Assume that you want to estimate an unknown parameter by using a noisyreceived signal for which you know the mean value and the covariance matrixof the noise but not its probability density function (pdf). You also know thatthe relationship between the unknown parameter and the received signal islinear. Would you use the BLUE estimation method, or the MaximumLikelihood estimation method? Justify your answer.

Firstly the full meaning of BLUE is "Best Linear Unbiased Estimator"

Answered: Assume that you want to estimate an…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Consider the following regression model: Yi = B1 + B2X2i + ß3X3i + ß4X4i + ui Using the model above show that the maximum likelihood estimator for the variance, var (ui||X2i, X3i, B4X4i), is biased (be sure to comment of the nature of the bias).
Define what an endogenous variable is, describe three scenarios that may cause a problem of endogeneity, and what are minimal assumptions needed for a good instrument. Tobit models are used to model censored and corner solution data. Explain what the difference between these two types of data is, and how does it affect the interpretation of Tobit models? What is the difference between a logit and a probit model, and why would are they preferred over a linear probability model (LPM) Explain what it means for a variable to possess a unit root. What are the implications for regression analysis if one uses variables with Unit roots? Explain what serial correlation is, how do you test for it, and why it invalidates the standard calculation of standard errors in time series data. Describe what does it mean to have a spurious regression, why could it happen, and what are the consequences in terms of t-statistics and goodness of fit measures?
Consider a binary response variable y and a predictor variable x. The following table contains the parameter estimates of the linear probability model (LPM) and the logistic regression model, with the associated p-values shown in parentheses. Variable Intercept x LPM Logistic -6.90 (0.06) 0.19 (0.06) a. Test for the significance of the intercept and the slope coefficients at the 5% level in both models. Coefficients Intercept Slope -0.67 (0.02) 0.07 (0.03) LPM Logistic b. What is the predicted probability implied by the linear probability model for x=20 and x= 35? Note: Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places. Report the probability between 0 and 1 (not in %).
The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.7 auto accidents per day with a variance of 0.0025 . The actuaries of the company claim that the variance of the number of accidents per day is no longer equal to 0.0025. Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis H0 and the alternative hypothesis H1 that we would use for this test. H0 : ? H1 : ?
A large university is planning to build a new parking garage on campus that will be paid for by a larger student parking fee. The student newspaper wanted to determine what proportion of the students favor the new garage. They email a random sample of 100 students and find that 30 of them are in favor of the new garage. What is the parameter of interest in this study?
A snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.34. A dietician is asked to test this claim and finds that a random sample of 16 servings has a variance of 1.22. At α=0.05, is there enough evidence to reject the manufacturer's claim? Assume the population is normally distributed. Complete parts (a) through (e) below.
The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.7 auto accidents per day with a variance of 0.0025. The actuaries of the company claim that the variance of the number of accidents per day is no longer equal to 0.0025. Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis H and the alternative hypothesis H, that we would use for this test. H0:__H 1:__
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In this problem, we consider target detection in a radar system. Upon observing a realization a of the random variable X which represents the return signal in noise, a decision has to be made as to whether the target is present or absent. The target amplitude is known and equal to A > 0. The observation is made in zero-mean Gaussian noise W whose variance is known and equal to 2. If the target is present (hypothesis H1), X = A+W. If the target is absent (hypothesis Ho), X = W . The likelihood ratio test for this problem is stated as follows: If fi (x)/fo(x) > n= decide in favor of H1; otherwise, decide in favor of Ho.lf n = 1, determine the probability of correct detection (target declared present when indeed present) and the probability of false alarm (target declared present when in fact absent). Express these probabilities in terms of the ratio a = A/o. If a = 4, which of the following represents the correct probabilities of false alarm and correct detection, respectively? O None of…
You are interested in the effect of school spending (measured in dollars per student) on test scores (in points) for elementary school students. In a large random sample of data, you find for every additional $100 spent per student test scores increase by 10 points, on average holding other factors constant. Furthermore, the covariance between spending and test scores is 250.00 and the variance of test scores is 49.00. What is the R2 from the OLS regression of test scores on spending? I was not given a regression equation or any other data.
Select all statements that are true of the least-squares regression line. ) It assumes a linear relationship between the explanatory and the response variable. R-squared is the portion of sample variance in the explanatory variable that can be explained by variation in the response variable. ) It can be used to predict the mean response of the explanatory variable. | R-squared is the portion of sample variance in the y variable that can be explained by variation in the x variable.

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