16 <strong>np</strong>cdensgradientsarguments will need to be supplied as necessary to specify the bandwidth type,kernel types, training data, and so on.a logical value specifying whether to return estimates of the gradients at theevaluation points. Defaults to FALSE.... additional arguments supplied to specify the bandwidth type, kernel types, andso on. This is necessary if you specify bws as a p+q-vector and not a conbandwidthobject, and you do not desire the default behaviours. To do this, you may specifyany of bwmethod, bwscaling, bwtype, cxkertype, cxkerorder,cykertype, cykerorder, uxkertype, uykertype, oxkertype, oykertype,as described in <strong>np</strong>cdensbw.datanewdatatxdattydatexdateydatan optional data frame, list or environment (or object coercible to a data frame byas.data.frame) containing the variables in the model. If not found in data,the variables are taken from environment(bws), typically the environmentfrom which <strong>np</strong>cdensbw was called.An optional data frame in which to look for evaluation data. If omitted, thetraining data are used.a p-variate data frame of sample realizations of explanatory data (training data).Defaults to the training data used to compute the bandwidth object.a q-variate data frame of sample realizations of dependent data (training data).Defaults to the training data used to compute the bandwidth object.a p-variate data frame of explanatory data on which conditional densities will beevaluated. By default, evaluation takes place on the data provided by txdat.a q-variate data frame of dependent data on which conditional densities will beevaluated. By default, evaluation takes place on the data provided by tydat.Details<strong>np</strong>cdens and <strong>np</strong>cdist implement a variety of methods for estimating multivariate conditionaldistributions (p + q-variate) defined over a set of possibly continuous and/or discrete (unordered,ordered) data. <strong>The</strong> approach is based on Li and Racine (2004) who employ ‘generalized productkernels’ that admit a mix of continuous and discrete datatypes.Three classes of kernel estimators for the continuous datatypes are available: fixed, adaptive nearestneighbor,and generalized nearest-neighbor. Adaptive nearest-neighbor bandwidths change witheach sample realization in the set, x i , when estimating the density at the point x. Generalizednearest-neighbor bandwidths change with the point at which the density is estimated, x. Fixedbandwidths are constant over the support of x.Training and evaluation i<strong>np</strong>ut data may be a mix of continuous (default), unordered discrete (tobe specified in the data frames using factor), and ordered discrete (to be specified in the dataframes using ordered). Data can be entered in an arbitrary order and data types will be detectedautomatically by the routine (see <strong>np</strong> for details).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.
<strong>np</strong>cdens 17Value<strong>np</strong>cdens returns a condensity object, similarly <strong>np</strong>cdist returns a condistributionobject. <strong>The</strong> generic accessor functions fitted, se, and gradients, extract estimated values,asymptotic standard errors on estimates, and gradients, respectively, from the returned object. Furthermore,the functions summary and plot support objects of both classes. <strong>The</strong> returned objectshave the following components:xbwybwxevalbandwidth(s), scale factor(s) or nearest neighbours for the explanatory data,txdatbandwidth(s), scale factor(s) or nearest neighbours for the dependent data, tydatthe evaluation points of the explanatory datayeval the evaluation points of the dependent datacondens or condistestimates of the conditional density (cumulative distribution) at the evaluatio<strong>np</strong>ointsconderrcongradstandard errors of the conditional density (cumulative distribution) estimatesif invoked with gradients = TRUE, estimates of the gradients at the evaluatio<strong>np</strong>ointscongerr if invoked with gradients = TRUE, standard errors of the gradients at theevaluation pointslog_likelihoodlog likelihood of the conditional density estimateUsage IssuesIf you are using data of mixed types, then it is advisable to use the data.frame function toconstruct your i<strong>np</strong>ut data and not cbind, since cbind will typically not work as intended onmixed data types and will coerce the data to the same type.Author(s)Tristen Hayfield 〈hayfield@phys.ethz.ch〉, Jeffrey S. Racine 〈racinej@mcmaster.ca〉ReferencesAitchison, J. and C.G.G. Aitken (1976), “Multivariate binary discrimination by the kernel method,”Biometrika, 63, 413-420.Hall, P. and J.S. Racine and Q. Li (2004), “Cross-validation and the estimation of conditional probabilitydensities,” Journal of the American Statistical Association, 99, 1015-1026.Li, Q. and J.S. Racine (2007), No<strong>np</strong>arametric Econometrics: <strong>The</strong>ory and Practice, Princeton UniversityPress.Pagan, A. and A. Ullah (1999), No<strong>np</strong>arametric Econometrics, Cambridge University Press.Scott, D.W. (1992), Multivariate Density Estimation. <strong>The</strong>ory, Practice and Visualization, NewYork: Wiley.Silverman, B.W. (1986), Density Estimation, London: Chapman and Hall.
- Page 1 and 2: The np PackageFebruary 16, 2008Vers
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- Page 37 and 38: npudens 37Author(s)Tristen Hayfield
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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
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npqcmstest 83npqcmstestKernel Consi
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npqcmstest 85Author(s)Tristen Hayfi
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npqreg 87ftol = 1.19209e-07,tol = 1
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npqreg 89Li, Q. and J.S. Racine (20
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npreg 91Usagenpreg(bws, ...)## S3 m
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npreg 93residR2MSEMAEMAPECORRSIGNif
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npreg 95summary(model)# Use npplot(
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npreg 97# - this may take a few min
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npreg 99# then a noisy samplen
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npregbw 101## S3 method for class '
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npregbw 103ckerorderukertypeokertyp
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npregbw 105ReferencesAitchison, J.
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npsigtest 107bw
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npsigtest 109Author(s)Tristen Hayfi
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npindex 111Usagenpindex(bws, ...)##
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npindex 113MAEMAPECORRSIGNif method
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npindex 115x2
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npindex 117# x1 is chi-squared havi
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npindexbw 119# plotting via persp()
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npindexbw 121methodnmultithe single
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npindexbw 123allows one to deploy t
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npscoef 125x1
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npscoef 127Valueeydatezdaterrorsres
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npscoef 129# We could manually plot
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npscoefbw 131optim.abstol,optim.max
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npscoefbw 133optim.maxattemptsmaxim
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npscoefbw 135ReferencesAitchison, J
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uocquantile 137uocquantileCompute Q
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INDEX 139npconmode, 29npindex, 110n