!!!!...... Hello Today I leave about of "statistical estimation", I hope will be helpful.
In statistical inference estimate is called the set of techniques to give an approximate value of a parameter of a population from data provided by a sample. For example, an estimate of the mean of a given feature of a population of size N would be the average of the same characteristic for a sample size
n.1
The estimate is divided into three sections, each of which has different methods used depending on the characteristics and purposes of the study:
-point estimate: 2
* Method of moments;
* maximum likelihood method;
* Method of least squares;
-Estimation intervals.
-Bayesian estimation.
Now, here I'll post an explanation of each method ...
> Point estimation
consists in estimating the value of the parameter using a single value obtained from a given formula. For example, in order to estimate the average size of a particular group of individuals, a sample can be taken as the point estimate and provide the average size of individuals. Most important of an estimator, is to be an efficient estimator. Ie is unbiased (unbiased) and stable in the sample (minimum variance).
> Interval Estimation
consists in obtaining an interval within which the parameter will be estimated with some probability. In the interval estimation uses the following concepts:
confidence interval
The confidence interval is an expression of the type [θ1, θ2] or θ1 ≤ θ ≤ θ2, where θ is the parameter to be estimated. This interval contains the parameter estimate with certainty or a certain confidence level. But sometimes you can change this interval when the sample does not guarantee or an equivalent axiom circustancial.
parameter variability
If not known, an approximation can be obtained on the data provided by scientific literature or in a pilot study. There are also methods to calculate the sample size which ignore this aspect. Usually used as a measure of this variability and population standard deviation is denoted σ.
Estimation error
is a measure of accuracy that corresponds to the amplitude of the confidence interval. The more accuracy is desired in the estimation of a parameter, the narrower will be the confidence interval and, if you maintain or reduce the error, more occurrences should be included in the study sample. Failure to include new observations to the sample, the error is made to increase accuracy. E is often called, according to the formula E = θ2 - θ1.
Confidence Limit
The probability
that the true value of the parameter estimate in the population will be within the confidence interval obtained. The confidence level is denoted by (1-α), but usually is usually expressed with a percentage ((1-α) * 100%). Taken as usual confidence level of 95% or 99%, corresponding to α values \u200b\u200bof 0.05 and 0.01 respectively.
α value
also called level of significance. Is the probability (in per unit) to fail in our estimation, that is, the difference between certainty (1) and the confidence level (1-α). For example, in an estimate with a confidence level of 95%, the α value is (100-95) / 100 = 0.05.
critical value
Represented by Zα / 2. The value of the abscissa in a distribution that leaves his right an area equal to α / 2 with 1-α confidence level. Normally the critical values \u200b\u200bare tabulated or can be calculated on the basis of population distribution. For example, for a normal distribution with mean 0 and standard deviation 1, the critical value for α = 0.05 was calculated as follows: searches the distribution table that value (Or best guess), under the column "Area", observing that corresponds to -1.64. Then Zα / 2 = 1.64. If the mean or standard deviation of normal distribution does not correspond to the table, you can make the change of variable t = (X-μ) / σ is calculated.
With these definitions, if after the removal of a sample is said that "3 is a mean estimate with a margin of error of 0.6 and a confidence level of 99%," we interpret that the true value the average is between 2.7 and 3.3, with a probability of 99%. The values \u200b\u200b2.7 and 3.3 are obtained by subtracting and adding, respectively, half the error, for the range confidence according to the definitions given.
For a fixed sample size, the concepts of error and confidence level are related. If we admit a major mistake, that is, increase the size of the confidence interval, we also have a higher probability of success in our estimation, that is, a higher level of confidence.
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