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nonparametric kernel smoothing
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README.md

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kernelSmooth

nonparametric kernel smoothing for JavaScript

Installation

Via npm:

npm install kernel-smooth

Require as follows:

var kernel = require('kernel-smooth');

API

.density(xs, kernel, [bandwidth])

Given input data xs, a kernel function and a bandwidth (if not supplied, a default value of 0.5 is used), this function returns a basic kernel density estimator: a function of one variable, x, which when invoked returns the kernel density estimate for x. The returned function can also be called with a vector supplied as an argument for x. In this case, the density is evaluated is for each element of the vector and the vector of density estimates is returned.

.regression(xs, ys, kernel, [bandwidth])

Given input predictors xs and observed responses ys, a kernel function and a bandwidth (if not supplied, a default value of 0.5 is used), this function returns the Nadaraya & Watson kernel regression estimator: a function of one variable, x, which when invoked returns the estimate for y. The returned function can also be called with a vector supplied as an argument for x. In this case, predictions are generated for each element of the vector and the vector of predictions is returned.

.mutipleRegression(Xs, ys, kernel, [bandwidth])

Similar to .regression(), except that Xs should be a 2d array containing multiple predictors. Each element of Xs should has to be an array of length p, with p denoting the number of predictors. The returned estimator generates a prediction for a new data point x = (x_1, ..., x_p). If a 2d array is supplied instead, predictions are generated for multiple data points at once, where each row (= element of the outer array) is assumed to be a datum x = (x_1, ..., x_p).

Choice of Kernel function

For the kernel parameter in above functions, you should supply a univariate function K(x) which satisfies K(x) >= 0, integrates to one, has zero mean and unit variance. See the functions in the exported .fun object for a list of already implemented kernel functions.

.fun

This object of the module holds the following kernel functions to be used for kernel smoothing:

.gaussian(x)

Gaussian kernel, pdf of standard normal distribution.

.boxcar(x)

Boxcar kernel, defined as 0.5 if |x| <= 1 and 0 otherwise.

.epanechnikov(x)

Epanechnikov kernel. Equal to zero if |x| > 1. Otherwise defined as 0.75 * (1 - x^2).

.tricube(x)

Tricube kernel function. Equal to zero if |x| > 1 and otherwise equal to (70/81) * (1-|x|^3)^3.

.silverman(x)

For input vector x, calculate the optimal bandwidthe using Silverman's rule of thumb. This utility function can be used to calculate an appropriate bandwidth for the case in which a Gaussian kernel is used and one has reason to believe that the data points x_i are drawn from a normal distribution.

License

MIT © Philipp Burckhardt

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