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Choosing the number of perturbed datasets to generate is also something of an art The extant literature does not specify a particular number of samples that is guaranteed to be suf cient for all cases Parker (1997) and Parker et al (2000) use as many as 100 and as few as four samples in their Monte Carlo arithmetic analysis Parker (1997) also shows that in all but pathological cases, the distribution of the means of coef cients calculated under random rounding are normal, which suggests that 30 to 50 samples should be adequate Moreover, since the perturbation technique can be replicated inde nitely, one can simply rerun the analysis, increasing the number of samples, until the variance across replications is acceptable for the substantive problem at hand 433 Tests of Global Optimality Another sensitivity test involves noting the responsiveness of a search algorithm to starting values.

Some described Chinese business style as soft, though I never knew what to make of such commentary Factory owners were aggressive more than anything else, and perhaps even a bit cruel This one factory owner had encouraged his prospective customer to board a plane in the United States and y all the way to China Once the investment in time and money had been made, the factory took advantage On the way to our next stop, Doug said that he would probably end up giving the factory the order anyway He had an important customer back home that was already counting on the shipment of tubing Even if he made no money at all on the order, there was some value, he said, in keeping his customer satis ed.

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For the cases of interest in statistical applications we usually consider eigenvalues of only those matrices that can be proved to have only real eigenvalues. Eigenvectors. eigenvector z of an n n matrix A is of dimension n 1. These are de ned by the relationship. Az = lz, which can be written as Az = lIz. Now moving Iz to the left-hand side, we have (A - lI)z = 0. In the example above where n = 2 this relation is a system of two equations when the matrices are explicitly written out. For the 2 2 symmetric matrix above the two equations are

Researchers who analyze complex functions are probably already aware that a poor choice of starting values may lead the search algorithm horribly astray: for example, leading the search algorithm onto a discontinuity with no maximum Here, we brie y explain the problem that multiple optima poses to a search algorithm, discuss some strategies for selecting starting values that might reveal a global optimum, and explore some tests that have been proposed to identify if a global optima has been found 4331 Problem Identifying the Global Optimum Once an algorithm reaches convergence, how certain can a researcher be that the optimum reached is truly the global and not merely a local optimum If the maximization function is globally concave, the local optimum and the global optimum are the same (Goldfeld and Quandt 1972; Gill et al 1981; Nocedal and Wright 1999).

Why didn t Chinese manufacturers take the same approach with their own customers, and why were they eternally focused on shortterm gambits Chinese business leaders were continually preaching how they valued relationships, and yet it was more often foreigners who understood what it really meant..

If the organization s culture is friendly to it, spontaneous knowledge sharing will happen when virtual meeting rooms are easily available. Many, if not most, corporate portals feature links to community or collaboration where discussion boards can be found. These are often dedicated to the business line associated with the employee, but some companies provide discussion space for general use and access, permitting conversation across business lines. As we pointed out in 7, Choosing and Using Technology, commercial portal products vary in their ability to integrate applications from different vendors. Many portals bundle the eRooms message board, whereas others allow standalone discussion

Unfortunately, if the function is known to have several local optima, there is no known way of guaranteeing that a global optimum will be found in a nite amount of time (Veall 1990, p 1460) Commonly used search algorithms can get stuck at a local optimum, thereby missing the true global maximum Searching the entire parameter space for global optimum is often too computationally intensive, especially when there are a large number of righthand-side variables in the equation to be estimated Multiple optima may exist more frequently than most political scientists realize Consider this example from Goldfeld and Quandt (1972, pp 21 22): Yi = a + a 2 xi + ui where ui is iid N 0, 2 (418).

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