Definition§
An unbiased estimator is a statistical method used to estimate a population parameter in such a way that the expected value of the estimate equals the true value of the population parameter. In other words, the method is considered unbiased if, when applied to many random samples from the population, the average of the results equals the actual population parameter.
Examples§
- Credit Card Balances: Consider a scenario where you are tasked with estimating the average account balance of credit card holders in a city. If multiple random samples are taken from the entire city’s credit card holders, and each sample’s average balance is calculated, the mean of these averages should equal the actual average balance of all account holders in the city for the estimator to be considered unbiased.
- Heights of Students: Suppose you want to estimate the average height of students at a university. If you were to choose several random samples of students over a period, and the average height from these samples matches the real average height of all university students, your estimator is unbiased.
Frequently Asked Questions (FAQs)§
Q1: What makes an estimator unbiased? A1: An estimator is unbiased if the expected value (mean) of its sampling distribution is equal to the true value of the parameter being estimated.
Q2: Why is unbiasedness important? A2: Unbiasedness ensures that, on average, our estimates are correct and not systematically off, which increases the reliability and accuracy of the inference we make about the population.
Q3: Can an estimator be both unbiased and inconsistent? A3: Yes, it is possible for an estimator to be unbiased but inconsistent. An unbiased estimator might not converge to the true parameter value as sample size increases (lack of consistency).
Q4: How can we test if an estimator is unbiased? A4: To test if an estimator is unbiased, one can compute the expected value of the estimator and verify if it equals the true parameter.
Q5: Are there situations where a biased estimator is preferred? A5: Yes, in some cases, biased estimators are preferred if they offer significantly lower variance or mean squared error compared to unbiased estimators, making them more stable or reliable in practical applications.
Related Terms§
- Estimator: A statistic used to estimate the value of a population parameter.
- Biased Estimator: An estimator with a systematic error, where the expected value of the estimate does not equal the true population parameter.
- Sampling Distribution: The probability distribution of a given statistic based on a random sample.
- Population Parameter: A value that quantitatively describes a characteristic of a population.
Online References§
Suggested Books for Further Studies§
- “Statistical Inference” by George Casella and Roger L. Berger
- “Introduction to the Theory of Statistics” by Alexander M. Mood, Franklin A. Graybill, and Duane C. Boes
Fundamentals of Unbiased Estimator: Statistics Basics Quiz§
Thank you for exploring the intricate details of unbiased estimators and testing your knowledge with our sample quiz questions. Continue your statistical journey with confidence!
