teori statistika ii (s2) · 2/2/2017 · pendugaan parameter 1 teori statistika ii (s1-stk) dr....
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Pendugaan Parameter
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Teori Statistika II (S1-STK)
Dr. Kusman Sadik, M.Si
Departemen Statistika IPB, 2017
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.
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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.
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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.
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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.
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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? .
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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.
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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.
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Misalkan 𝜃 adalah penduga bagi 𝜃 berdasarkan contoh acak X1, X2, ..., Xn.
Ragam penduga : 𝑉(𝜃 )
Galat baku : 𝑉(𝜃 )
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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
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