Nonlinear Nonparametric Statistics: Using Partial Moments
Preface
This book presents the Nonlinear Nonparametric Statistics (NNS) framework as a coherent toolkit for modeling dependence, uncertainty, prediction, and decision-making without imposing restrictive distributional assumptions.
The chapters are organized to move from foundational concepts to practical modeling workflows:
- first principles of nonlinear dependence and directional relationships,
- nonparametric methods for regression, classification, and density-based tasks,
- time-series forecasting frameworks for univariate and multivariate settings,
- and implementation guidance for applied research and production analytics.
The central theme is consistent throughout: when data are asymmetric, heavy-tailed, nonlinear, or regime-sensitive, useful structure can still be extracted directly from the data-generating process using directional and nonparametric methods.
Executive Summary
This book is designed for readers who want mathematically grounded methods that remain practical in real-world settings where classical assumptions can fail.
At a high level, the NNS framework emphasizes:
- distribution-agnostic modeling rather than strict parametric family selection,
- directional dependence and causation diagnostics instead of purely symmetric association summaries,
- nonlinear predictive systems that can adapt to heterogeneous signal structures,
- and modular workflows in R so methods can be combined for exploratory analysis, forecasting, and risk assessment.
Readers can use the text in two ways:
- Sequentially, as a complete conceptual arc from core definitions to advanced forecasting systems.
- As a reference, by jumping directly to method-specific chapters and accompanying implementation examples.
Whether your domain is economics, finance, operations, policy, or scientific research, the goal is the same: to provide robust, interpretable, and applied nonparametric tools for difficult data.
About the Examples Repository
This book is designed to be used alongside the companion examples repository:
The repository is organized as a practical application layer. Conceptual and theoretical development lives in the book, while reproducible scripts and end-to-end demonstrations live in the examples.
A useful way to navigate both resources together is:
- Read the chapter for the theoretical framework and notation.
- Open the matching section in
examples/README.mdfor runnable code patterns. - Adapt those scripts to your own data and evaluate with your domain constraints.
The examples repository is intended for hands-on implementation, not as a substitute for the proofs and derivations developed in the text. Keep the repository disclaimer in mind when applying any script directly to production or policy settings; examples are instructional templates and should be validated, stress-tested, and context-calibrated before operational use.