fdars.smoothing¶

Nonparametric smoothing methods for scalar-valued data.

Functions¶

Function	Description
`nadaraya_watson`	Nadaraya-Watson kernel smoother
`local_linear`	Local linear regression smoother
`local_polynomial`	Local polynomial regression smoother
`knn_smoother`	K-nearest neighbors smoother
`optim_bandwidth`	Optimal bandwidth selection via cross-validation

fdars.nadaraya_watson(x, y, x_new, bandwidth, kernel="gaussian")

Nadaraya-Watson kernel regression estimator.

Parameter	Type	Default	Description
`x`	`ndarray (n,)`		Predictor values
`y`	`ndarray (n,)`		Response values
`x_new`	`ndarray (m,)`		Points at which to evaluate the smoother
`bandwidth`	`float`		Kernel bandwidth
`kernel`	`str`	`"gaussian"`	`"gaussian"`, `"epanechnikov"`, or `"tricube"`

Returns	Type	Description
smoothed	`ndarray (m,)`	Smoothed values at `x_new`

x, y = np.sort(np.random.rand(100)), np.random.randn(100)
x_new = np.linspace(0, 1, 200)
y_hat = fdars.nadaraya_watson(x, y, x_new, bandwidth=0.1)

fdars.local_linear(x, y, x_new, bandwidth, kernel="gaussian")

Local linear regression smoother. Fits a linear model in a kernel-weighted neighborhood around each evaluation point.

Parameter	Type	Default	Description
`x`	`ndarray (n,)`		Predictor values
`y`	`ndarray (n,)`		Response values
`x_new`	`ndarray (m,)`		Evaluation points
`bandwidth`	`float`		Kernel bandwidth
`kernel`	`str`	`"gaussian"`	`"gaussian"`, `"epanechnikov"`, or `"tricube"`

Returns	Type	Description
smoothed	`ndarray (m,)`	Smoothed values at `x_new`

y_hat = fdars.local_linear(x, y, x_new, bandwidth=0.1)

fdars.local_polynomial(x, y, x_new, bandwidth, degree=1, kernel="gaussian")

Local polynomial regression smoother of arbitrary degree.

Parameter	Type	Default	Description
`x`	`ndarray (n,)`		Predictor values
`y`	`ndarray (n,)`		Response values
`x_new`	`ndarray (m,)`		Evaluation points
`bandwidth`	`float`		Kernel bandwidth
`degree`	`int`	`1`	Polynomial degree
`kernel`	`str`	`"gaussian"`	`"gaussian"`, `"epanechnikov"`, or `"tricube"`

Returns	Type	Description
smoothed	`ndarray (m,)`	Smoothed values at `x_new`

y_hat = fdars.local_polynomial(x, y, x_new, bandwidth=0.1, degree=2)

fdars.knn_smoother(x, y, x_new, k)

K-nearest neighbors smoother. Averages the response of the k closest observations.

Returns	Type	Description
smoothed	`ndarray (m,)`	Smoothed values at `x_new`

y_hat = fdars.knn_smoother(x, y, x_new, k=10)

fdars.optim_bandwidth(x, y, criterion="gcv", kernel="gaussian",
                      n_grid=50, h_min=None, h_max=None)

Select optimal bandwidth for kernel smoothing via cross-validation.

Parameter	Type	Default	Description
`x`	`ndarray (n,)`		Predictor values
`y`	`ndarray (n,)`		Response values
`criterion`	`str`	`"gcv"`	`"gcv"` or `"cv"`
`kernel`	`str`	`"gaussian"`	`"gaussian"`, `"epanechnikov"`, or `"tricube"`
`n_grid`	`int`	`50`	Number of grid points for bandwidth search
`h_min`	`float` or `None`	`None`	Minimum bandwidth; `None` for auto
`h_max`	`float` or `None`	`None`	Maximum bandwidth; `None` for auto

Returns	Type	Description
result	`dict`	Keys: `h_opt` (optimal bandwidth), `criterion`, `value` (criterion value)

result = fdars.optim_bandwidth(x, y, criterion="gcv")
y_hat = fdars.nadaraya_watson(x, y, x_new, bandwidth=result["h_opt"])