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These ``magnitude'' parameters are also problematic to estimate using traditional methods; however, as with a they can be simply and effectively estimated from the logscale diagram For simplicity we will continue the.

} static final Result result = new Result(); public static void main(String[] args) { boardSize = ; FJTaskRunnerGroup tasks = new FJTaskRunnerGroup(); int[] initialBoard = new int[0]; // start with empty board tasksexecute(new NQueens(initialBoard)); int[] board = resultawait(); // } final int[] sofar; // initial configuration }

discussion for the LRD case only However, an essentially identical procedure, estimator de nition, and properties hold in the self-similar case For other kinds of scaling also, magnitude parameters can be de ned and estimated in a similar way; however, this will not be discussed here We brie y summarize the results of Veitch and Abry [74, 75] for a twodimensional joint estimator ^ ; cf of long-range dependence One of the powerful a ^ ^ properties of a is that its statistics are entirely independent of the speci c form of the mother wavelet, depending on the coef cients of the linear regression and the amount of data nj at each scale It is this feature that allows an explicit expression for its variance to be obtained independently of the wavelet basis.

The device number for a HAL function is determined by the top 16 bits of the associated HAL group number passed to the function. If a handler already exists for the HAL group, this handler will not be registered.

It is clear that ^ this property is shared by a vj yj , the unbiased estimator of the intercept a of the same linear regression de ning a (The coef cients vj are given by vj Sjj Sj j = s2 SSjj Sj2 , cf Eq (223)) From Eq (216) it is apparent j that whereas a is simply the slope in the logscale diagram, the magnitude parameter ^ cf is related to the intercept, being essentially proportional to 2a , a quantity that ^ ^ retains the wavelet independence advantages of a Unfortunately, 2a does not correspond exactly to cf but rather to the dimensionless quantity cf C a; c0 , and an attempt to isolate the former necessarily brings in a wavelet dependence.

typedef TInt (*THalFunc)(TAny*,TInt,TAny*,TAny*);

It is advantageous, however, to study cf C as the largest ``wavelet-independent part'' cf , d ^ ^ ^ and to de ne subsequently the estimator of cf as cf cf C=C, where C is an estimator of the integral C a; c0 , which will not be detailed here It can be shown ^ ^ [75] that C has small variance, so that the properties of cf closely resemble those of ^ d d cf C More speci cally, de ne cf C p2a , where p is a wavelet-independent bias correcting (and variance reducing) factor given by p G nj =2 exp c nj =2 vj ; G vj nj =2.

NQueens(int[] board) { thissofar = board; public void run() { if (!resultsolved()) { int row = sofarlength; if (row >= boardSize) resultset(sofar); else {

which is typically close to 1 (here c is the Psi function, not the wavelet!). This d estimator is unbiased and complex, but explicit expressions for the variance of cf C (and covariance of (^ ; cf C)) are obtainable, and again the Cramer Rao bound is a d attained in the limit nj large, provided the additional condition vj =nj 3 0 is also satis ed for each j in j1 ; j2 . Based on these explicit expressions for (^ ; cf C), very a d accurate approximate expressions (which to rst order are also wavelet independent) can be derived for the covariance matrix of (^ ; cf ). a ^ The estimator cf is asymptotically unbiased and ef cient, and approximately lognormally distributed. The correlation coef cient of (^ ; cf ) is negative and large in a ^ magnitude: typically around 0:9. As before, simulation studies show [75] that the above properties hold to an excellent approximation, even for small size data, upon mild departures from ID1. An example of the joint estimation is given in the lefthand plot of Fig. 2.2. 2.3.2.5 Comparisons with Other Estimators In the evaluation of an estimator both statistical and computational aspects must be considered. The logscale diagram

The arguments to this are the pointer registered with the HAL handler, the HAL function number and two optional arguments, the de nition of which are dependent on the HAL function. They are usually used to read or write data passed from the client to the handler. Let s take a look at how the LCD extension registers its HAL handler with the system. This is done when the extension is initialized:

P ton > u du as x 3 I: