Accuracy of point and Interval estimator

statistics

#1

I am currently studying about the Statistical Interference in which I have found that there are two types of estimation.

Point Estimation - A point estimate of a population parameter is a single value of a statistic.

Interval Estimation -An interval estimate is defined by two numbers, between which a population parameter is said to lie.

I want to know the accuracy of this two estimation with respect to each other.


#2

Hi @sid100158,

Let us take an example and check the accuracy for both the cases

data1 <- data.frame(x=seq(from=1,to=100),y=c(seq(from=1,to=30),seq(from=60,to=90),seq(from=1,to=39)))

The data looks like this

Point Estimation
We will use a simple linear model and get the results

The blue line is the predicted value from the model

Interval Estimation

train$lwr <- as.data.frame(predict(model,train,interval="predict",level=0.8))$lwr
train$upr <- as.data.frame(predict(model,train,interval="predict",level=0.8))$upr
ggplot(data=train,aes(x=x,y=y)) + geom_point(color='RED') + geom_point(aes(x=x,y=lwr),color='BLUE') + geom_point(aes(x=x,y=upr),color='BLUE')

We get the following results

The two blue lines determine the lower and upper ranges of the predicted values

If we change the confidence interval from 80% to 95%, there will be a change in the levels

So we can see that an Interval Estimate gives us a probabilistic range between which the values can lie. It is always better if you are visually seeing it
If you are feeding the predicted values programmatically into the system you can use the Point Estimator

Hope this has helped a bit

Regards,
Anant