... example, if a variable y depends on x and lagged x, yt = &x, + fi2xI_ ,, it is not likely that /3, and p2 are independent a priori since if I tell you something about /3,, it is likely to alter your ... when Y is regressed on X The sum-of-squared prediction errors is then the cross-validation penalty P2 = q?/A!f;;= (~ep4;‘ /~M;‘ )cM;;‘ , i=l i i i (7.2) Ch 5: Model Choice 323 which is called SSPE ... by Allen (1974) It is discussed by Hocking (1972, 1976) and studied by Stone (1974) The penalty P2 is just a weighted error sum-of-squares times the sum-of-squares of the inverse diagonal elements...
... Chapter Consumer Choice and Demand in Traditional and Network Markets Q1 Q2 P1 – P2 Ed = ½ (Q1 + Q2 ) ÷ ½ (P1 P2 ) Where the subscripts and represent two distinct points, or prices, on the demand ... for each and every quantity of jeans At price P2 , for instance, consumers will now buy only Q1 jeans (not Q3 , as before); and they will now pay only P2 for Q1 jeans not P3 , as before _ Thus, ... quantity of the good or service consumed is the same in both markets If the price is raised to P2 , however, the response is substantially greater in market D1 than in D2 In D1 , consumers will...
... primes is infinite Proof Suppose there were only a finite number of primes, say p , p2 , , p n Let N = p1 p2 · · · pn + Evidently none of the primes p1 , , pn divides N Lemma 1.1 Every ... we argue by induction Our proof shows that pn+1 ≤ p1 p2 · · · pn + But now, by our inductive hypothesis, n pn+1 ≤ 22 +22 +···+2n p1 < 22 , p2 < 22 , , pn < 22 It follows that But 21 + 22 + ... induction on n Since n/p1 = p2 · · · pr = q1 · · · qj · · · qs ˆ (where the ‘hat’ indicates that the factor is omitted), and since n/p1 < n, we deduce that the factors p2 , , pr are the same...