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Continuous Probability Distributions Commonly Used in Financial Econometrics 357 Xn be identically distributed and independent o ...

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359 Appendix C inferential Statistics i n Appendix A, we provided the basics of descriptive statistics. Our focus in this append ...

360 The Basics of financial economeTrics The general problem that we address is the process of gaining informa- tion on the true ...

Inferential Statistics 361 In our discussion, we will assume that individual draws are performed independently and under identic ...

362 The Basics of financial economeTrics based on nothing but luck; in the best case, a guess might be justified by some experie ...

Inferential Statistics 363 once again obtain a normal random variable. Thus, any linear estimator will be normal. This is an ext ...

364 The Basics of financial economeTrics due to the uncertainty associated with each individual draw. For the param- eter θ and ...

Inferential Statistics 365 for whatever the true parameter value θ may be. Hence, we stated the bias as an ultimately preferable ...

366 The Basics of financial economeTrics If we are concerned about some estimator’s properties, we may reason- ably have to rema ...

Inferential Statistics 367 Law of large numbers. Let XX()^1 ==(, 1 ()()()^1 XX 211 ,,... n),XX()^2 (, 1 ()^2 XX()(),,... ) 2 n ( ...

368 The Basics of financial economeTrics Consistency. An estimator θˆn is a consistent estimator for θ if it converges in probab ...

Inferential Statistics 369 where σX^2 denotes the common variance of each drawing. This variance can be minimized with respect t ...

370 The Basics of financial economeTrics just a single number. This may increase the likelihood that the true param- eter is one ...

Inferential Statistics 371 of error α. Then, with probability 1 – α, the true parameter is covered by the interval [l(X), u(X)]. ...

372 The Basics of financial economeTrics confidence interval depends on the outcome x. By design, as we have just shown, the int ...

Inferential Statistics 373 Setting Up the Hypotheses Since in statistical inference we intend to gain information about some unk ...

374 The Basics of financial economeTrics decision Rule The object of hypothesis testing is to make a decision about these hypoth ...

Inferential Statistics 375 the statistic t(x) either leads to rejection of the null hypothesis (i.e., δ(x) = d 0 ), or not (i.e. ...

376 The Basics of financial economeTrics hypothesis holds. Unfortunately, however, we do not know whether we com- mit an error o ...