Taylor's Theorem for Random Functions: A Statistical Foundation

280.9 KB of research materials by Yifan Yang, last updated April 2026, address the measurability of intermediate points when applying Taylor's and mean value theorems to random functions and vectors. The work provides a rigorous foundation for expansions used in statistical methods like maximum likelihood and M-estimation, with illustrative examples included.

Use Cases

• Rigorously justifying Taylor expansions in asymptotic proofs based on the theorems for random functions
• Developing new statistical estimation methods based on the provided measurable intermediate point constructions
• Teaching advanced probability theory concepts based on the illustrative examples for random vectors

Strengths

• Provides formal theorems addressing a specific, often-overlooked measurability issue in statistics.
• Includes illustrative examples for common statistical methods like maximum likelihood estimation.
• Released under a permissive CC-BY-4.0 license for reuse.

Limitations

• The 280.9 KB size indicates a limited scope, likely a research paper rather than a large dataset.
• Column-level documentation is absent; field semantics must be inferred after download.
• Row count is unknown, which may limit suitability assessment.

Provenance

Source

Yifan Yang

Collection Method

Theoretical mathematical research and proof development.

Time Range

Publication date is unspecified; last platform update was April 2026.

Freshness

Last updated 2026-04-13 12:58:53; freshness should be verified.

Geography

Spatial coverage is not applicable for this theoretical work.