npscoef {np} | R Documentation

## Smooth Coefficient Kernel Regression

### Description

`npscoef` computes a kernel regression estimate of a one (1) dimensional dependent variable on p-variate explanatory data, using the model Y_i = t(W_i) * gamma(Z_i) + u_i where t(W_i)=(1,t(X_i)), given a set of evaluation points, training points (consisting of explanatory data and dependent data), and a bandwidth specification. A bandwidth specification can be a `scbandwidth` object, or a bandwidth vector, bandwidth type and kernel type.

### Usage

    npscoef(bws, ...)

    ## S3 method for class 'formula'
    npscoef(bws, data = NULL, newdata = NULL, y.eval =
    FALSE, ...)

    ## S3 method for class 'call'
    npscoef(bws, ...)

    ## Default S3 method:
    npscoef(bws, txdat, tydat, tzdat, ...)

    ## S3 method for class 'scbandwidth'
    npscoef(bws,
            txdat = stop("training data 'txdat' missing"),
            tydat = stop("training data 'tydat' missing"),
            tzdat = NULL,
            exdat,
            eydat,
            ezdat,
            residuals = FALSE,
            errors = TRUE,
            iterate = TRUE,
            maxiter = 100,
            tol = .Machine$double.eps,
            leave.one.out = FALSE,
            betas = FALSE,
            ...)

### Arguments

`bws` | a bandwidth specification. This can be set as a `scbandwidth` object returned from an invocation of `npscoefbw`, or as a vector of bandwidths, with each element i corresponding to the bandwidth for column i in `tzdat`. If specified as a vector additional arguments will need to be supplied as necessary to specify the bandwidth type, kernel types, training data, and so on.
`...` | additional arguments supplied to specify the regression type, bandwidth type, kernel types, selection methods, and so on. To do this, you may specify any of `bwscaling`, `bwtype`, `ckertype`, `ckerorder`, as described in `npscoefbw`.
`data` | an optional data frame, list or environment (or object coercible to a data frame by `as.data.frame`) containing the variables in the model. If not found in data, the variables are taken from `environment(bws)`, typically the environment from which `npscoefbw` was called.
`newdata` | An optional data frame in which to look for evaluation data. If omitted, the training data are used.
`y.eval` | If `newdata` contains dependent data and `y.eval = TRUE`, `np` will compute goodness of fit statistics on these data and return them. Defaults to `FALSE`.
`txdat` | a p-variate data frame of explanatory data (training data), which, by default, populates the columns 2 through p+1 of W in the model equation, and in the absence of `zdat`, will also correspond to Z from the model equation. Defaults to the training data used to compute the bandwidth object.
`tydat` | a one (1) dimensional numeric or integer vector of dependent data, each element i corresponding to each observation (row) i of `txdat`. Defaults to the training data used to compute the bandwidth object.
`tzdat` | an optionally specified q-variate data frame of explanatory data (training data), which corresponds to Z in the model equation. Defaults to the training data used to compute the bandwidth object.
`exdat` | a p-variate data frame of points on which the regression will be estimated (evaluation data).By default, evaluation takes place on the data provided by `txdat`.
`eydat` | a one (1) dimensional numeric or integer vector of the true values of the dependent variable. Optional, and used only to calculate the true errors.
`ezdat` | an optionally specified q-variate data frame of points on which the regression will be estimated (evaluation data), which corresponds to Z in the model equation. Defaults to be the same as `txdat`.
`errors` | a logical value indicating whether or not asymptotic standard errors should be computed and returned in the resulting `smoothcoefficient` object. Defaults to `TRUE`.
`residuals` | a logical value indicating that you want residuals computed and returned in the resulting `smoothcoefficient` object. Defaults to `FALSE`.
`iterate` | a logical value indicating whether or not backfitted estimates should be iterated for self-consistency. Defaults to `TRUE`.
`maxiter` | integer specifying the maximum number of times to iterate the backfitted estimates while attempting to make the backfitted estimates converge to the desired tolerance. Defaults to `100`.
`tol` | desired tolerance on the relative convergence of backfit estimates. Defaults to `.Machine$double.eps`.
`leave.one.out` | a logical value to specify whether or not to compute the leave one out estimates. Will not work if `e[xyz]dat` is specified. Defaults to `FALSE`.
`betas` | a logical value indicating whether or not estimates of the components of gamma should be returned in the `smoothcoefficient` object along with the regression estimates. Defaults to `FALSE`.

