Search for tag: "estimator"

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Estimation of Model Parameters duration 26 minutes 43 seconds Estimation of Model Parameters Estimation of Model Parameters	Estimation of Model Parameters Methods for estimating the coefficients in the simple linear regression model are investigated. The least squares method is a purely mathematical approach, requiring no statistical assumptions other… least squares residuals geometric approach best linear unbiased estimator linear estimator assumptions From Jane Harvill 85 plays 0
Asymptotic Evaluations for Interval Estimation duration 4 minutes 14 seconds Asymptotic Evaluations for Interval Estimation Asymptotic Evaluations for Interval Estimation	Asymptotic Evaluations for Interval Estimation In this lesson, some approximate and asymptotic versions of confidence sets are explored. The purpose here is to illustrate some methods that will be of use in more complicated situations, methods… maximum likelihood estimator wald-type interval information number delta method score interval wilks interval From Jane Harvill 129 plays 0
Asymptotic Evaluations of Point Estimators duration 41 minutes 59 seconds Asymptotic Evaluations of Point Estimators Asymptotic Evaluations of Point Estimators	Asymptotic Evaluations of Point Estimators There are several properties to be considered when considering a point estimator from an asymptotic perspective. In this lesson, the concepts of consistency and efficiency are investigated. As… consistent efficient asymptotic relative efficiency maximum likelihood estimator regularity conditions limiting variances asymptotic variance information number cramer-rao lower bound From Jane Harvill 291 plays 0
Example: Find Confidence Interval by Inverting… duration 16 minutes 16 seconds Example: Find Confidence Interval by Inverting… Example: Find Confidence Interval by Inverting CDF of an Estimator	Example: Find Confidence Interval by Inverting CDF of an Estimator A confidence interval estimator for the shift parameter is found by inverting the CDF of a sufficient statistic for the parameter. confidence interval estimator cumulative distribution function factorization theorem order statistics From Jane Harvill 487 plays 0
Example: Using a Pivot to Find a Confidence… duration 8 minutes 33 seconds Example: Using a Pivot to Find a Confidence… Example: Using a Pivot to Find a Confidence Interval for Normal Variance	Example: Using a Pivot to Find a Confidence Interval for Normal Variance A confidence interval estimator for the variance of a normal distribution is found using a pivotal quantity. pivotal quantity confidence interval estimator sampling distributions From Jane Harvill 1,926 plays 0
Example: Illustrating Finding a Confidence Bound… duration 7 minutes 54 seconds Example: Illustrating Finding a Confidence Bound… Example: Illustrating Finding a Confidence Bound for Normal Mean	Example: Illustrating Finding a Confidence Bound for Normal Mean In this example, finding an upper confidence bound for the mean of a normal population is illustrated. The method used is the inversion of the acceptance region of the UMP test from the Karlin Rubin… karlin rubin theorem acceptance region confidence interval estimator From Jane Harvill 89 plays 0
Likelihood Ratio Tests duration 18 minutes 19 seconds Likelihood Ratio Tests Likelihood Ratio Tests	Likelihood Ratio Tests The likelihood ratio method of hypothesis testing is related to maximum likelihood estimators. Likelihood ratio tests are as widely used as maximum likelihood estimation. In this lesson, we provide… likelihood ratio test maximum likelihood estimator restricted maximization likelihood ratio test statistic sufficient statistic From Jane Harvill 483 plays 0
Find the Bayes estimator of the rate of a Poisson… duration 11 minutes 12 seconds Find the Bayes estimator of the rate of a Poisson… Find the Bayes estimator of the rate of a Poisson distribution	Find the Bayes estimator of the rate of a Poisson distribution This example illustrates how to find the Bayes estimator, under squared error loss function, of the rate of a Poisson distribution if the prior distribution on the rate is a gamma distribution. bayes estimator parameter space support prior distribution posterior distribution marginal distribution posterior mean gamma distribution From Jane Harvill 241 plays 0
Find the MLE of the rate of a Poisson distribution duration 6 minutes 25 seconds Find the MLE of the rate of a Poisson distribution Find the MLE of the rate of a Poisson distribution	Find the MLE of the rate of a Poisson distribution Example to illustrate finding the maximum likelihood estimator of the rate of a Poisson distribution. maximum likelihood estimator poisson distribution extremum maximum From Jane Harvill 318 plays 0
