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Questions and Answers
Which branch of statistics deals with estimating the values of parameters based on measured empirical data that has a random component?
Which branch of statistics deals with estimating the values of parameters based on measured empirical data that has a random component?
- Descriptive statistics
- Inferential statistics
- Estimation theory (correct)
- Hypothesis testing
What does an estimator attempt to do in estimation theory?
What does an estimator attempt to do in estimation theory?
- Determine the exact values of the parameters
- Approximate the unknown parameters using the measurements (correct)
- Analyze the relationship between the parameters
- Predict the future values of the parameters
What are the two approaches generally considered in estimation theory?
What are the two approaches generally considered in estimation theory?
- Sampling approach and modeling approach
- Probabilistic approach and deterministic approach
- Probabilistic approach and set-membership approach (correct)
- Frequentist approach and Bayesian approach
In the probabilistic approach, what does the probability distribution of the measured data depend on?
In the probabilistic approach, what does the probability distribution of the measured data depend on?
What is an example scenario where estimation theory can be applied?
What is an example scenario where estimation theory can be applied?
Which approach in estimation theory assumes that the measured data vector belongs to a set which depends on the parameter vector?
Which approach in estimation theory assumes that the measured data vector belongs to a set which depends on the parameter vector?
What does the parameter sought represent in estimation theory?
What does the parameter sought represent in estimation theory?
What does the probabilistic approach in estimation theory assume about the measured data?
What does the probabilistic approach in estimation theory assume about the measured data?
What is the main goal of an estimator in estimation theory?
What is the main goal of an estimator in estimation theory?
In estimation theory, what does the value of the parameters affect?
In estimation theory, what does the value of the parameters affect?
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Study Notes
Estimation Theory
- Branch of statistics that deals with estimating the values of parameters based on measured empirical data with a random component.
Role of Estimator
- Attempts to approximate the unknown parameter value from the data.
Approaches in Estimation Theory
- Two general approaches: Probabilistic Approach and Set-Membership Approach.
Probabilistic Approach
- Probability distribution of the measured data depends on the unknown parameter vector.
Set-Membership Approach
- Assumes the measured data vector belongs to a set which depends on the parameter vector.
Applications of Estimation Theory
- Can be applied in scenarios where a parameter needs to be estimated from noisy data, such as signal processing or image processing.
Role of Parameters
- The parameter sought represents the unknown quantity of interest.
- The value of the parameters affects the behavior of the system or process.
Goal of an Estimator
- The main goal of an estimator is to produce an estimate that is close to the true parameter value.
Probabilistic Approach Assumptions
- Assumes that the measured data is a realization of a random variable.
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