Method Crosswalk

A practical map from np and npRmpi functions to statistical targets, examples, implementation notes, and theory references.
Keywords

np, npRmpi, methods, theory, crosswalk, documentation

This page maps the main np and npRmpi function families to the statistical object being estimated, the Gallery examples that are most useful to start with, and the book chapters where the method is developed or discussed.

It is not a replacement for the package help pages. Use ?npreg, ?npcdens, ?npconmode, and related help pages for argument-level details. This page is meant to answer a different question: “What method am I using, where is it explained, and how does it connect to the package implementation?”

The Princeton book (Li and Racine 2007) is the foundational theory reference for many of the core mixed-data kernel estimators. The Cambridge book (Racine 2019a) is later and more package/workflow oriented, and it covers additional examples, entropy-based material, semiparametric workflows, and computational considerations. This crosswalk therefore points to the most useful source for each method rather than treating one book as the only route.

Implementation details added after the printed treatments, such as recent local-polynomial degree search, conditional-quantile gradients, or MPI-aware plot/bootstrap machinery, are labeled as package implementation extensions.

How To Use This Page

If you want… Use this route
Runnable examples Start with the Gallery page linked in the method row.
Argument details Open the package help page in R.
Theory and derivations Use the chapter and section pointers listed here.
MPI behavior Read the method row, then see MPI and Large Data.
Function lookup Use Reference and Function Lookup.

Core Methods

Task Main functions Statistical target Best first Gallery page
Regression npreg, npregbw Conditional mean or regression function \(E[Y \mid X=x]\) Kernel Primer, Worked Examples
Unconditional density npudens, npudensbw Density \(f(x)\) Density, Distribution, Quantiles
Unconditional distribution npudist, npudistbw Distribution \(F(x)\) Density, Distribution, Quantiles
Conditional density npcdens, npcdensbw Conditional density \(f(y \mid x)\) Density, Distribution, Quantiles
Conditional distribution npcdist, npcdistbw Conditional distribution \(F(y \mid x)\) Density, Distribution, Quantiles
Conditional quantile npqreg Conditional quantile \(q_\tau(x)=\inf\{y:F(y \mid x)\ge \tau\}\) Density, Distribution, Quantiles
Conditional mode / classification npconmode Modal outcome \(\arg\max_y \Pr(Y=y \mid X=x)\) Classification and Modes
Partially linear regression npplreg, npplregbw Partially linear model \(Y=X'\beta+\theta(Z)+\epsilon\) Semiparametric Models
Single-index model npindex, npindexbw Index regression \(E[Y \mid X]=g(X'\beta)\) Semiparametric Models
Smooth-coefficient model npscoef, npscoefbw Varying coefficients \(Y=X'\beta(Z)+\epsilon\) Semiparametric Models

