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Estimation of a single parameter of some probability distributions using L2 optimization

Jiwoong Kim

TL;DR

This paper discusses asymptotic properties of the resulting estimator and compares the proposed estimator with other estimators.

Abstract

We propose a minimum distance estimation of a rate parameter of some probability distributions. This paper discusses asymptotic properties of the resulting estimator. Next, we compare the proposed estimator with other estimators.

Estimation of a single parameter of some probability distributions using L2 optimization

TL;DR

This paper discusses asymptotic properties of the resulting estimator and compares the proposed estimator with other estimators.

Abstract

We propose a minimum distance estimation of a rate parameter of some probability distributions. This paper discusses asymptotic properties of the resulting estimator. Next, we compare the proposed estimator with other estimators.
Paper Structure (6 sections, 5 theorems, 27 equations)

This paper contains 6 sections, 5 theorems, 27 equations.

Table of Contents

  1. Introduction
  2. Minimum distance estimation
  3. Estimation of a rate parameter $\beta$
  4. Prerequisites for the asymptotic properties of MD estimation
  5. MD estimation of $\beta$
  6. Conclusion

Key Result

Lemma 2.1

Suppose (u.1)-(u.3) hold. Let $\widehat{\beta}$ denote the MD estimator which solves the optimization problem in (eq:opt). Then, there exists $\delta_{n}$ such that

Theorems & Definitions (10)

  • Lemma 2.1
  • Theorem 2.1
  • Remark 2.1
  • proof
  • Lemma 2.2
  • Remark 2.2
  • Lemma 2.3
  • proof
  • Theorem 2.2
  • proof