Teori Statistika II (STK304)

Dr. Kusman Sadik, M.Si

Departemen Statistika IPB, 2019/2020

Pendugaan Parameter

IPB University─ Bogor Indonesia ─ Inspiring Innovation with Integrity

The aim of statistical inference is to make certain

determinations with regard to the unknown constants

(parameters) figuring in the underlying distribution.

This is to be done on the basis of data, represented by the

observed values of a random sample drawn from said

distribution.

Actually, this is the so-called parametric statistical inference

as opposed to the nonparametric statistical inference.

Parametric statistical inference : (1) Point estimation, (2)

Interval estimation, and (3) Testing hypotheses.

2

The purpose of statistics is to use the information

contained in a sample to make inferences about

the population from which the sample is taken.

Because populations are characterized by

numerical descriptive measures called

parameters, the objective of many statistical

investigations is to estimate the value of one or

more relevant parameters.

3

For example, a manufacturer of washing

machines might be interested in estimating the

proportion p of washers that can be expected to

fail prior to the expiration of a one-year guarantee

time.

Other important population parameters are the

population mean, variance, and standard

deviation.

4

For example, we might wish to estimate the mean

waiting time µ at a supermarket check-out station

or the standard deviation of the error of

measurement σ of an electronic instrument.

To simplify our terminology, we will call the

parameter of interest in the experiment the target

parameter.

5

6

7

Many different estimators (rules for estimating) may be obtained for the same population parameter. This should not be surprising.

Each estimator represents a unique human subjective rule for obtaining a single estimate.

This brings us to a most important point: Some estimators are considered good, and others, bad.

How can we establish criteria of goodness to compare statistical estimators? .

8

9

Suppose that we wish to specify a point estimate for a population parameter that we will call θ . The estimator of θ will be indicated by the symbol , read as “ θ hat.”

We would like the mean or expected value of the distribution of estimates to equal the parameter estimated; that is, E( ) = θ .

Point estimators that satisfy this property are said to be unbiased.

̂

̂

10

11

12

We want the variance of the distribution of

the estimator V( ) to be as small as

possible.

Given two unbiased estimators of a

parameter θ, and all other things being

equal, we would select the estimator with the

smaller variance.

̂

13

14

Misalkan 𝜃 adalah penduga bagi 𝜃 berdasarkan contoh acak X1, X2, ..., Xn.

Ragam penduga : 𝑉(𝜃 )

Galat baku : 𝑉(𝜃 )

15

16

17

18

19

20

21

22

23

24

25

1. Roussas, G. 2015. An Introduction to Probability and Statistical

Inference 2nd Edition. Elsevier Inc.

2. Hogg RV , McKean JW, Craig AT. 2013. Introduction to

Mathematical Statistics 7th Edition. Pearson Prentice Hall.

3. Wackerly D, Mendenhall W, Scheaffer RL. 2008. Mathematical

Statistics with Applications 7th Edition, Duxbury Thomson

Learning.

4. Catatan Kuliah

26

Bisa di-download di

kusmansadik.wordpress.com

27

28