Core Method Source Pointers

Task Theory and implementation orientation
Regression Princeton, Regression, Chapter 2, especially Sections 2.1, 2.2, 2.4, and 2.5; Princeton, Kernel Estimation with Mixed Data, Chapter 4, especially Sections 4.2 and 4.4; Cambridge, Conditional Mean Function Estimation, Chapter 6. Local-polynomial and automatic degree-search options can materially change the fitted estimator. The current ll route is implemented as local polynomial degree 1 where applicable.
Unconditional density Princeton, Density Estimation, Chapter 1, especially Sections 1.1, 1.3, 1.6, 1.8, and 1.9; Princeton, Kernel Estimation with Mixed Data, Chapter 4; Cambridge, Continuous Density and Cumulative Distribution Functions, Chapter 2; Cambridge, Mixed-Data Probability Density and Cumulative Distribution Functions, Chapter 3.
Unconditional distribution Princeton, Density Estimation, Chapter 1, especially Sections 1.4 and 1.5; Cambridge, Continuous Density and Cumulative Distribution Functions, Chapter 2, especially smooth kernel CDF material; Cambridge, Mixed-Data Probability Density and Cumulative Distribution Functions, Chapter 3.
Conditional density Princeton, Conditional Density Estimation, Chapter 5, especially Sections 5.1-5.4; Princeton, Kernel Estimation with Mixed Data, Chapter 4; Cambridge, Conditional Probability Density and Cumulative Distribution Functions, Chapter 4.
Conditional distribution Princeton, Conditional CDF and Quantile Estimation, Chapter 6, especially Sections 6.1, 6.2, and 6.5; Princeton, Conditional Density Estimation, Chapter 5; Cambridge, Conditional Probability Density and Cumulative Distribution Functions, Chapter 4.
Conditional quantile Princeton, Conditional CDF and Quantile Estimation, Chapter 6, especially Sections 6.3-6.5; Cambridge, Conditional Probability Density and Cumulative Distribution Functions, Chapter 4, especially conditional CDF and quantile material; Nelsen (2006) for quasi-inverse language. Gradients and standard errors are recent implementation extensions.
Conditional mode / classification Cambridge, Conditional Probability Density and Cumulative Distribution Functions, Chapter 4, especially Binary Choice and Multinomial Choice Models; Princeton, Conditional Density Estimation, Chapter 5; Princeton, Kernel Estimation with Mixed Data, Chapter 4. Non-local-constant routes use proper fitted probabilities before modal selection.
Partially linear regression Princeton, Semiparametric Partially Linear Models, Chapter 7, especially Sections 7.1, 7.2, and 7.4; Cambridge, Semiparametric Conditional Mean Function Estimation, Chapter 8, especially Robinson’s Partially Linear Model. Current local-polynomial/NOMAD behavior treats the nuisance regressions as child-specific local-polynomial fits, followed by the final partially linear solve.
Single-index model Princeton, Semiparametric Single Index Models, Chapter 8, especially Sections 8.1, 8.2.1, 8.4, 8.5, and 8.10; Cambridge, Semiparametric Conditional Mean Function Estimation, Chapter 8, especially single-index material.
Smooth-coefficient model Princeton, Additive and Smooth (Varying) Coefficient Semiparametric Models, Chapter 9, especially Sections 9.3-9.3.4; Cambridge, Semiparametric Conditional Mean Function Estimation, Chapter 8, especially Varying Coefficient Models.

Tests And Diagnostics

Task Main functions What the test asks Best first Gallery page
Mean model specification npcmstest Does a parametric conditional-mean model appear misspecified against a nonparametric alternative? Significance and Specification
Quantile model specification npqcmstest Does a parametric conditional-quantile model appear misspecified? Significance and Specification
Significance testing npsigtest Which regressors are statistically relevant in a nonparametric regression? Significance and Specification
Density equality npdeneqtest Are distributions or densities equal across groups? Entropy and Testing
Univariate density features npunitest Does a univariate density have the specified feature? Entropy and Testing
Symmetry npsymtest Is a distribution symmetric? Entropy and Testing
Dependence npdeptest, npsdeptest Are variables dependent or serially dependent? Entropy and Testing

Test Source Pointers

Task Theory and implementation orientation
Mean model specification Princeton, Model Specification Tests, Chapter 12, especially Section 12.1 and Section 12.1.2; Cambridge, Conditional Mean Function Estimation, Chapter 6, for package-facing model assessment context.
Quantile model specification Princeton, Model Specification Tests, Chapter 12; Princeton, Conditional CDF and Quantile Estimation, Chapter 6; Cambridge, Conditional Probability Density and Cumulative Distribution Functions, Chapter 4.
Significance testing Princeton, Model Specification Tests, Chapter 12, especially Sections 12.3 and 12.3.5; Princeton, Nonsmoothing Tests, Chapter 13, especially Section 13.3 where applicable; Cambridge, Conditional Mean Function Estimation, Chapter 6.
Density equality Princeton, Model Specification Tests, Chapter 12, especially Section 12.2; Princeton, Nonsmoothing Tests, Chapter 13, especially Section 13.2; Cambridge, Continuous Density and Cumulative Distribution Functions, Chapter 2, and Mixed-Data Probability Density and Cumulative Distribution Functions, Chapter 3.
Univariate density features Cambridge, Continuous Density and Cumulative Distribution Functions, Chapter 2, especially entropy and density-test material; Princeton testing chapters where applicable.
Symmetry Cambridge, Continuous Density and Cumulative Distribution Functions, Chapter 2; Princeton, Nonsmoothing Tests, Chapter 13, and Model Specification Tests, Chapter 12, where density-feature tests are treated.
Dependence Cambridge, Continuous Density and Cumulative Distribution Functions, Chapter 2; Princeton, Nonsmoothing Tests, Chapter 13, especially Sections 13.4 and 13.5; Princeton, Model Specification Tests, Chapter 12, especially Sections 12.4.1 and 12.4.3.

