parameter-estimation Parameter Estimation ¶ Fundamentals ¶ Problem Statement Suppose that the population distribution follows a parameteric model $f(x|\theta)$ and given a random sample $X_1,X_2, ..., X_n$ from the population $X_i\tilde{} f(x|\theta)$, estimate the parameter of interest $\theta$ Basic assumption in parametric estimation is that the population distribution follows some parameteric model . Here, parametric models are those of the form: $$\mathcal{F}=f(x,\theta), \theta\in\Theta$$ where $\Theta\subset R^k$ is the parameter space, and $\theta$ is the parameter. Example Normal distribution has two parameters $\mu$ and $\sigma$ Terminologies Estimator $\hat{\theta}$ is a rule to calculate an estimate of a given quantity (model parameter) based on observed data. Estimate is a fixed value of that estimator for a particular observed sample. Statistic