alR (version 2.2.0)

mmKDE: Moment matching for kernel density estimators.

Description

Estimate parameters of a linear model by matching the moments of kernel density estimators.

Usage

mmKDE(formula, data = list(), xin, type, ...)
# S3 method for default
mmKDE(formula, data = list(), xin, type, ...)
# S3 method for mmKDE
print(x, ...)
# S3 method for mmKDE
summary(object, ...)
# S3 method for summary.mmKDE
print(x, ...)
# S3 method for formula
mmKDE(formula, data = list(), xin, type, ...)
# S3 method for mmKDE
predict(object, newdata = NULL, ...)

Arguments

formula

An LHS ~ RHS formula, specifying the linear model to be estimated.

data

A data.frame which contains the variables in formula.

xin

Numeric vector of length equal to the number of independent variables, of initial values, for the parameters to be estimated.

type

An integer specifying the bandwidth selection method used, see bw.

...

Arguments to be passed on to the control argument of the optim function.

x

An mmKDE object.

object

An mmKDE object.

newdata

The data on which the estimated model is to be fitted.

Value

A generic S3 object with class mmKDE.

mmKDE.default: A list with all components from optim, as well as:

• intercept: Did the model contain an intercept TRUE/FALSE?

• coefficients: A vector of estimated coefficients.

• df: Degrees of freedom of the model.

• error: The value of the objective function.

• fitted.values: A vector of estimated values.

• residuals: The residuals resulting from the fitted model.

• call: The call to the function.

• h_y: The KDE bandwidth estimator for the dependent variable.

• h_X: The KDE bandwidth estimator for the independent variables, i.e. \(\mathbf{X}\underline{\hat{\beta}}\).

• MOMy: The first \(n\) non central moments of the dependent variable, where $\(n\) is the number of columns in the design matrix.

• MOMX: The first \(n\) non central moments of the independent variables \(\mathbf{X}\underline{\hat{\beta}}\), where $\(n\) is the number of columns in the design matrix.

summary.mmKDE: A list of class summary.mmKDE with the following components:

• call: Original call to mmKDE function.

• coefficients: A vector with parameter estimates.

• moments: A matrix of the first \(n\) moments of the dependent and independent variables that were matched. The final row corresponds to the estimated bandwidth parameters for each, i.e. h_y and h_X, respectively.

• r.squared: The \(r^{2}\) coefficient.

• adj.r.squared: The adjusted \(r^{2}\) coefficient.

• sigma: The residual standard error.

• df: Degrees of freedom for the model.

• error: Value of the objective function.

• residSum: Summary statistics for the distribution of the residuals.

print.summary.mmKDE: The object passed to the function is returned invisibly.

predict.mmKDE: A vector of predicted values resulting from the estimated model.

Methods (by class)

• default: default method for mmKDE.

• mmKDE: print method for mmKDE.

• mmKDE: summary method for mmKDE.

• summary.mmKDE: print method for summary.mmKDE.

• formula: formula method for mmKDE.

• mmKDE: predict method for mmKDE.

Examples

# NOT RUN {
x <- 1:10
y <- x+rnorm(10)
XIn <- lm(y~x)
mmKDE.default(y~x, xin=coef(XIn), type=-1)

u <- 11:20
v <- u+rnorm(10)
XIn <- lm(y~x)
mom <- mmKDE(y~x, xin=coef(XIn), type=-1)
predict(mom, newdata=data.frame(y=v, x=u))

# }