Nadaraya-Watson Envelope Channel
The Nadaraya-Watson envelope strategy is a statistical approach used for nonparametric regression analysis. It is based on the Nadaraya-Watson kernel estimator, which estimates the conditional expectation of a dependent variable given a set of independent variables. The envelope strategy involves constructing an envelope around the kernel estimator to provide a measure of uncertainty about the estimated function.
The envelope is created by calculating upper and lower bounds for the kernel estimator based on the variance of the estimated function at each point. This allows for the construction of confidence intervals that can be used to assess the significance of the estimated function.
The Nadaraya-Watson envelope strategy is a useful tool in situations where there is little prior knowledge about the relationship between the independent and dependent variables. It is particularly well-suited for datasets with nonlinear relationships, as it can capture complex patterns and relationships that may be missed by traditional linear regression techniques.
The Nadaraya-Watson kernel estimator is based on the following formula:
where: f(x) is the estimated value of the dependent variable at a given value of the independent variable x w(i,y) is the weight assigned to each observation based on its distance from the point (x,y) y is the value of the dependent variable for a given observation The weights are typically defined using a kernel function, such as the Gaussian kernel or the Epanechnikov kernel, which assigns higher weights to observations closer to the point of interest and lower weights to observations further away.
The Nadaraya-Watson envelope strategy involves calculating upper and lower bounds for the kernel estimator at each point based on the variance of the estimated function. These bounds can be used to construct confidence intervals and assess the significance of the estimated function. The exact formula for the envelope depends on the specific kernel function used and the level of confidence desired.
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The execution of the bundle essentially refers to the calculation of these values, which are then handled by the Steer Protocol.