Transposed conditionals, shrinkage, and direct and indirect unbiasedness
1Department of Statistics, University of Glasgow, UK. stephen@stats.gla.ac.uk
Epidemiology (Cambridge, Mass.)
|August 16, 2008
Summary
Direct unbiasedness does not guarantee accurate parameter estimation. Inverse unbiasedness is required for accurate average estimates, revealing shrinkage as an unavoidable aspect of statistical inference.
Area of Science:
- Statistical inference
- Decision theory
Background:
- Conventional unbiasedness (direct unbiasedness) ensures estimates average to the true parameter.
- This property does not imply the parameter averages to the estimate.
Discussion:
- Inverse unbiasedness is a distinct property crucial for accurate average estimation.
- Understanding this distinction clarifies the role of shrinkage in statistical methods.
Key Insights:
- Direct unbiasedness is not a prerequisite for sound statistical inferences.
- Shrinkage is a fundamental consequence of inverse unbiasedness and statistical estimation.
Outlook:
- Re-evaluating the necessity of direct unbiasedness in statistical modeling.
- Exploring the implications of inverse unbiasedness for developing robust estimation techniques.
Related Concept Videos
01:12Hindsight Biases
Hindsight bias leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did. Can you relate this to the phrase "Hindsight is 20/20" now?
01:31Confirmation Biases
The confirmation bias is the tendency to focus on information that confirms our existing beliefs and ignore information that is inconsistent with our expectations. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis. Have you ever fallen prey to the confirmation bias, either as the source or target of such bias?
03:26Framing Effects
Information is everywhere and its presentation—such as how and when items are presented—can impact our perceptions and decisions surrounding the info. This broad concept umbrellas framing effects—influences that occur due to the way information is framed in its appearance, whether it’s purely the order or the specific wording of a message. Let’s take a look at numerous ways in which two versions of something can objectively say the same thing, yet we respond in different ways based on the...
01:16Hypothesis Test for Test of Independence
The test of independence is a chi-square-based test used to determine whether two variables or factors are independent or dependent. This hypothesis test is used to examine the independence of the variables. One can construct two qualitative survey questions or experiments based on the variables in a contingency table. The goal is to see if the two variables are unrelated (independent) or related (dependent). The null and alternative hypotheses for this test are:
H0: The two variables (factors)...
H0: The two variables (factors)...
01:21Introduction to Test of Independence
In statistics, the term independence means that one can directly obtain the probability of any event involving both variables by multiplying their individual probabilities. Tests of independence are chi-square tests involving the use of a contingency table of observed (data) values.
The test statistic for a test of independence is similar to that of a goodness-of-fit test:
The test statistic for a test of independence is similar to that of a goodness-of-fit test:
01:14Errors In Hypothesis Tests
When performing a hypothesis test, there are four possible outcomes depending on the actual truth (or falseness) of the null hypothesis and the decision to reject or not.