Finding the maximum likelihood estimator of the… duration 6 minutes 16 seconds Finding the maximum likelihood estimator of the… Finding the maximum likelihood estimator of the upper bound of a uniform(0, B) distribution	Finding the maximum likelihood estimator of the upper bound of a uniform(0, B) distribution This example illustrates how to find the maximum likelihood estimator (MLE) of the upper bound of a uniform(0, B) distribution. In this example, calculus cannot be used to find the MLE since the… maximum likelihood estimator uniform distribution From Jane Harvill 971 plays 0
Point Estimation: A Review duration 40 minutes 49 seconds Point Estimation: A Review Point Estimation: A Review	Point Estimation: A Review This lesson reviews point estimation from a frequentist perspective. Method of moments and maximum likelihood methods are reviewed. Following that is a discussion of decision theory, optimal… frequentist perspective method of moments maximum likelihood information number decision theory loss function risk function best estimator best unbiased estimator cramer-rao lower bound rao-blackwell theorem complete sufficient exponential family From Jane Harvill 112 plays 0
Sufficiency and Unbiased duration 11 minutes 36 seconds Sufficiency and Unbiased Sufficiency and Unbiased	Sufficiency and Unbiased In the previous lesson on best unbiased estimators and the Cramer-Rao Lower Bound, the concept of sufficiency was not used. We will now consider how sufficiency is a powerful tool in our search for… sufficient statistic complete family rao-blackwell theorem best unbiased estimator lehmann-scheffe theorem unique best unbiased estimator From Jane Harvill 293 plays 0
Best Unbiased Estimator duration 19 minutes 22 seconds Best Unbiased Estimator Best Unbiased Estimator	Best Unbiased Estimator As we saw in the previous lesson, a comparison of estimators based on the mean squared error (MSE) may not yield a clear favorite. It turns out there is no "one best MSE" estimator. The… best unbiased estimator cramer-rao lower bound From Jane Harvill 497 plays 0
Bayes Estimators duration 15 minutes 24 seconds Bayes Estimators Bayes Estimators	Bayes Estimators The Bayesian approach to statistics is fundamentally different from the classical approach that we have been discussing. However, some aspects of the Bayesian approach can be quite helpful to other… bayes estimator prior distribution posterior distribution marginal distribution conjugate family From Jane Harvill 258 plays 0
Maximum Likelihood Estimators duration 20 minutes 42 seconds Maximum Likelihood Estimators Maximum Likelihood Estimators	Maximum Likelihood Estimators The method of maximum likelihood is, by far, the most popular technique for deriving estimators. It is based on finding a function of the data at which the likelihood achieves a global maximum. In… maximum likelihood estimator derivatives invariance property From Jane Harvill 271 plays 0
Introduction to Point Estimation duration 4 minutes 58 seconds Introduction to Point Estimation Introduction to Point Estimation	Introduction to Point Estimation An overview of the next two weeks' lessons is provided. Following that, a brief overview of point estimation is discussed point estimator methods of finding estimators methods of evaulating estimators estimator estimate From Jane Harvill 132 plays 0
Convergence Concepts duration 51 minutes 22 seconds Convergence Concepts Convergence Concepts	Convergence Concepts In this lesson, the effect of allowing the sample size n to increase to infinity is considered. Although this idea is not practical, it does provide useful approximations for the finite-sample case.… convergence in probability weak law of large numbers convergence almost surely strong law of large numbers consistent estimator convergence in distribution central limit theorem slutsky's theorem chebychev's inequality From Jane Harvill 321 plays 0
Sums of Random Variables from a Random Sample duration 36 minutes 55 seconds Sums of Random Variables from a Random Sample Sums of Random Variables from a Random Sample	Sums of Random Variables from a Random Sample When a random sample is drawn, some summary of the values is usually computed. Any well-defined summary may be expressed mathematically as a function of an n-dimension vector. The domain of that… random sample iid statistic sampling distribution unbiased estimator location-scale family exponential family sample mean sample variance sample standard deviation From Jane Harvill 184 plays 0