point estimation
/ POYNT ess-tih-MAY-shun /
When someone asks 'how heavy is this parcel?' and you reply '2 kilograms,' you have given a single best-guess number. Point estimation is exactly that, made rigorous: using sample data to produce one number as our best guess of an unknown population quantity. It is the most basic answer statistics can give — a single value, not a range and not a yes/no decision.
The recipe that turns data into that number is called an estimator, and the actual number it spits out for one dataset is the estimate. For example, the sample mean (add up the values, divide by how many there are) is the natural estimator of the population mean; the sample variance estimates the population variance. An estimator is a rule applied to random data, so it is itself random and has a sampling distribution; the estimate is one fixed realization of it. Good estimators tend to land near the truth on average and to wobble little, which is why we judge them by bias, consistency, and efficiency.
Point estimates are the raw material of every actuarial calculation: the estimated claim frequency, the fitted mortality rate, the projected investment return all begin as point estimates. But a point estimate alone is dangerously naked — it carries no admission of how uncertain it is. An estimated mean claim of $1,820 means something very different if it could plausibly be $1,815 to $1,825 versus $1,200 to $2,400. That is precisely why a responsible actuary almost never reports a point estimate without an accompanying standard error or confidence interval.
From 200 observed deaths among 10,000 policyholders aged 60, an actuary's point estimate of the annual mortality rate at age 60 is simply 200 / 10,000 = 0.02, or 2%.
A single number — 2% — as the best guess of an unknown true rate.
A point estimate is almost never exactly the true value; treating it as exact, with no error band, is the cardinal sin of careless analysis.