LPPHonest: Honest inference at a point

Description Usage Arguments Details Value Note See Also Examples

View source: R/LPP_lp.R

Description

Calculate estimators and one- and two-sided CIs based on local polynomial estimator under second-order Taylor or Hölder smoothness class.

Usage

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LPPHonest(formula, data, subset, point = 0, M, kern = "triangular",
  na.action, opt.criterion, h, se.method = "nn", alpha = 0.05, beta = 0.8,
  J = 3, sclass = "H", order = 1, se.initial = "ROTEHW")

Arguments

formula

object of class "formula" (or one that can be coerced to that class) of the form outcome ~ independent_variable

data

optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the outcome and independent variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which the function is called.

subset

optional vector specifying a subset of observations to be used in the fitting process.

point

specifies the point X_0 at which to do inference

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.

na.action

function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of options (usually na.omit).

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.

h

Bandwidth. If not supplied, optimal bandwidth is computed according to criterion given by opt.criterion.

se.method

Vector with methods for estimating standard error of estimate. If NULL, standard errors are not computed. The elements of the vector can consist of the following methods:

"nn"

Nearest neighbor method

"EHW"

Eicker-Huber-White, with residuals from local regression (local polynomial estimators only).

"demeaned"

Use EHW, but instead of using residuals, estimate sigma^2_i by subtracting the estimated intercept from the outcome (and not subtracting the estimated slope). Local polynomial estimators only.

"plugin"

Plug-in estimate based on asymptotic variance. Local polynomial estimators in RD only.

"supplied.var"

Use conditional variance supplied by sigma2 / d instead of computing residuals

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.

J

Number of nearest neighbors, if "nn" is specified in se.method.

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.

"ROTEHW"

Based on residuals from a local linear regression using a triangular kernel and ROT bandwidth

"ROTdemeaned"

Based on sum of squared deviations of outcome from estimate of intercept in local linear regression with triangular kenrel and ROT bandwidth

Details

The bandwidth is calculated to be optimal for a given performance criterion, as specified by opt.criterion. It is calculated using the function LPPOptBW. Alternatively, the bandwidth can be specified by h.

Value

Returns an object of class "LPPResults". The function print can be used to obtain and print a summary of the results. An object of class "LPPResults" is a list containing the following components

estimate

Point estimate. This estimate is MSE-optimal if opt.criterion="MSE"

maxbias

Maximum bias of estimate

sd

Standard deviation of estimate

lower, upper

Lower (upper) end-point of a one-sided CI based on estimate. This CI is optimal if opt.criterion="OCI"

hl

Half-length of a two-sided CI based on estimate, so that the CI is given by c(estimate-hl, estimate+hl). The CI is optimal if opt.criterion="FLCI"

eff.obs

Effective number of observations used by estimate

h

Bandwidth used

naive

Coverage of CI that ignores bias and uses qnorm(1-alpha/2) as critical value

call

the matched call

Note

subset is evaluated in the same way as variables in formula, that is first in data and then in the environment of formula.

See Also

LPPOptBW

Examples

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# Lee dataset
LPPHonest(voteshare ~ margin, data = lee08, subset = margin>0,
          kern = "uniform", M = 0.1, h = 10, sclass = "T")

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