Statistics notes

Statistics 240 Lecture Notes

So far, we have been concerned with nonparametric tests and procedures: tests and procedures with minimal assumptions about the probability distribution that gives rise to the data. Examples of the kinds of assumptions we have made in various places are that the distribution is continuous, that the observations are iid, that subjects are randomized into treatment and control, etc. We now consid...

Course Notes - Statistics

Notes on Statistics

h. t-Test: This is one of the most powerful and widely used statistical tests. The ttest (Student's t) is used to calculate the confidence intervals of a measurement when the population standard deviation ()) is not know. Which is usually the case. The t-test is also used to compare two averages. The t-test corrects for the uncertainty of the sample standard deviation (s) caused by taking a sma...

TI Statistics - Extra notes

Statistics Oral Exam Notes 2008

(a) complete statistic: T (X) is complete w.r.t. a family P if ∀g : R → R measurable, E[g(T )] = 0 ∀P ∈ P ⇒ g = 0 a.s. w.r.t. P. (b) sufficient statistic:: We define a sub σ-field Σ ⊆ Bn to be sufficient for P (or equivalently, Θ) if ∀A ∈ Bn, ∃fA Σ-measurable s.t. ∀P ∈ P, fA(x) = EP [1A|Σ] a.s. wrt P (i.e. the conditional expectations given Σ is independent of the law of X, P ∈ P).We say T (X) ...