Modal Regression

Performing nonparametric modal regression based on kernel density estimator.

• Paper reference: Chen, Yen-Chi, et al. "Nonparametric modal regression." The Annals of Statistics 44.2 (2016): 489-514.
• Contact: yenchic@uw.edu

ModalRegression.R:

This contains two functions: RegMS1d and RegMS2d.

RegMS1d

RegMS1d = function(X, Y, G.x=X, G.y=Y, h.x, h.y, iter=100, tolerance=1e-8)

• Input:

  • X: covariate, 1 dimension
  • Y: response, 1 dimension
  • G.x: grid of covariate
  • G.y: grid of response
  • h.x: smoothing parameter for covariate
  • h.y: smoothing parameter for response
  • iter: maximal number of iteration
  • tolerance: the tolerance level of shifting step

• Output:

  • Estimated local modes from each point of (G.x, G.y)

RegMS2d

RegMS2d = function(X,Y, G.x=X, G.y=Y, h.x, h.y, iter=100,tolerance=1e-8)

• Input:

  • X: covariate, 2 dimension
  • Y: response, 1 dimension
  • G.x: grid of covariate
  • G.y: grid of response
  • h.x: smoothing parameter for covariates
  • h.y: smoothing parameter for response
  • iter: maximal number of iteration
  • tolerance: the tolerance level of shifting step

• Output:

  • Estimated local modes from each point of (G.x, G.y)

Ex1_DualCurve.R:

A script on the dual curve simulation data. The analysis includes estimating the modal curves, prediction sets and comparison to the local regression.

• Section 1: Generate Data
• Section 2: Modal regression
• Section 3: Representing by curves
• Section 4: Prediction set (non-optimized)
• Section 5: Comparison to local regression

Ex2_3Mixture.R:

A script on the three mixture simulation data. The analysis is essentially the same as dual curve but we also present bandwidth selection and comparison to mixture regression.

• Section 1: Generate Data
• Section 2: Modal Regression
• Section 3: Bandwidth selection via minizming prediction set
• Section 4: Optimal result
• Section 5: Prediction set
• Section 6: Local regression
• Section 7: Mixture regression