theory of estimation and qualities of a good estimator
Theory of Estimation
•Statistical estimation is the procedure of using a sample statistic to estimate a population parameter.
•A Statistic is used to estimate a parameter is called an estimator,
•The value taken by the estimator is called an estimate.
•for example, the sample mean(say 7.65) is an estimator of the population mean.
Statistical estimation is divided into two major categories:
Point Estimation
•In point estimation, a single statistic is used to provide an estimate of the population parameter;
•Change in sample will cause deviation in estimate;
Interval Estimation
•An interval estimate is a range of values within which a researcher can say with some confidence that the population parameter falls;
•This range is called confidence interval;
Qualities of a good estimator:
•A good estimator is one which is close to the true value of the parameter as possible.
•A good estimator must possess the following characteristics:
i.Unbiasedness
ii.Consistency
iii.Efficiency
iv.Sufficiency
Unbiasedness: this is a desirable property for a good estimator to have; “unbiasedness” refers to the fact that a sample mean is an unbiased estimator of a population mean because the mean of the sampling distribution of a sample means taken from the same population is equal to the population mean itself;
•Efficiency: it refers to the size of the standard error of the statistic; if two statistic are compared from a sample of the same size & try to decide which is a good estimator; the statistic that has a smaller standard error or standard deviation of the sampling distribution will be selected.
Consistency: a statistic is a consistent estimator if the sample size increases, it becomes almost certain that the value of statistic comes very close to the value of the population parameter;
•Sufficiency: an estimator is sufficient if it makes so much use of the information in the sample that no other estimator could extract from the sample additional information about the population estimator being estimated;
Hope your doubts are clear, feel free to ask questions in the comments
•Statistical estimation is the procedure of using a sample statistic to estimate a population parameter.
•A Statistic is used to estimate a parameter is called an estimator,
•The value taken by the estimator is called an estimate.
•for example, the sample mean(say 7.65) is an estimator of the population mean.
Statistical estimation is divided into two major categories:
Point Estimation
•In point estimation, a single statistic is used to provide an estimate of the population parameter;
•Change in sample will cause deviation in estimate;
Interval Estimation
•An interval estimate is a range of values within which a researcher can say with some confidence that the population parameter falls;
•This range is called confidence interval;
Qualities of a good estimator:
•A good estimator is one which is close to the true value of the parameter as possible.
•A good estimator must possess the following characteristics:
i.Unbiasedness
ii.Consistency
iii.Efficiency
iv.Sufficiency
Unbiasedness: this is a desirable property for a good estimator to have; “unbiasedness” refers to the fact that a sample mean is an unbiased estimator of a population mean because the mean of the sampling distribution of a sample means taken from the same population is equal to the population mean itself;
•Efficiency: it refers to the size of the standard error of the statistic; if two statistic are compared from a sample of the same size & try to decide which is a good estimator; the statistic that has a smaller standard error or standard deviation of the sampling distribution will be selected.
Consistency: a statistic is a consistent estimator if the sample size increases, it becomes almost certain that the value of statistic comes very close to the value of the population parameter;
•Sufficiency: an estimator is sufficient if it makes so much use of the information in the sample that no other estimator could extract from the sample additional information about the population estimator being estimated;
Hope your doubts are clear, feel free to ask questions in the comments
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