All Matches

Solution Library

Expert Answer

Textbooks

Search Textbook questions, tutors and Books

Oops, something went wrong!

Change your search query and then try again

Result Not Found

Books FREE
Tutors
Study Help
Hire a Tutor
AI Study Help New

Search
Sign In
Register

study help
business
statistical sampling to auditing

Questions and Answers of Statistical Sampling To Auditing

Explain how one can distinguish between the equal-probability contours of the Normal, Student’s t and Pearson type II bivariate densities.
Explain why zero correlation does not imply independence in the case of the Student’s t and Pearson type II bivariate distributions.
Explain how an increase in correlation will affect the bivariate exponential density.What does that mean for the scatterplot?
Explain why the notion of correlation makes no sense in the case of random variables measured on the nominal scale.
(a) Define the following measures of dependence: (i) cross-product ratio, (ii) Yule’s Q,(iii) gamma coefficient.(b) Explain why these measures can be used for nominal- and ordinal-scale data.(c)
The data in Appendix 5.A (Lai and Xing, 2008, p. 71) denote log-returns on six stocks, with monthly observations from August 2000 to October 2005, where PFE=Pfizer, INTEL=Intel, CITI=Citigroup,
Explain how the notion of conditioning enables us to deal with the dimensionality problem raised by joint distributions of samples.
Explain why the reduction f (x, y) = f (y|x)·fx(x) raises a problem due to the fact that{ f (y|X = x; ϕ1), ∀x∈RX} represents as many conditional distributions as there are possible values of x
Define and explain the following concepts:(a) conditional moment functions;(b) regression function;(c) skedastic function;(d) homoskedasticity;(e) heteroskedasticity.
Consider the joint distribution as given below:(a) Derive the conditional distributions of (Y|X = x) for all values of X.(b) Derive the regression and skedastic functions for the distributions in
Let the joint density function of two random variables X and Y be xy 01 2 0 .1 .2 .2 1 .2.1.2
Compare and contrast the concepts E[Y|X = x] and E[Y|σ(X)].
From the bivariate distributions in Chapter 7:(a) Collect the regression functions which are: (i) linear in the conditioning variable,(ii) linear in parameters, and (iii) the intersection of (i) and
Explain the notion of linear regression. Explain the difference between linearity in x and linearity in the parameters.
Consider the joint Normal distribution denoted by (x) ~N ((m). (012 011 012 022 (7.65) (a) For values = 1, 2 = 1.5, 11 = 1,012 = 0.8, 22 = 2, plot E(Y|X = x) and Var(Y|Xx) for x = 0, 1,2. (b) Plot
Explain the concept of stochastic conditional moment functions.
Explain the notion of weak exogeneity. Why do we care?
Explain what one could do when weak exogeneity does not hold for a particular reduction as given in (7.64).
Explain the concept of a statistical generating mechanism and discuss its role in empirical modeling.
LetY be a random variable and define the error term by u = Y −E(Y|σ(X)). Show that by definition, this random variable satisfies the following properties:[i] E(u|σ(X)) = 0, [ii] E(u·X|σ(X)) =
Explain the difference between temporal and contemporaneous dependence.
Compare and contrast the statistical GMs of:(a) the simple Normal model,(b) the linear/Normal regression model, and(c) the linear/Normal autoregressive model.
Compare and contrast the simple Normal and Normal/linear regression models in terms of their probability and sampling models.
Compare and contrast the Normal/linear and Student’s t regression models in terms of their probability and sampling models.
Explain why the statistical and structural (substantive) models are based on very different information.
Discuss why a statistical misspecified model provides a poor basis for reliable inference concerning the substantive questions of interest.
Explain how the purely probabilistic construal of a statistical model enables one to draw a clear line between the statistical and substantive models.
Explain how the discussion about dependence and regression models in relation to the bivariate distribution f (x, y; φ) can be used to represent both synchronous and temporal dependence, by
Discuss the purely probabilistic construal of a regression model proposed in this chapter and explain why it enables one to distinguish between a statistical and a substantive(structural) model.
(a) Why do we need the notion of a stochastic process? How does it differ from the concept of a random variable?(b) Explain why the claim that when one assumes an IID sample, there is no need to use
(a) Explain the notion of a sample path of a stochastic process and contrast it to viewing the process as a sequence of random variables.(b) Compare the notions of index and probability averages.
(a) Explain the classification of stochastic processes using the index set and the state space.(b) Explain why the notion of a stochastic process is relevant in modeling all types of data:
Explain intuitively the Kolmogorov extension theorem for a stochastic process {Xt, t ∈N} and discuss its significance for modeling purposes.
