108 <strong>np</strong>sigtestValuexdatydatboot.methodboot.numboot.typeindexrandom.seeda p-variate data frame of explanatory data (training data) used to calculate theregression estimators.a one (1) dimensional numeric or integer vector of dependent data, each elementi corresponding to each observation (row) i of xdat.a character string used to specify the bootstrap method. iid will generate independentidentically distributed draws. wild will use a wild bootstrap. wildrademacherwill use a wild bootstrap with Rademacher variables. Defaultsto bootstrap.an integer value specifying the number of bootstrap replications to use. Defaultsto 399.a character string specifying whether to use a ‘Bootstrap I’ or ‘Bootstrap II’method (see Racine, Hart, and Li (2006) for details). <strong>The</strong> ‘Bootstrap II’ methodre-runs cross-validation for each bootstrap replication and uses the new crossvalidatedbandwidth for variable i and the original ones for the remaining variables.Defaults to boot.type="I".a vector of indices for the columns of xdat for which the test of significanceis to be conducted. Defaults to (1,2,. . . ,p) where p is the number of columns inxdat.an integer used to seed R’s random number generator. This is to ensure replicability.Defaults to 42.... additional arguments supplied to specify the bandwidth type, kernel types, selectionmethods, and so on, detailed below.<strong>np</strong>sigtest returns an object of type sigtest. summary supports sigtest objects. It hasthe following components:InPthe vector of statistics Inthe vector of P-values for each statistic in InIn.bootstrap contains a matrix of the bootstrap replications of the vector In, each columncorresponding to replications associated with explanatory variables in xdat indexedby index (e.g., if you selected index = c(1,4) then In.bootstrapwill have two columns, the first being the bootstrap replications of In associatedwith variable 1, the second with variable 4).Usage 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.Caution: bootstrap methods are, by their nature, computationally intensive. This can be frustratingfor users possessing large datasets. For exploratory purposes, you may wish to override the defaultnumber of bootstrap replications, say, setting them to boot.num=99 A version of this package usingthe Rmpi wrapper is under development that allows one to deploy this software in a clusteredcomputing environment to facilitate computation involving large datasets.
<strong>np</strong>sigtest 109Author(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.Li, Q. and J.S. Racine (2007), No<strong>np</strong>arametric Econometrics: <strong>The</strong>ory and Practice, Princeton UniversityPress.Racine, J.S., J. Hart, and Q. Li (2006), “Testing the significance of categorical predictor variablesin no<strong>np</strong>arametric regression models,” Econometric Reviews, 25, 523-544.Racine, J.S. (1997), “Consistent significance testing for no<strong>np</strong>arametric regression,” Journal of Businessand Economic Statistics 15, 369-379.Wang, M.C. and J. van Ryzin (1981), “A class of smooth estimators for discrete distributions,”Biometrika, 68, 301-309.Examples# EXAMPLE 1 (INTERFACE=FORMULA): For this example, we simulate 100 draws# from a DGP in which z, the first column of X, is an irrelevant# discrete variableset.seed(12345)n
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npcdens 15npcdensKernel Conditional
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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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