Which of the following statements is true? Group of answer choices A.an unbiased estimator is consistent...
Which of the following statements is true?
Group of answer choices
A.an unbiased estimator is consistent if its variance goes to zero as the sample size gets large.
B.a biased estimator is consistent if its bias goes to zero as the sample size gets large.
C. a consistent estimator is biased in small samples.
D.all unbiased estimators are consistent.
E. all consistent estimators are unbiased.
Homework Answers
Suppose we have an unbiased estimator T for the parameter
. Since, it is unbiased, we should have 
.
Now, if the variance of T tends to 0, if the sample size gets large
and goes to infinity, then we can say that T is both consistent and
unbiased.
Hence, correct answer -> an unbiased estimator is consistent if
its variance goes to zero as the sample size gets large.
Add Answer to:
Which of the following statements is true?
Group of answer choices
A.an unbiased estimator is consistent...
Please give detailed steps. Thank you. 5. Let {X1, X2,..., Xn) denote a random sample of...
Please give detailed steps. Thank you.
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Please give detailed steps. Thank you.
5. Let {X1, X2,..., Xn) denote a random sample of size N from a population d escribed by a random variable X. Let's denote the population mean of X by E(X) - u and its variance by Consider the following four estimators of the population mean μ : 3 (this is an example of an average using only part of the sample the last 3 observations) (this is an example of a weighted average)...
3. Suppose we observe 5 values from an unknown distribution: (1,7,5, 16,4). (a) Find the sample mean (which is often used as an estimator of the population mean) (b) Find the sample variance (which is often used as an estimator of the population variance). (c) In general, the estimators above are both unbiased and consistent for the population mean and variance, respectively Bias and consistency are both measures of the central tendency of an estimators. One is more relevant in...
Which of the following statements is true? (a) If the calculated value of F statistic is higher than the critical value, we reject the alternative hypothesis in favor of the null hypothesis. (b) The F statistic is always nonnegative as SSR, is never smaller than SSRur. (C) Degrees of freedom of a restricted model is always less than the de- grees of freedom of an unre- stricted model. (d) The F statistic is more flexible than the t statistic to...
(1) True or False: Please specify your reasons. (i) An estimator is unbiased, if its expected value across different samples equals to the true value of the parameter. (ii) OLS estimator is always unbiased. (iii) We can use n- i-, û to estimate the error variance o2 because it is unbiased. (iv) If the sample size increases, we can have a better estimates of sd(Bo) and sd(B1).
1. If OLS estimators satisfy asymptotic normality, it implies that a. they are approximately normally distributed b. they are approximately normally distributed in samples with less than 10 observations large enough sample sizes c. they have a constant mean equal to zero and variance equal to d. they have a constant mean equal to one and variance equal to o 2 In a multiple regression model, the OLS estimator is consistent if a. there is no correlation between the dependent...
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Which of the statements about large-sample estimation is correct? (1) An estimator should be unbiased and the spread (as measured by the mean) should be as small as possible. (2) The distance between an estimate and the true value of the statistic is called the error of estimation. (3) The 95% Margin of error is: 1.96 Standard error of the estimator. (4) A good confidence interval is as wide as possible.
Which of the statements about large-sample estimation is correct? (1) An estimator should be unbiased and the spread (as measured by the mean) should be as small as possible. (2) The distance between an estimate and the true value of the statistic is called the error of estimation. (3) The 95% Margin of error is: 1.96 x Standard error of the estimator. (4) A good confidence interval is as wide as possible.
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