Parameter estimation is a core concept in Statistics and Machine Learning where the goal is to use observed data to infer the values of unknown parameters in a model.
쮽킍 What it means
In simple terms:
You assume a model (with some unknown parameters), collect data, and then estimate those parameters so the model best explains the data.
Example:
If you believe data follows a straight line
[
y = mx + b
]
you estimate the parameters (m) (slope) and (b) (intercept).
쮽큊 Common Methods
1. Maximum Likelihood Estimation (MLE)
Chooses parameters that maximize the probability of observing the given data.
-
Widely used in statistics and ML
-
Example: estimating mean and variance of a normal distribution
2. Method of Moments
Matches sample moments (like mean, variance) with theoretical ones.
-
Simpler than MLE
-
Sometimes less accurate
3. Least Squares Estimation
Minimizes the sum of squared errors between predicted and observed values.
\min_{\theta} \sum_{i=1}^{n} (y_i – f(x_i,\theta))^2
-
Common in regression problems
-
Foundation of linear regression
4. Bayesian Estimation
Uses prior knowledge + observed data to estimate parameters.
-
Based on Bayes’ theorem
-
Produces a distribution of possible values rather than a single estimate
쮽큈 Types of Estimates
-
Point estimate ᔒ single value (e.g., mean = 5)
-
Interval estimate ᔒ range of values (confidence interval)
ᨙ Properties of Good Estimators
-
Unbiasedness ᔒ correct on average
-
Consistency ᔒ improves with more data
-
Efficiency ᔒ low variance
-
Sufficiency ᔒ uses all relevant information
쮾텠 Real-world Applications
-
Training models in Deep Learning
-
Estimating population statistics
-
Signal processing
-
Econometrics and forecasting