A complete estimator – weighted combination is a method of estimating the probability distribution of a parameter by combining the estimation from multiple sources. A weighted combination of two (or more) component estimators. Mainly used in sample survey work. A complete estimator is a method used to sample survey work which takes into account all the available information for a population or study area. It involves collecting data from all individuals in the sample, rather than randomly selecting a subset of those individuals. 

Uses of Complete Estimator

The goal of using this method is to accurately represent the entire population, enabling researchers to make more reliable inferences about the population as a whole. Generally speaking, complete estimators are considered to be more reliable than other survey estimation techniques because they provide an accurate representation of the population’s characteristics and trends. 

Demographic Data

Additionally, because demographic data is collected from all participants, it can be used to identify any potential sample biases that may have been introduced due to selection effects or sampling error. This enables researchers to make corrections when necessary and ensure that their analyses are based on accurate information. 

Estimation of Multiple Parameters

The idea behind this approach is to combine the estimated values from different sources and assign a weight to each source depending on its accuracy and relevance. This approach is used when the exact value of the parameter cannot be known, or is not available. The weighted combination can also be applied to estimate multiple parameters, for example in regression analysis. 

In this case, each of the associated features are assigned different weights based on their individual importance in predicting the outcome variable. The weights are then multiplied by the associated estimates and summed up to determine the overall prediction. This technique can also be used to combine estimators which may have different levels of bias or variance. 

In such cases, more accurate estimates can be obtained by assigning higher weights to those estimators with lower biases or variances. Furthermore, when dealing with high-dimensional data, it might not always be practical to obtain an exact solution due to limited sample sizes or computational complexity. Weighted combinations offer an efficient way of getting approximate solutions with reasonable accuracy. 

By using a weighted combination of estimators, we can combine their respective estimation errors and obtain more accurate estimates than either one alone could provide. Additionally, it allows us to effectively use data from multiple sources and take advantage of any potential correlations between them which would otherwise be difficult or impossible to capture without such methods. 

Estimators are Statistical Models

Estimators are statistical models that use data to make predictions or estimate parameters of a population. They are commonly used in fields such as economics, medicine, and social sciences. There are several advantages and disadvantages of using estimators.

Advantages

1. Estimators are cost-effective – they often require less resources than conducting a full-scale study or experiment.
2. They can be used to make predictions on a population that might be too large to study systematically.
3. They can be used in situations where a full-scale study is not possible, such as when the population being studied is rare or hard to reach.
4. Estimators can provide a way to estimate population parameters that are not directly observable, such as average income or IQ scores.
5. Estimators can be used to test theories and hypotheses, and to identify areas for further research.

Disadvantages

1. Estimators are based on assumptions, and these assumptions may not be valid for all populations or situations.
2. Estimators may produce biased or inaccurate results if the data used to develop them is not representative of the population being studied.
3. Estimators may be affected by outliers, or extreme values in the data that can skew the results.
4. Estimators may not take into account other factors that may be affecting the outcome being studied, which can lead to inaccurate or incomplete results.

Summary

Estimators may require complex statistical models or methods, which can be difficult to interpret and communicate to others. In summary, estimators are a useful tool for making predictions and estimating population parameters, but they also have limitations that should be carefully considered before use. It is important to understand the assumptions, biases, and potential sources of error associated with estimators, and to use them in conjunction with other research methods to ensure accurate and comprehensive results.