Advanced And Workflow APIs

These functions are useful, but they are not the main starting point for most users.

  • npksum: lower-level mixed-kernel sums for custom workflows. Start with Build With npksum. The relevant source is the estimator family being reconstructed; Cambridge, Practicum, Chapter 14, and Computational Considerations, Chapter 12, provide package-facing examples and computational context.
  • npreghat, npcdenshat, npcdisthat, npudenshat, npudisthat, npsemihat: fast post-estimation and helper workflows. Start with Reference and Function Lookup. These are advanced APIs; their source usually follows the estimator family rather than a separate book derivation.
  • plot, se, gradients, compute.bootstrap.errors: plot surfaces, intervals, standard errors, and derivative accessors. Start with Plotting and Intervals. Current plot/bootstrap and some gradient behavior are implementation extensions.
  • np.options, np.kernels, npseed: reproducibility, global options, and kernel choices. Start with Kernel Primer. Princeton, Density Estimation, Chapter 1, is the natural kernel/CDF background; package documentation is the source for exact option behavior.
  • npuniden.boundary, npuniden.reflect, npuniden.sc, uocquantile: support and boundary workflows. Start with Reference and Function Lookup. Cambridge, Continuous Density and Cumulative Distribution Functions, Chapter 2, provides bounded-domain and boundary-correction context.
  • npcopula: mixed-data copula and copula-density workflows. Start with Density, Distribution, Quantiles. Cambridge, Mixed-Data Probability Density and Cumulative Distribution Functions, Chapter 3, especially Smooth Kernel Copula Function Estimation with Mixed-Data, and Princeton, Topics in Applied Nonparametric Estimation, Chapter 20, Section 20.4, are the main source pointers.
  • npregiv, npregivderiv: instrumental-variable regression routes. Start with Reference and Function Lookup. Princeton, Instrumental Variables and Efficient Estimation of Semiparametric Models, Chapter 16, Princeton, Endogeneity in Nonparametric Regression Models, Chapter 17, and Cambridge, Conditional Mean Function Estimation with Endogenous Predictors, Chapter 7, are the main source pointers.
  • npRmpi.init, npRmpi.quit, npRmpi.session.info: MPI setup, cleanup, and runtime diagnostics. Start with MPI and Large Data. Cambridge, Computational Considerations, Chapter 12, especially parallelism, provides general context; package runtime documentation is the source for exact behavior.

Book Source Key

This section records the chapter-level map used above. It is intentionally chapter-first: if you own or can access the books, these are the places to start.

