• Skip to primary navigation
  • Skip to main content
  • Skip to primary sidebar
  • Skip to footer
Finance Train

Finance Train

High Quality tutorials for finance, risk, data science

  • Home
  • Data Science
  • CFA® Exam
  • PRM Exam
  • Tutorials
  • Careers
  • Products
  • Login

Best Linear Unbiased Estimator (B.L.U.E.)

FRM Part 1, Statistics

This lesson is part 3 of 3 in the course Basic Statistics - FRM

The Need

There are several issues when trying to find the Minimum Variance Unbiased (MVU) of a variable.

  • The Probability Density Function (PDF) is not known
  • It is difficult to model the PDF
  • Even in cases where the PDF is known it is difficult to arrive at the estimate of the minimum variance

The intended approach in such situations is to use a sub-optiomal estimator and impose the restriction of linearity on it.

  • This estimator is not biased.
  • The minimum variance can be arrived at using only the first and second moments of the probability density function (PDF).
  • It has more practical usefulness as the complete PDF is never required.
  • The variance of this estimator is the lowest among all unbiased linear estimators.

Definition

The following steps summarize the construction of the Best Linear Unbiased Estimator (B.L.U.E)

  1. Define a linear estimator.
  2. It must have the property of being unbiased.
  3. The mimimum variance is then computed.
  4. The conditions under which the minimum variance is computed need to be determined.
  5. This then needs to be put in the form of a vector.

The BLUE becomes an MVU estimator if the data is Gaussian in nature irrespective of if the parameter is in scalar or vector form.

In order to estimate the BLUE there are only two details needed. They are scaled mean and the covariance the first and second moments respectively.

Advantages over Disadvantages

If data can be modeled to have linear observations in noise then the Gauss-Markov theorem can be used to find the BLUE. The Markov theorem generalizes the BLUE result to the case where the ranks are less than full.

BLUE is applicable to amplitude estimation of known signals in noise. However it is to be noted that noise need not necessarily be Gaussian is nature.

The biggest disadvantage of BLUE is that is already sub-optimal in nature and sometimes it is not the right fit to problem in question.

Previous Lesson

‹ Interpretation of Skewness, Kurtosis, CoSkewness, CoKurtosis

Next Lesson

›

Join Our Facebook Group - Finance, Risk and Data Science

Posts You May Like

How to Improve your Financial Health

CFA® Exam Overview and Guidelines (Updated for 2021)

Changing Themes (Look and Feel) in ggplot2 in R

Coordinates in ggplot2 in R

Facets for ggplot2 Charts in R (Faceting Layer)

Reader Interactions

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Primary Sidebar

In this Course

  • Calculate and Interpret Covariance and Correlations
  • Interpretation of Skewness, Kurtosis, CoSkewness, CoKurtosis
  • Best Linear Unbiased Estimator (B.L.U.E.)

Latest Tutorials

    • Data Visualization with R
    • Derivatives with R
    • Machine Learning in Finance Using Python
    • Credit Risk Modelling in R
    • Quantitative Trading Strategies in R
    • Financial Time Series Analysis in R
    • VaR Mapping
    • Option Valuation
    • Financial Reporting Standards
    • Fraud
Facebook Group

Membership

Unlock full access to Finance Train and see the entire library of member-only content and resources.

Subscribe

Footer

Recent Posts

  • How to Improve your Financial Health
  • CFA® Exam Overview and Guidelines (Updated for 2021)
  • Changing Themes (Look and Feel) in ggplot2 in R
  • Coordinates in ggplot2 in R
  • Facets for ggplot2 Charts in R (Faceting Layer)

Products

  • Level I Authority for CFA® Exam
  • CFA Level I Practice Questions
  • CFA Level I Mock Exam
  • Level II Question Bank for CFA® Exam
  • PRM Exam 1 Practice Question Bank
  • All Products

Quick Links

  • Privacy Policy
  • Contact Us

CFA Institute does not endorse, promote or warrant the accuracy or quality of Finance Train. CFA® and Chartered Financial Analyst® are registered trademarks owned by CFA Institute.

Copyright © 2021 Finance Train. All rights reserved.

  • About Us
  • Privacy Policy
  • Contact Us