inferenceDataObjectTime-class | R Documentation |

A class that contains all possible information for inference over linear parameters and/or nonparametric field in spatio-temporal regression with
differential regularization problem. This object can be used as parameter in smoothing function of the fdaPDE library `smooth.FEM.time`

.

At least one between test and interval must be nonzero. `n_cov`

, `coeff`

and `beta0`

, if provided, need to be coherent.
`dim`

and `locations`

, if provided, need to be coherent.
The usage of `inferenceDataObjectTimeBuilder`

is recommended for the construction of an object of this class.

`test`

A vector of integers taking value 0, 1 or 2; if 0 no test is performed, if 1 one-at-the-time tests are performed, if 2 a simultaneous test is performed.

`interval`

A vector of integers taking value 0, 1, 2 or 3; if 0 no confidence interval is computed, if 1 one-at-the-time confidence intervals are computed, if 2 simultaneous confidence intervals are computed, if 3 Bonferroni confidence intervals are computed.

`type`

A vector of integers taking value 1, 2, 3 or 4 corresponding to Wald, Speckman, Eigen-Sign-Flip, Enhanced-Eigen-Sign-Flip inferential approach.

`component`

A vector of integers taking value 1, 2 or 3, indicating whether the inferential analysis should be carried out respectively for the parametric, nonparametric or both the components.

`exact`

An integer taking value 1 or 2. If 1 an exact computation of the test statistics will be performed, whereas if 2 an approximated computation will be carried out (not implemented in this version).

`dim`

Dimension of the problem, it is equal to 2 in the 1.5D and 2D cases and equal to 3 in the 2.5D and 3D cases.

`n_cov`

Number of covariates taken into account in the linear part of the regression problem.

`locations`

A matrix of numeric coefficients with columns of dimension

`dim`

. When nonparametric inference is requested it represents the set of spatial locations for which the inferential analysis should be performed. The default values is a one-dimensional matrix of value 1 indicating that all the observed location points should be considered. In the sign-flip and eigen-sign-flip implementations only observed points are allowed.`locations_indices`

A vector of indices indicating which spatial points have to be considered among the observed ones for nonparametric inference. If a vector of location indices is provided then the slot 'location' is discarded.

`locations_are_nodes`

An integer taking value 1 or 2; in the first case it indicates that the selected locations to perform inference on f are all coinciding with the nodes; otherwise it takes value 2;

`time_locations`

A vector of numeric coefficients containing the set of times of interest for inference on the nonparametric component. This parameter can be

`NULL`

. In this case the temporal locations are assumed to coincide with the`time_locations`

provided to the smoothing functions. Used only if`component`

is not 1.`coeff`

A matrix of numeric coefficients with columns of dimension

`n_cov`

and each row represents a linear combination of the linear parameters to be tested and/or to be estimated via confidence interval.`beta0`

Vector of null hypothesis values for the linear parameters of the model. Used only if

`test`

is not 0 and`component`

is not 2.`f0`

Function representing the expression of the nonparametric component f under the null hypothesis. Used only if

`component`

is not 1.`f0_eval`

Matrix of f0 evaluations at the chosen space and time locations. It will be eventually set later in checkInferenceParametersTime, if nonparametric inference is required.

`f_var`

An integer taking value 1 or 2. If 1 local variance estimates for the nonlinear part of the model will be computed, whereas if 2 they will not.

`quantile`

Vector of quantiles needed for confidence intervals, used only if interval is not 0.

`alpha`

1 minus confidence level vector of sign-flipping approaches confidence intervals. Used only if interval is not 0.

`n_flip`

An integer representing the number of sign-flips in the case of sign-flipping approaches.

`tol_fspai`

A real number greater than 0 specifying the tolerance for FSPAI algorithm, in case of non-exact inference (not implemented in this version).

`definition`

An integer taking value 0 or 1. If set to 1, the class will be considered as created by the function

`inferenceDataObjectTimeBuilder`

, leading to avoid some of the checks that are performed on inference data within smoothing functions.

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