Princeton

  • Chapter 1, Density Estimation: Sections 1.1, Univariate Density Estimation; 1.3, Univariate Bandwidth Selection: Cross-Validation Methods; 1.4, Univariate CDF Estimation; 1.5, Univariate CDF Bandwidth Selection; 1.6, Multivariate Density Estimation; 1.8, Multivariate Bandwidth Selection; 1.9, Asymptotic Normality of Density Estimators.
  • Chapter 2, Regression: Sections 2.1, Local Constant Kernel Estimation; 2.2, Local Constant Bandwidth Selection; 2.4, Local Linear Kernel Estimation; 2.5, Local Polynomial Regression.
  • Chapter 4, Kernel Estimation with Mixed Data: Sections 4.1, Smooth Estimation of Joint Distributions with Discrete Data; 4.2, Smooth Regression with Discrete Data; 4.4, Regression with Mixed Data: Relevant Regressors.
  • Chapter 5, Conditional Density Estimation: Sections 5.1, Conditional Density Estimation: Relevant Variables; 5.2, Conditional Density Bandwidth Selection; 5.3, Conditional Density Estimation: Irrelevant Variables; 5.4, The Multivariate Dependent Variables Case.
  • Chapter 6, Conditional CDF and Quantile Estimation: Sections 6.1-6.2, conditional CDF estimation; 6.3, Nonparametric Estimation of Conditional Quantile Functions; 6.5, mixed-data conditional CDF and quantile estimation.
  • Chapter 7, Semiparametric Partially Linear Models: Sections 7.1, Partially Linear Models; 7.2, Robinson’s Estimator; 7.4, Semiparametric Efficiency Bounds.
  • Chapter 8, Semiparametric Single Index Models: Sections 8.1, identification; 8.2.1, Ichimura’s Method; 8.4, bandwidth selection; 8.5, Klein and Spady’s Estimator; 8.10, multinomial discrete choice.
  • Chapter 9, Additive and Smooth (Varying) Coefficient Semiparametric Models: Sections 9.3-9.3.4, varying/smooth coefficient models and related tests.
  • Chapter 12, Model Specification Tests: Sections 12.1, parametric regression functional form; 12.2, equality of PDFs; 12.3, regression-function tests; 12.4, PDF-related tests.
  • Chapter 13, Nonsmoothing Tests: Sections 13.1, functional-form tests; 13.2, equality of densities; 13.3, significance testing; 13.4-13.5, conditional CDF and serial-dependence tests.
  • Chapter 16, Instrumental Variables and Efficient Estimation of Semiparametric Models: Sections 16.1-16.3, semiparametric IV models and conditional moment restrictions.
  • Chapter 17, Endogeneity in Nonparametric Regression Models: Sections 17.1-17.5, nonparametric IV/endogeneity models and estimators.
  • Chapter 20, Topics in Applied Nonparametric Estimation: Section 20.4, copula-based semiparametric estimation.

Cambridge

  • Chapter 2, Continuous Density and Cumulative Distribution Functions: smooth kernel density, CDF, and quantile estimation; multivariate extensions; entropy and information measures; bounded-domain examples.
  • Chapter 3, Mixed-Data Probability Density and Cumulative Distribution Functions: mixed-data density/CDF estimation; multivariate extension; smooth kernel copula estimation with mixed data.
  • Chapter 4, Conditional Probability Density and Cumulative Distribution Functions: smooth conditional density; smooth conditional CDF; conditional quantile estimation; binary choice and multinomial choice models.
  • Chapter 6, Conditional Mean Function Estimation: local constant and local polynomial regression; multivariate local-polynomial extension; mixed-data marginal effects; predictor relevance; shape-constrained regression.
  • Chapter 7, Conditional Mean Function Estimation with Endogenous Predictors: ill-posed inverse problems and identification; parametric and nonparametric instrumental regression.
  • Chapter 8, Semiparametric Conditional Mean Function Estimation: Robinson’s partially linear model; varying coefficient models; semiparametric single-index models.
  • Chapter 12, Computational Considerations: binning, transforms, parallelism, tree/multipole methods, and computationally efficient kernel estimation in R.
  • Chapter 14, Practicum: applied np examples, npksum(), nonparametric density/regression, consistent inference, semiparametric models, and nonparametric discrete choice.

References

Hayfield, T., and J. S. Racine. 2008. “Nonparametric Econometrics: The np Package.” Journal of Statistical Software 27 (5): 1–32. https://doi.org/10.18637/jss.v027.i05.
Ho, A. T., K. P. Huynh, and D. T. Jacho-Chavez. 2011. “npRmpi: A Package for Parallel Distributed Kernel Estimation in R.” Journal of Applied Econometrics 26: 344–49.
Li, Q., and J. S. Racine. 2007. Nonparametric Econometrics: Theory and Practice. Princeton University Press. https://press.princeton.edu/books/hardcover/9780691121611/nonparametric-econometrics.
Nie, Z., and J. S. Racine. 2012. “The Crs Package: Nonparametric Regression Splines for Continuous and Categorical Predictors.” The R Journal 4 (2): 48–56. https://doi.org/10.32614/rj-2012-012.
Racine, J. S. 2019a. An Introduction to the Advanced Theory and Practice of Nonparametric Econometrics: A Replicable Approach Using R. Cambridge University Press. https://doi.org/10.1017/9781108649841.
Racine, J. S. 2019b. Reproducible Econometrics Using R. Oxford University Press. https://doi.org/10.1093/oso/9780190900663.001.0001.
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