The central limit theorem (CLT) for degenerate U-statistics with a variable symmetric kernel function has been studied under dependence by many authors, since it has many important applications in ...

The central limit theorem for degenerate variable U-statistics under dependence

Nonparametric least squares estimation in derivative families

In this paper, we derive the central limit theorem (CLT) for quadratic error where the Nadaraya-Watson regression estimator is employed under dependence. Our results may be applicable for various nonparametric regression models including nonlinear auto-regressive model. In addition, we discuss the usefulness of our results for obtaining test statistics specifying a regression model under dependence. The proof uses CLT for variable degenerate U -statistics due to Kim and Luo (in press) .

Central limit theorem for quadratic errors of Nadaraya–Watson regression estimator under dependence

In this paper, one uses the idea of Cauchy-transformation to construct a Cauchy-transformation kernel density estimator underlying the condition of strong mixing. The uniformly strong consistency and convergence rates of the proposed estimator are obtained underlying the papers of Cai and Roussas (1) and Kim and Lee (6). The proposed estimator can improve the boundary effects of the empirical (or uniform)-transformation kernel density estimator in the boundary area. Besides, the proposed estimator can also be applied to estimate the hazard function.

/pdf/uniformly-consistency-of-the-cauchy-transformation-kernel-48ykb75hay.pdf

Uniformly Consistency of the Cauchy-Transformation Kernel Density Estimation Underlying Strong Mixing

Until now integrated square error (ISE) for kernel smoothing estimators has been thoroughly investigated in the context of bandwidth selection, while little work has been done for its alternative, average square error (ASE), mainly because ASE and ISE have been regarded to be nearly equivalent. In this paper convergence rate of ASE and difference between ISE and ASE are studied, which reveals that curse of dimension affects square errors in regression setting and there exists a cutoff point in dimension where ASE and ISE are no longer asymptotically equivalent.

Convergence rates for average square errors for kernel smoothing estimators

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

Dennis D. Cox

Author Tools

Chat about Author

Papers

Convergence rates for average square errors for kernel smoothing estimators