### Value

`npscoef` returns a `smoothcoefficient` object. The generic functions `fitted`, `residuals`, `coef`, `se`, and `predict`, extract (or generate) estimated values, residuals, coefficients, bootstrapped standard errors on estimates, and predictions, respectively, from the returned object. Furthermore, the functions `summary` and `plot` support objects of this type. The returned object has the following components:

`eval` | evaluation points
`mean` | estimation of the regression function (conditional mean) at the evaluation points
`merr` | if `errors = TRUE`, standard errors of the regression estimates
`beta` | if `betas = TRUE`, estimates of the coefficients gamma at the evaluation points
`resid` | if `residuals = TRUE`, in-sample or out-of-sample residuals where appropriate (or possible)
`R2` | coefficient of determination (Doksum and Samarov (1995))
`MSE` | mean squared error
`MAE` | mean absolute error
`MAPE` | mean absolute percentage error
`CORR` | absolute value of Pearson's correlation coefficient
`SIGN` | fraction of observations where fitted and observed values agree in sign

### Usage Issues

If you are using data of mixed types, then it is advisable to use the `data.frame` function to construct your input data and not `cbind`, since `cbind` will typically not work as intended on mixed data types and will coerce the data to the same type.

Support for backfitted bandwidths is experimental and is limited in functionality. The code does not support asymptotic standard errors or out of sample estimates with backfitting.

### Author(s)

Tristen Hayfield tristen.hayfield@gmail.com, Jeffrey S. Racine racinej@mcmaster.ca

### References

Aitchison, J. and C.G.G. Aitken (1976), “Multivariate binary discrimination by the kernel method,” Biometrika, 63, 413-420.

Cai Z. (2007), “Trending time-varying coefficient time series models with serially correlated errors,” Journal of Econometrics, 136, 163-188.

Doksum, K. and A. Samarov (1995), “Nonparametric estimation of global functionals and a measure of the explanatory power of covariates in regression,” The Annals of Statistics, 23 1443-1473.

Hastie, T. and R. Tibshirani (1993), “Varying-coefficient models,” Journal of the Royal Statistical Society, B 55, 757-796.

Li, Q. and J.S. Racine (2007), Nonparametric Econometrics: Theory and Practice, Princeton University Press.

Li, Q. and J.S. Racine (2010), “Smooth varying-coefficient estimation and inference for qualitative and quantitative data,” Econometric Theory, 26, 1-31.

Pagan, A. and A. Ullah (1999), Nonparametric Econometrics, Cambridge University Press.

Li, Q. and D. Ouyang and J.S. Racine (2013), “Categorical semiparametric varying-coefficient models,” Journal of Applied Econometrics, 28, 551-589.

Wang, M.C. and J. van Ryzin (1981), “A class of smooth estimators for discrete distributions,” Biometrika, 68, 301-309.

### See Also

`bw.nrd`, `bw.SJ`, `hist`, `npudens`, `npudist`, `npudensbw`, `npscoefbw`

### Examples

    ## Not run:
    # EXAMPLE 1 (INTERFACE=FORMULA):

    n <- 250
    x <- runif(n)
    z <- runif(n, min=-2, max=2)
    y <- x*exp(z)*(1.0+rnorm(n,sd = 0.2))
    bw <- npscoefbw(y~x|z)
    model <- npscoef(bw)
    plot(model)

    # EXAMPLE 1 (INTERFACE=DATA FRAME):

    n <- 250
    x <- runif(n)
    z <- runif(n, min=-2, max=2)
    y <- x*exp(z)*(1.0+rnorm(n,sd = 0.2))
    bw <- npscoefbw(xdat=x, ydat=y, zdat=z)
    model <- npscoef(bw)
    plot(model)

    ## End(Not run)

[Package np version 0.60-9 Index]