2009. 5. 14. 02:04
@GSMC/홍대형: Statistical Communication Theory
Yates and Goodman
Chapter 7 Parameter Estimation Using the Sample Mean
statistical inference
http://en.wikipedia.org/wiki/Statistical_inference
Statistical inference or statistical induction comprises the use of statistics and random sampling to make inferences concerning some unknown aspect of a population
7.1 Sample Mean: Expected Value and Variance
The sample mean converges to a constant as the number of repetitions of an experiment increases.
Althouth the result of a single experiment is unpredictable, predictable patterns emerge as we collect more and more data.
sample mean
= numerical average of the observations
: the sum of the sample values divided by the number of trials
7.2 Deviation of a Random Variable from the Expected Value
Markov Inequality
: an upper bound on thte probability that a sample value of a nonnegative random variable exceeds the expected value by any arbitrary factor
http://en.wikipedia.org/wiki/Markov_inequality
Chebyshev Inequality
: The probability of a large deviation from the mean is inversely proportional to the square of the deviation
http://en.wikipedia.org/wiki/Chebyshev_inequality
7.3 Point Estimates of Model Parameters
http://en.wikipedia.org/wiki/Estimation_theory
estimating the values of parameters based on measured/empirical data. The parameters describe an underlying physical setting in such a way that the value of the parameters affects the distribution of the measured data. An estimator attempts to approximate the unknown parameters using the measurements.
http://en.wikipedia.org/wiki/Point_estimation
the use of sample data to calculate a single value (known as a statistic) which is to serve as a "best guess" for an unknown (fixed or random) population parameter
relative frequency (of an event)
point estimates :
bias
consistency
accuracy
consistent estimator
: sequence of estimates which converges in probability to a parameter of the probability model.
mean square error
: expected squared difference between an estimate and the estimated parameter
http://en.wikipedia.org/wiki/Law_of_large_numbers
7.4 Confidence Intervals
accuracy of estimate
confidence interval
: difference between a random variable and its expected value
confidence coefficient
: probability that a sample value of the random variable will be within the confidence interval
Chapter 7 Parameter Estimation Using the Sample Mean
statistical inference
http://en.wikipedia.org/wiki/Statistical_inference
Statistical inference or statistical induction comprises the use of statistics and random sampling to make inferences concerning some unknown aspect of a population
7.1 Sample Mean: Expected Value and Variance
The sample mean converges to a constant as the number of repetitions of an experiment increases.
Althouth the result of a single experiment is unpredictable, predictable patterns emerge as we collect more and more data.
sample mean
= numerical average of the observations
: the sum of the sample values divided by the number of trials
7.2 Deviation of a Random Variable from the Expected Value
Markov Inequality
: an upper bound on thte probability that a sample value of a nonnegative random variable exceeds the expected value by any arbitrary factor
http://en.wikipedia.org/wiki/Markov_inequality
Chebyshev Inequality
: The probability of a large deviation from the mean is inversely proportional to the square of the deviation
http://en.wikipedia.org/wiki/Chebyshev_inequality
7.3 Point Estimates of Model Parameters
http://en.wikipedia.org/wiki/Estimation_theory
estimating the values of parameters based on measured/empirical data. The parameters describe an underlying physical setting in such a way that the value of the parameters affects the distribution of the measured data. An estimator attempts to approximate the unknown parameters using the measurements.
http://en.wikipedia.org/wiki/Point_estimation
the use of sample data to calculate a single value (known as a statistic) which is to serve as a "best guess" for an unknown (fixed or random) population parameter
relative frequency (of an event)
point estimates :
bias
consistency
accuracy
consistent estimator
: sequence of estimates which converges in probability to a parameter of the probability model.
The sample mean is an unbiased, consistent estimator of the expected value of a random variable.
The sample variance is a biased estimate of the variance of a random variable.
mean square error
: expected squared difference between an estimate and the estimated parameter
The standard error of the estimate of the expected value converges to zero as n grows without bound.
http://en.wikipedia.org/wiki/Law_of_large_numbers
7.4 Confidence Intervals
accuracy of estimate
confidence interval
: difference between a random variable and its expected value
confidence coefficient
: probability that a sample value of the random variable will be within the confidence interval
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