What is the difference between the joint distribution and functional perspectives on stochastic processes? Why should we care?
(a) Explain the concepts of Markov dependence and homogeneity.(b) Explain the relationships between Markov, partial sums, and independent increments processes.(c) What is the relationship between
(a) Explain the concept of a partial sum stochastic process and the type of separable heterogeneity it gives rise to.(b) Explain why separable heterogeneity often gives rise to operational models.(c)
(a) Compare and contrast a partial sum process and a martingale process.(b) Explain the probabilistic structure of a random walk process and contrast it to that of a Normal random walk.
Compare and contrast a Brownian motion and a Wiener process.
Explain the following notions of dependence: (a) independence, (b) Markov dependence,(c) Markov dependence of order p, (d) m-dependence, (e) asymptotic independence,(f) non-correlation, (g)
(a) Explain the relationship between ψ-mixing and a mixingale, and discuss the appropriateness of such probabilistic assumptions for empirical modeling purposes.(b) Explain the notion of ergodicity
(a) Explain the following notions of heterogeneity: (a) identical distribution, (b) strict stationarity, (c) first-order stationarity, (d) second-order stationarity, (e) mth-order stationarity.(b)
Compare and contrast the stochastic processes: (a) white-noise process, (b) innovation process, (c) martingale difference process. (d) Explain why a martingale difference process can accommodate
Explain the notion of a Markov chain process and discuss the case where it is homogeneous.
Explain the notion of a Poisson process and relate it to the associated “waiting times”process.
Explain the probabilistic structure of a martingale process and relate it to that of a martingale difference process.
Consider the IID process {Xt, t = 1, 2, 3, . . .} such that E(Xt) = μ=0, t = 1, 2, . . . Show that the process {M = ()k, 1=1,2,3,...} is a martingale.
Let{Sk = kt=1 Yt, t∈N} be a simple random walk process, where Y = 2Z-1, Ry:={-1,1}, teN, {Z, TEN) is an IID Bernoulli process, Z, BerlID(p, p(1 - p)). Show that for p = .5, {Sk=Y, teN) is a
Compare and contrast a white-noise process {Zt, t∈N} when the underlying distribution is Normal vs. Student’s t in terms of the respective conditional processes{(Zt|σ(Zt−1, . . . , Z1), t∈N}.
Explain how a Gaussian, Markov, stationary process can give rise to an AR(1)model. Compare the resulting model when the process is Student’s t, Markov, and stationary.
AnARMA(p,q) representation constitutes a parsimonious version of an MA(∞).
Explain the probabilistic structure of a Wiener process and compare it with that of a Brownian motion process.
Explain how a Brownian motion process can be changed into a second-order stationary process by a transformation of the index.
Compare and contrast the Normal autoregressive model and the Normal/linear regression model specified in Chapter 7.
Compare and contrast the statistical GM of an AR(1) model (Table 8.3) with that of a Weibull hazard-based model (Table 8.8).
Explain the statistical parameterization of the AR(1) model (Table 8.3) and discuss any problems that arise when testing the following hypotheses:(a) H0: α1 = 1 vs. H1: α1 < 1;(b) H0: α1 = 1 vs.
(a) “When using weekly observations on speculative prices, using the average of daily prices, one could invoke the central limit theorem to justify using the Normal distribution for modeling such
“There is no point in using the Student’s t distribution in modeling speculative prices.One should adopt the Normal distribution at the outset because as the number of observations increases the
Discuss the following syllogism by a gambler betting on red or black in roulette: “For the last 6 times in a row the ball stopped in a red; if the WLLN is valid, it means that the probability that
“The law of large numbers and the central limit theorem hold for stochastic processes for which we need to postulate restrictions of three types: (a) distribution, (b)dependence, and (c)
“Poisson’s WLLN postulates complete heterogeneity for the Bernoulli random variables involved but implicitly assumes asymptotic homogeneity.” Discuss.
Explain Borel’s strong law of large numbers and discuss why:(a) it gives rise to “potential” learning from data;(b) the SLLN does not imply that limn→∞ xn=p;(c) it does not imply that for a
How does the law of large numbers relate to the central limit theorem?
Explain the conclusion of Bernstein’s WLLN and discuss which assumptions are crucial for the validity of the conclusion.
Compare and contrast Bernoulli’s WLLN with that of Bernstein.
Explain how the conditions underlying Lyapunov’s CLT ensure that no one random variable in the sequence dominates the summation.
(a) Consider the IID sequence {Xk, k ∈ N} with E(Xk) = 0, Var(Xk) = σ2. Define the sequence {Yk, k ∈ N}, where Yk = a + bXk, k = 1, 2, . . . Do the SLLN, WLLN, and CLT hold for the sequence {Yk,
Discuss the relationship between the Lindeberg and Feller conditions and their connection with the CLT.
Discuss the relationship between the Lindeberg and uniform asymptotic negligibility conditions.
