Entry
Reader's guide
Entries A-Z
Subject index
Best Linear Unbiased Estimator
The term best linear unbiased estimator (BLUE) comes from application of the general notion of unbiased and efficient estimation in the context of linear estimation. In statistical and econometric research, we rarely have populations with which to work. We typically have one or a few SAMPLES drawn from a population. Our task is to make meaningful statistical inferences about parameter estimates based upon sample statistics used as estimators. Here, the statistical properties of estimators have a crucial importance because without estimators of good statistical properties, we could not make credible statistical inferences about population parameters. We desire estimators to be unbiased and efficient. In other words, we require the expected value of estimates produced by an estimator to be equal to the true value of population parameters. We also require the variance of the estimates produced by the estimator to be the smallest among all unbiased estimators. We call an estimator the best unbiased estimator (BUE) if it satisfies both conditions. The class of BUE estimators may be either linear or nonlinear. If a BUE estimator comes from a linear function, then we call it a best linear unbiased estimator (BLUE).
For a more sophisticated understanding of the term BLUE, we need to delve into the meaning of the terms “estimator,” “unbiased,” “best,” and “linear” in more detail.
Estimator
An estimator is a decision rule for finding the value of a population parameter using a sample statistic. For any population parameter, whether it is a population average, dispersion, or MEASURE OF ASSOCIATION between variables, there are usually several possible estimators. Good estimators are those that are, on average, close to the population parameter with a high degree of certainty.
Unbiasedness
With unbiasedness, we require that, under repeated sampling, the expected value of the sample estimates produced by an estimator will equal the true value of the population parameter. For example, suppose we estimate from a sample a bivariate LINEAR REGRESSION ŷi = ^β0 + ^β1xi + εi in order to find the parameters of a population regression function yi = β0 + β1xi + εi. Unbiasedness requires that the expected values of ^β0 and ^β1 equal the actual values of β0 and β1in the population. Mathematically, this is expressed E[^β0] = β and E[^β1] = β1. Intuitively, unbiasedness means that the sample estimates will, on average, produce the true population parameters. However, this does not mean that any particular estimate from a sample will be correct. Rather, it means that the estimation rule used to produce the estimates will, on average, produce the true population parameter.
Efficiency
The term best refers to the efficiency criterion. Efficiency means that an unbiased estimator has minimum variance compared to all other unbiased estimators. For example, suppose we have a sample drawn from a normal population. We can estimate the midpoint of the population using either the mean or the median. Both are unbiased estimators of the midpoint. However, the mean is the more efficient estimator because, under repeated sampling, the variance of the sample medians is approximately 1.57 times larger than the variance of the sample means. The rationale behind the efficiency criterion is to increase the probability that sample estimates fall close to the true value of the population parameter. Under repeated sampling, the estimator with the smaller variance has a higher probability of yielding estimates that are closer to the true value.
...
- Analysis of Variance
- Association and Correlation
- Association
- Association Model
- Asymmetric Measures
- Biserial Correlation
- Canonical Correlation Analysis
- Correlation
- Correspondence Analysis
- Intraclass Correlation
- Multiple Correlation
- Part Correlation
- Partial Correlation
- Pearson's Correlation Coefficient
- Semipartial Correlation
- Simple Correlation (Regression)
- Spearman Correlation Coefficient
- Strength of Association
- Symmetric Measures
- Basic Qualitative Research
- Basic Statistics
- F Ratio
- N(n)
- t-Test
- X¯
- Y Variable
- z-Test
- Alternative Hypothesis
- Average
- Bar Graph
- Bell-Shaped Curve
- Bimodal
- Case
- Causal Modeling
- Cell
- Covariance
- Cumulative Frequency Polygon
- Data
- Dependent Variable
- Dispersion
- Exploratory Data Analysis
- Frequency Distribution
- Histogram
- Hypothesis
- Independent Variable
- Measures of Central Tendency
- Median
- Null Hypothesis
- Pie Chart
- Regression
- Standard Deviation
- Statistic
- Causal Modeling
- Discourse/Conversation Analysis
- Econometrics
- Epistemology
- Ethnography
- Evaluation
- Event History Analysis
- Experimental Design
- Factor Analysis and Related Techniques
- Feminist Methodology
- Generalized Linear Models
- Historical/Comparative
- Interviewing in Qualitative Research
- Latent Variable Model
- Life History/Biography
- Log-Linear Models (Categorical Dependent Variables)
- Longitudinal Analysis
- Mathematics and Formal Models
- Measurement Level
- Measurement Testing and Classification
- Multilevel Analysis
- Multiple Regression
- Qualitative Data Analysis
- Sampling in Qualitative Research
- Sampling in Surveys
- Scaling
- Significance Testing
- Simple Regression
- Survey Design
- Time Series
- ARIMA
- Box-Jenkins Modeling
- Cointegration
- Detrending
- Durbin-Watson Statistic
- Error Correction Models
- Forecasting
- Granger Causality
- Interrupted Time-Series Design
- Intervention Analysis
- Lag Structure
- Moving Average
- Periodicity
- Serial Correlation
- Spectral Analysis
- Time-Series Cross-Section (TSCS) Models
- Time-Series Data (Analysis/Design)
- Trend Analysis
- Loading...
Get a 30 day FREE TRIAL
-
Watch videos from a variety of sources bringing classroom topics to life -
Read modern, diverse business cases
-
Explore hundreds of books and reference titles
Read next
More like this
Sage Recommends
We found other relevant content for you on other Sage platforms.
Have you created a personal profile? Login or create a profile so that you can save clips, playlists and searches