What is meant by a consistent estimator?


Question from: Ms Damiana De Santis | Last updated: September 20, 2021

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In statistics, consistency is a desirability property of estimators. Basically, an estimator is consistent if, as the information increases, ie the sample size, its probability distribution is concentrated in correspondence with the value of the parameter to be estimated.

What is the estimator of μ?

In the case of the parameter μ, for example, it turns out that the sample mean is a more efficient estimator than the sample median or the sample mode, whatever the value of μ.

When is an estimator Blue?

An estimator (v.) That has minimal variance (v.) In the class of linear and undistorted estimators; a BLUE estimator is, therefore, more efficient in relation to this class (see Efficiency).

How is the bias of an estimator calculated?

The estimator T = t (X1, X2, …, Xn) of θ is said to be undistorted if • It is called the distortion (or bias) of an estimator T of θ: The distortion can be positive (on average T overestimates θ) or negative (on average T underestimates θ). and the inequality holds in the strict sense for at least a value of θ.

When is an estimator linear?

An estimator (see) which is a linear function of the sample observations (for example, the sample mean).

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When is an estimator great?

In general, there is no criterion for determining which estimator for a given quantity is the best. … The goodness of an estimator is in fact evaluated on the basis of properties such as correctness, asymptotic correctness, consistency and efficiency that are linked to this average deviation.

When is an estimator used?

Whenever a sample statistic is used to estimate a parameter, it is called an estimator. Its realization in the observed sample constitutes the precise estimate of the parameter.

What is meant by data bias or distortion?

Distortion or bias is an intentional or unintentional change in the design and / or conduct of a clinical study and in the analysis and evaluation of data, which may affect the results. The bias can affect the results of a clinical study and make them unreliable.

How is the sampling error calculated?

To correctly calculate the sampling error it is necessary that individuals are chosen with total randomness. In this way it is possible to predict and calculate in advance the difference between the sample and the population.

What does bias mean in statistics?

Biases are systematic errors; they may occur in the design or execution of a study, determine an incorrect estimate of the association between exposure and disease risk. They are distinguished from random errors (random errors or random misclassification), as exemplified below.

How do you calculate the expected value of a game?

For example, the toss of a coin can lead to two different outcomes: heads or tails. In this case, each of the two outcomes has a probability of occurring equal to 50%. I assume the V value[testa]= 100 (win) and V.[croce]= 0 (loss), the expected value of the game is 50 (100 X 0.5 + 0 X 0.5).

When is the sample variance used?

Both variance and sample variance are indicators of statistical dispersion. However, the variance is used on the entire statistical population, while the sample variance is used only on a sample of the population.

When is one statistic enough?

Sufficient statistics

Intuitively, a statistic U = h (X) is sufficient for a if U contains all the information relating to a available in the entire data vector X. Formally, U is sufficient for a if the conditional distribution of X given U does not depend on a.

What does the point estimate refer to?

PUNCTUAL PARAMETER ESTIMATION means the set of inferential methods that allow to attribute a value to a population parameter, using the data of an observed random sample (x1, x2,…, xn) and processing them.

How is point estimate calculated?

after collecting the data, the values ​​of X in the sample are known quantities: the observed modalities x1, …, xn (unitary distribution). x1 = 50000.92 x2 = 49998.70 x3 = 49998.89 x4 = 50000.47, the sample mean Cx = 49999.74 will be our point estimate (by analogy) of the true length µ.

When is the sample proportion estimator correct or not biased?

Correctness of an estimator

An estimator is correct or undistorted of the unknown parameter if it averages, as the samples vary, the value of the unknown parameter. Therefore, if the expected value of the estimator vc is equal to the unknown parameter, the estimator is correct.

What is meant by sampling error?

The random variation means that a measurement carried out on a sample does not provide a value identical to that obtained by measuring the entire population: there is always – a certain error, which is called sampling error.

What does sampling mean?

[procedimento usato per formare il campione] ≈ sampling. ‖ Choice, selection.

What should be the probability of extraction in a simple random sampling?

The probability (a priori) that a unit is chosen in each extraction is equal to 1 / N, so the overall probability that this unit is part of the sample is equal to n / N (equal to the sampling fraction).

When is an estimator not biased?

A biased estimator is an estimator that for some reason has an expected value other than the quantity it estimates; an undistorted estimator is called a correct estimator. While the term bias may have a negative connotation, this is not necessarily true in the context of statistics.

What are the three levels of Bias?


  • 3.1 The anchor bias.
  • 3.2 Apophenia.
  • 3.3 The confirmation bias.
  • 3.4 The hindsight bias or hindsight bias.
  • 3.5 Outcome bias or result bias.
  • 3.6 Seductive detail bias.
  • 3.7 Memory bias.

How is bias measured?

Bias is the quiescent current of the tube and is a vital parameter for both the sound of the amplifier and the life of the power tubes. There are various methods of measuring bias, but the simplest is to place a resistor in series at the cathode and measure the voltage drop across it.

What does parameter estimation mean?

statistical estimation, assignment on the basis of sample data of one or more numerical values ​​to an unknown parameter, usually indicated with θ, which characterizes a population (for example, the average height of the Italian population in a given period).

Who are the admirers?

aestimator -oris]. – 1. Who or who esteems, that is, judges, evaluates: the Church, most just esteem of virtues (Segneri); spec. who makes an estimate of the value of an object, even as a sales assistant.

What is the sample proportion?

Sample proportion

It is a vc defined as the average of the vc (Bernoulli) that make up the sample and allows us to infer the unknown probability of success of the population.


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