Convergence in probability implies convergence in distribution but more stringent conditions are needed for the CLT than those for the LLN. Explain why.
Explain how the CLT can be extended beyond the scaled summations.
Explain how the FCLT improves upon the classical CLT.
Compare and contrast the classical CLT and FCLT in the case of second-order stationary processes.
Explain intuitively why “converges in probability” is a stronger mode of convergence than “converges in distribution.”
Explain intuitively why “converges almost surely” is a stronger mode of “convergence than converges in probability.”
Compare and contrast convergence almost surely and rth-order convergence.
“For modeling purposes specific distribution assumptions are indispensable as suggested by the Berry–Esseen result.” Discuss.
(a) Compare and contrast Linderberg’s CLT (Table 9.19) with that for second-order martingale difference processes (Table 9.22).(b) Compare and contrast Chebyshev’s “near” CLT, which was
Explain why the interpretation of mathematical probability plays a crucial role in determining the type and nature of statistical modeling and inference.
(a) Compare and contrast the degrees of belief and model-based frequentist interpretations of probability.(b) Explain why the criticism that the model-based frequentist interpretation of probability
(a) Explain briefly the difference between the model-based and von Mises frequentist interpretations of probability.(b) Using your answer in (a), explain why (i) the circularity charge, (ii) the
(a) Discuss the common features of the model-based frequentist interpretation of probability and Kolmogorov’s complexity interpretation of probability.(b) Discuss the relationship between the
Explain why for subjective probabilities associated with two independent events A and B of: Pr(A) = .5, Pr(B) = .7, Pr(A ∩ B) = .2 is not coherent.
(a) Compare and contrast the subjective and logical (objective) “degrees of belief”interpretations of probability.(b) Briefly compare and contrast the frequentist and Bayesian approaches to
In the case of the simple Bernoulli model, explain the difference between frequentist inference based on a sampling distribution of an estimator of θ, say f ( θ (x); θ), ∀x∈Rn and Bayesian
(a) “. . . likelihoods are just as subjective as priors” (Kadane, 2011, p. 445). Discuss.(b) Discuss the following claims by Koop et al. (2007, p. 2):frequentists argue that situations not
Compare and contrast Karl Pearson’s approach to statistics with that of R. A. Fisher, and explain why the former implicitly assumes that the data constitute a realization of an IID sample.
(a) Compare and contrast the following: (i) sample vs. sample realization, (ii) estimator vs. estimate, (iii) distribution of the sample vs. likelihood function.(b) Explain briefly why frequentist
“The various limit theorems relating to the asymptotic behavior of the empirical cumulative distribution function, in conjunction with the validity of the probabilistic assumptions it invokes,
For the random variable X, where E(X) = 0 and Var(X) = 13, derive an upper bound on the probability of the event {|X −.6| > .1}. How does this probability change if one knows that X U(−1, 1)?
For the random variable X, where E(X) = 0 and Var(X) = 1, derive an upper bound on the probability of the event {|X − .6| > .1}. How does this probability change if one knows that X N(0, 1)?
(a) (i) In Example 10.25 with ε = .1, evaluate the required sample size n to ensure that (ii) Calculate the increase in n needed for the same upper bound (.02) with ε =.05.(iii) Repeat (i) and
(a) “For modeling purposes specific distribution assumptions are indispensable if we need precise and sharp results. Results based on bounded moment conditions are invariably imprecise and
Explain briefly what we do when we construct an estimator. Why is an estimator a random variable?
“Defining the sampling distribution of an estimator is in theory trivial but technically very difficult.” Discuss.
Explain what the primary aim of an estimator is, and why its optimality can only be assessed via its sampling distribution.
For the Bernoulli statistical model (Table 11.1):(a) Discuss whether the following functions constitute possible estimators of θ:(b) For those that constitute estimators, derive their sampling
Explain briefly the properties of unbiasedness and efficiency of estimators.
“In assessing the optimality of an estimator we need to look at the first two moments of its sampling distribution only.” Discuss.
Explain briefly what a consistent estimator is. What is the easiest way to prove consistency for estimators with bounded second moments?
Explain briefly the difference between weak and strong consistency of estimators.

Showing 1100 - 1200 of 3033

First
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Last

Services

Sitemap
Fun
Definitions
Become Tutor
Study Help Categories
Recent Questions
Expert Questions

Company Info

Security
Copyrights
Privacy Policy
Terms & Conditions
SolutionInn Fee
Scholarship

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Campus Ambassador

Secure Payment

Download Our App

© 2024 SolutionInn. All Rights Reserved