# RDOptBW.fit: Optimal bandwidth selection in RD In kolesarm/RDHonest: Honest inference in sharp regression discontinuity designs

## Description

Basic computing engine called by `RDOptBW` used to find optimal bandwidth

## Usage

 ```1 2 3``` ```RDOptBW.fit(d, M, kern = "triangular", opt.criterion, bw.equal = TRUE, alpha = 0.05, beta = 0.8, sclass = "H", order = 1, se.initial = "IKEHW") ```

## Arguments

 `d` object of class `"RDData"` `M` Bound on second derivative of the conditional mean function. `kern` specifies kernel function used in the local regression. It can either be a string equal to `"triangular"` (k(u)=(1-|u|)_{+}), `"epanechnikov"` (k(u)=(3/4)(1-u^2)_{+}), or `"uniform"` (k(u)= (|u|<1)/2), or else a kernel function. `opt.criterion` Optimality criterion that bandwidth is designed to optimize. It can either be based on exact finite-sample maximum bias and finite-sample estimate of variance, or asymptotic approximations to the bias and variance. The options are: `"MSE"`Finite-sample maximum MSE `"FLCI"`Length of (fixed-length) two-sided confidence intervals. `"OCI"`Given quantile of excess length of one-sided confidence intervals The finite-sample methods use conditional variance given by `sigma2`, if supplied. Otherwise, for the purpose of estimating the optimal bandwidth, conditional variance is assumed homoscedastic, and estimated using a nearest neighbor estimator. `bw.equal` logical specifying whether bandwidths on either side of cutoff should be constrainted to equal to each other. `alpha` determines confidence level, `1-alpha` for constructing/optimizing confidence intervals. `beta` Determines quantile of excess length to optimize, if bandwidth optimizes given quantile of excess length of one-sided confidence intervals. `sclass` Smoothness class, either `"T"` for Taylor or `"H"` for Hölder class. `order` Order of local regression 1 for linear, 2 for quadratic. `se.initial` Method for estimating initial variance for computing optimal bandwidth. Ignored if data already contains estimate of variance. "IKEHW"Based on residuals from a local linear regression using a triangular kernel and IK bandwidth "IKdemeaned"Based on sum of squared deviations of outcome from estimate of intercept in local linear regression with triangular kernel and IK bandwidth "Silverman"Use residuals from local constant regression with uniform kernel and bandwidth selected using Silverman's rule of thumb, as in Equation (14) in IK "SilvermanNN"Use nearest neighbor estimates, rather than residuals "NN"Use nearest neighbor estimates, without assuming homoscedasticity

## Value

a list with the following elements

`hp`

bandwidth for observations above cutoff

`hm`

bandwidth for observations below cutoff, equal to `hp` unless `bw.equal==FALSE`

`sigma2m`, `sigma2p`

estimate of conditional variance above and below cutoff, from `d`

## Examples

 ```1 2 3``` ```## Lee data d <- RDData(lee08, cutoff=0) RDOptBW.fit(d, M=0.1, opt.criterion="MSE")[c("hp", "hm")] ```

kolesarm/RDHonest documentation built on April 3, 2018, 11:08 a.m.