nonparametric and semiparametric models-an introduction

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1、NonparametricandSemiparametricModelsAnIntroductionJanuary21,2005WolfgangH•ardleMarleneM•ullerStefanSperlichAxelWerwatz2Contents1Introduction211.1DensityEstimation.........................211.2Regression..............................231.2.1ParametricRegr

2、ession...................251.2.2NonparametricRegression.................271.2.3SemiparametricRegression................29INonparametricModels412Histogram452.1MotivationandDerivation.....................452.1.1Construction........................452.1.2D

3、erivation..........................472.1.3VaryingtheBinwidth...................482.2StatisticalProperties........................492.2.1Bias.............................502.2.2Variance...........................512.2.3MeanSquaredError...................

4、.522.2.4MeanIntegratedSquaredError..............532.2.5OptimalBinwidth.....................542.3DependenceoftheHistogramontheOrigin...........554Contents2.4AveragedShiftedHistogram....................573NonparametricDensityEstimation653.1MotivationandDe

5、rivation.....................653.1.1Introduction........................653.1.2Derivation..........................663.1.3VaryingtheBandwidth..................683.1.4VaryingtheKernelFunction...............683.1.5KernelDensityEstimationasaSumofBumps.....

6、723.2StatisticalProperties........................733.2.1Bias.............................733.2.2Variance...........................753.2.3MeanSquaredError....................763.2.4MeanIntegratedSquaredError..............773.3SmoothingParameterSelectio

7、n..................783.3.1Silverman'sRuleofThumb................783.3.2Cross-Validation......................803.3.3RenedPlug-inMethods.................833.3.4AnOptimalBandwidthSelector?!............843.4ChoosingtheKernel........................853.4.1

8、CanonicalKernelsandBandwidths............853.4.2AdjustingBandwidthsacrossKernels..........873.4.3OptimizingtheKernel...................883.5CondenceIntervalsandCondenceBands...........893.6MultivariateKernelDensityEstimation...