1. (BH 10.25) An important concept in frequentist statistics is that of a confidence interval (CI)....
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
1. (BH 10.25) An important concept in frequentist statistics is that of a confidence interval (CI). Suppose we observe data X from a distribution with parameter 0. Unlike in Bayesian statistics, is treated as a fixed but unknown constant; it is not given a prior distribution. A 95% confidence interval consists of a lower bound L(X) and upper bound U(X) such that P(L(X) < 0 < U(X)) = 0.95 for all possible values of 0. In the above statement, L(X) and U(X) are random variables, as they are functions of the r.v. X, whereas is a constant. The definition says that the random interval (L(X), U(X)) has a 95% chance of containing the true value of 0. Imagine an army of frequentists all over the world, independently generating 95% CIs. The jth frequentist observes data X, and makes a confidence interval for the parameter 0₁. Show that if there are n of these frequentists, then the fraction of their intervals which contain the corresponding parameter approaches 0.95 as n→∞0. Hint: Consider the indicator r.v. I; = I(L(X;) < 0; < U(X;)). j j 1. (BH 10.25) An important concept in frequentist statistics is that of a confidence interval (CI). Suppose we observe data X from a distribution with parameter 0. Unlike in Bayesian statistics, is treated as a fixed but unknown constant; it is not given a prior distribution. A 95% confidence interval consists of a lower bound L(X) and upper bound U(X) such that P(L(X) < 0 < U(X)) = 0.95 for all possible values of 0. In the above statement, L(X) and U(X) are random variables, as they are functions of the r.v. X, whereas is a constant. The definition says that the random interval (L(X), U(X)) has a 95% chance of containing the true value of 0. Imagine an army of frequentists all over the world, independently generating 95% CIs. The jth frequentist observes data X, and makes a confidence interval for the parameter 0₁. Show that if there are n of these frequentists, then the fraction of their intervals which contain the corresponding parameter approaches 0.95 as n→∞0. Hint: Consider the indicator r.v. I; = I(L(X;) < 0; < U(X;)). j j
Expert Answer:
Answer rating: 100% (QA)
ANS WER Let I j denote the indicator random variable for the j th confidence interval cont... View the full answer
Related Book For
Posted Date:
Students also viewed these accounting questions
-
Suppose the system below is consistent for all possible values of f and g. What can you say about the coefficients c and d? Justify your answer. 2x1 + 4x2 = ( cx1 + dx2 = g
-
In problem, determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find: (a) The domain and range (b) The intercepts, if any (c) Any symmetry...
-
In problem, determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find: (a) The domain and range (b) The intercepts, if any (c) Any symmetry...
-
1. Johnathan's utility for money is given by the exponential function: U(X)-4-4*100). a. Based on his utility function, what is his risk-odds for the S+/-1 deal, r($1)? b. Is Johnathan a deltaperson?...
-
For every 100 births in the United States, the number of boys follows, approximately, a normal curve with a mean of 51 boys and standard deviation of 5 boys. If the next 100 births in your local...
-
Because of their connection with secant lines, tangents, and instantaneous rates, limits of the form occur frequently in calculus. Evaluate this limit for the given value of x and function . (x) = 3x...
-
Find the general solution of each differential equation. When an initial condition is given, find the particular solution satisfying that condition. a. \(y^{\prime \prime}-3 y^{\prime}+2 y=20 e^{-2...
-
Suppose the Xs in the following table indicate locations where fire sprinkler heads need to be installed in an existing building. The S indicates the location of the water source to supply these...
-
Imagine that you are the CFO of U.S. Motorsport Entertainment Corporation and that you are trying to close the books on 2006, the first year of operation. Your financial auditors are asking you to...
-
For the past several years, Jolene Upton has operated a part-time consulting business from her home. As of July 1, 2019, Jolene decided to move to rented quarters and to operate the business, which...
-
canyou help me with questions B & C Exercise 4 (Value based controlling/ shareholder value concept) (15 points) In shareholder value approach rwacc is calculated by the following formula: \[ r_{\text...
-
Demonstrate the proposed IT solution's value to the organization about log 360 software. 1. Makes the organization less vulnerable to attacks. 2. Secure IT environment ensure smooth business...
-
(7) Let f(x) = esin(x2). Write down, but do not evaluate, an integral expression for the arclength of f(x) from x = = 4 to x = 7.
-
Riggs Company purchases sails and produces sailboats. It currently produces 1,200 sailboats per year, operating at normal capacity, which is about 80% of full capacity. Riggs purchases sails at $250...
-
What factors should be considered when determining the LRE? Support with research, legislation, and/or case law.
-
An annuity-immediate is paid monthly at a rate of $200,000 per annum for 12 years. The rate of interest is 6% per annum compounded semiannually in the first 4 years and 4% per annum convertible...
-
What is the term for the evenness with which the water is applied to the soil? Group of answer choices Application uniformity Anion efficiency Application efficiency Cation exchange capacity
-
What is a make-or-buy decision?
-
List the intercepts and test for symmetry: x 2 + y = 9.
-
Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. If the sequence is...
-
In problem, f() = sin and g() = cos . Find the exact value of each function below if = 60. Do not use a calculator. f()
-
You want to lease a set of golf clubs from Pings Ltd. for \($4,000.\) The lease contract is in the form of 24 months of equal payments at a 12% annual percentage rate (APR). Suppose payments are due...
-
Ernie Els wants to save money to meet two objectives. First, he would like to be able to retire 30 years from now with a retirement income of \($300,000\) per year for 20 years beginning at the end...
-
A 10-year annuity pays \($900\) per year, with payments made at the end of each year. The first \($900\) will be paid 5 years from now. If the APR is 8% and interest is compounded quarterly, what is...
Study smarter with the SolutionInn App