and 102: npregbw 101## S3 method for class '
Page 103 and 104: npregbw 103ckerorderukertypeokertyp
Page 105 and 106: npregbw 105ReferencesAitchison, J.
Page 107 and 108: npsigtest 107bw
Page 109 and 110: npsigtest 109Author(s)Tristen Hayfi
Page 111 and 112: npindex 111Usagenpindex(bws, ...)##
Page 113 and 114: npindex 113MAEMAPECORRSIGNif method
Page 115 and 116: npindex 115x2
Page 117 and 118: npindex 117# x1 is chi-squared havi
Page 119 and 120: npindexbw 119# plotting via persp()
Page 121 and 122: npindexbw 121methodnmultithe single
Page 123 and 124: npindexbw 123allows one to deploy t
Page 125 and 126: npscoef 125x1
Page 127 and 128: npscoef 127Valueeydatezdaterrorsres
Page 129 and 130: npscoef 129# We could manually plot
Page 131 and 132: npscoefbw 131optim.abstol,optim.max
Page 133: npscoefbw 133optim.maxattemptsmaxim
Page 137 and 138: uocquantile 137uocquantileCompute Q
Page 139: INDEX 139npconmode, 29npindex, 110n
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