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statistical-inference - Statistical Inference Chapter 12/13...

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Statistical Inference Chapter 12/13
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COMP 5340/6340 Statistical Inference 2 Statistical Inference Given a sample of observations from a population, the statistical inference consists in estimating characteristics of the population. A characteristic may be guessed to: Be a number (point estimation) Lay within an interval
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Point Estimation
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COMP 5340/6340 Statistical Inference 4 Random Sampling A sample is a subset of observations out of a population (in general, the all population is not observable) For correct inference, sampling must be random
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COMP 5340/6340 Statistical Inference 5 Point Estimate A statistic is any function of random variables constituting one or more samples, provided that the function does not depend on any unknown parameter values A point estimate of a parameter θ is a single number that can be regarded as the most plausible value of θ . A point estimate is obtained by selecting a suitable statistic and computing its value from a given sample. The selected statistic is called the point estimate of θ .
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COMP 5340/6340 Statistical Inference 6 Example We want to evaluate the packet loss rate on a given channel. 25 packets are sent. Let X = number of corrupted (lost) packets. The parameter to be estimated is p = the proportion of lost packets Propose an estimator
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COMP 5340/6340 Statistical Inference 7 Example (2) We assume that the waiting time for a bus is uniformly distributed. However, we do not know the upper limit of the probability distribution. We want to estimate this parameter of the uniform probability distribution. Propose an estimator
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COMP 5340/6340 Statistical Inference 8 Sampling Distribution Multiple samples can be drawn Each sample may yield a different estimate Therefore, the estimate is a random variable with a probability distribution. In order to “evaluate” an estimate, we want to have an idea of its: Central tendency Variability
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COMP 5340/6340 Statistical Inference 9 Unbiased Estimators A point estimator ˆ θ is said to be an unbiased estimator of θ if E(ˆ θ ) = θ for every possible value of θ . If θ is not unbiased, the difference E(ˆ θ ) – θ is called the bias. Intuitively, an unbiased estimator is one that can equally underestimate or overestimate a given parameter.
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COMP 5340/6340 Statistical Inference 10 Estimators Mean Median [Max(samples)-Min(samples)]/2 Trimmed mean Xtr(10)
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COMP 5340/6340
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