1. What is Bias of an Estimator?

Bias measures the systematic error of an estimator from the true parameter value. It represents the average difference between the expected value of the estimator and the true parameter it is trying to estimate.

2. How Does the Calculator Work?

The calculator uses the bias formula:

Where:

• \( \text{Bias} \) — Systematic error of the estimator (unitless)
• \( E[\hat{\theta}] \) — Expected value of the estimator
• \( \theta \) — True parameter value

Explanation: A bias of zero indicates an unbiased estimator, where the estimator's expected value equals the true parameter. Positive bias means overestimation, negative bias means underestimation.

3. Importance of Bias Calculation

Details: Understanding bias is crucial in statistical inference and machine learning. It helps assess estimator quality, guides model selection, and informs decisions about bias-variance tradeoff in predictive modeling.

4. Using the Calculator

Tips: Enter the expected value of your estimator and the true parameter value. Both values should be in the same units. The calculator will compute the bias, which is unitless and represents the systematic error.

5. Frequently Asked Questions (FAQ)

Q1: What does a bias of zero mean?
A: A bias of zero indicates an unbiased estimator, meaning on average the estimator equals the true parameter value across many samples.

Q2: Is zero bias always desirable?
A: While zero bias is generally desirable, sometimes biased estimators with lower variance may be preferred (bias-variance tradeoff).

Q3: How is bias different from variance?
A: Bias measures systematic error (accuracy), while variance measures random error (precision) of an estimator.

Q4: Can bias be negative?
A: Yes, negative bias indicates systematic underestimation of the true parameter value.

Q5: How do you reduce bias in estimators?
A: Bias can be reduced through better model specification, increased sample size, or using bias-corrected estimation methods.