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Parametric-rate inference for one-sided differentiable parameters.

Alexander R Luedtke1, Mark J van der Laan1

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Summary
This summary is machine-generated.

This study introduces a new method for estimating maximal parameters in non-regular statistical settings, providing accurate confidence intervals even when standard techniques fail. The approach is efficient and scales to large datasets, handling a growing number of predictors.

Keywords:
non-regular inferencestabilized one-step estimatorvariable screening

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Area of Science:

  • Statistics
  • Statistical Inference
  • Machine Learning

Background:

  • Estimating maximal parameters is crucial in statistical analysis.
  • Non-regular estimation problems, often arising from non-unique maximizing parameters, pose challenges for standard asymptotic techniques.
  • Existing methods struggle when the number of predictors (p) grows with sample size (n).

Purpose of the Study:

  • To develop a novel technique for constructing parametric-rate confidence intervals in non-regular estimation settings.
  • To ensure asymptotic efficiency for unique maximizing parameters.
  • To address the challenge of estimating maximal parameters when the number of predictors grows with the sample size.

Main Methods:

  • The study presents a new technique for developing parametric-rate confidence intervals.
  • Asymptotic efficiency is proven for unique maximizing parameters.
  • The method is applied to estimate maximal absolute correlation between an outcome and multiple predictors.

Main Results:

  • The proposed technique successfully provides parametric-rate confidence intervals in non-regular settings.
  • The estimator is asymptotically efficient when the maximizing parameter is unique.
  • The method accommodates scenarios where the number of predictors (p) grows with sample size (n), provided log p grows slower than sqrt(n).
  • The computational complexity for point estimates and confidence intervals is O(np), enabling scalability to massive datasets.

Conclusions:

  • A robust and scalable method for estimating maximal parameters in challenging non-regular statistical problems has been developed.
  • This technique overcomes limitations of traditional methods, particularly in high-dimensional settings.
  • The approach offers efficient computation, making it suitable for large-scale data analysis and improving statistical inference accuracy.