fdars (version 0.3.3)

fregre.np: Nonparametric Functional Regression

Description

Fits a functional regression model using kernel smoothing (Nadaraya-Watson). Supports fixed bandwidth (h), or k-nearest neighbors with global (kNN.gCV) or local (kNN.lCV) cross-validation.

Usage

fregre.np(
  fdataobj,
  y,
  h = NULL,
  knn = NULL,
  type.S = c("S.NW", "kNN.gCV", "kNN.lCV"),
  Ker = "norm",
  metric = metric.lp,
  ...
)

Value

A fitted regression object of class 'fregre.np' with components:

fitted.values

Fitted values

residuals

Residuals

h.opt

Optimal/used bandwidth (for type.S = "S.NW")

knn

Number of neighbors used (for kNN methods)

k.opt

Optimal k value(s) - scalar for global, vector for local

type.S

Type of smoother used

Ker

Kernel type used

fdataobj

Original functional data

y

Response vector

mdist

Distance matrix

sr2

Residual variance

metric

Metric function used

call

The function call

Arguments

fdataobj

An object of class 'fdata' (functional covariate).

y

Response vector.

h

Bandwidth parameter. If NULL and knn is NULL, computed automatically.

knn

Number of nearest neighbors to consider for bandwidth selection. Only used when type.S is "kNN.gCV" or "kNN.lCV".

type.S

Type of smoother: "S.NW" for Nadaraya-Watson with fixed h (default), "kNN.gCV" for k-NN with global CV (single k for all observations), "kNN.lCV" for k-NN with local CV (different k per observation).

Ker

Kernel type for smoothing. Default is "norm" (Gaussian).

metric

Distance metric function. Default is metric.lp.

...

Additional arguments passed to metric function.

Details

Three smoothing approaches are available:

Fixed bandwidth (type.S = "S.NW"): Uses a single bandwidth h for all predictions. If h is not provided, it is set to the median of non-zero pairwise distances.

k-NN Global CV (type.S = "kNN.gCV"): Selects a single optimal k for all observations using leave-one-out cross-validation. The bandwidth at each point is set to include k neighbors.

k-NN Local CV (type.S = "kNN.lCV"): Selects an optimal k_i for each observation i, allowing adaptive smoothing. Useful when the data has varying density across the functional space.

Examples

# Create functional data
t <- seq(0, 1, length.out = 50)
n <- 50
X <- matrix(0, n, 50)
for (i in 1:n) X[i, ] <- sin(2*pi*t) * i/n + rnorm(50, sd = 0.1)
y <- rowMeans(X) + rnorm(n, sd = 0.1)
fd <- fdata(X, argvals = t)

# Fixed bandwidth
fit1 <- fregre.np(fd, y, h = 0.5)

# k-NN with global CV
fit2 <- fregre.np(fd, y, type.S = "kNN.gCV", knn = 20)

# k-NN with local CV
fit3 <- fregre.np(fd, y, type.S = "kNN.lCV", knn = 20)