1. What Is Bias Of Estimator?

Bias measures the difference between an estimator's expected value and the true value of the parameter being estimated. It quantifies the systematic error in an estimation procedure.

2. How Does The Calculator Work?

The calculator uses the bias formula:

Where:

• \( E[\text{Estimator}] \) — Expected value of the estimator
• \( \text{True Value} \) — Actual value of the parameter being estimated
• \( \text{Bias} \) — Systematic error of the estimator (unitless)

Explanation: A bias of zero indicates an unbiased estimator, positive bias indicates overestimation, and negative bias indicates underestimation.

3. Importance Of Bias Calculation

Details: Understanding bias is crucial in statistical inference, model evaluation, and ensuring the reliability of estimation procedures across various fields including economics, engineering, and scientific research.

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 for meaningful comparison.

5. Frequently Asked Questions (FAQ)

Q1: What does a zero bias mean?
A: A zero bias indicates that the estimator is unbiased - on average, it correctly estimates the true parameter value.

Q2: How is bias different from variance?
A: Bias measures systematic error, while variance measures random error. The mean squared error combines both: MSE = Bias² + Variance.

Q3: Can we always achieve zero bias?
A: Not always. There's often a trade-off between bias and variance (bias-variance tradeoff). Sometimes accepting some bias can reduce overall error.

Q4: What are common sources of bias?
A: Selection bias, measurement bias, specification bias in models, and sampling bias are common sources that affect estimator accuracy.

Q5: How can bias be reduced?
A: Using appropriate sampling methods, proper model specification, cross-validation, and bias-correction techniques can help reduce estimator bias.