Jackknifing

Techniques to use for evaluations have been discussed by Cox and Tikvart (42), Hanna (43) and Weil et al. (44). Hanna (45) shows how resampling of evaluation data will allow use of the bootstrap and jackknife techniques so that error bounds can be placed about estimates. 

Efron B (1982) The jackknife, the bootstrap and other resampling techniques. Society for Industrial and Applied Mathematics, Philadelphia, PA... 

The second method, the leave-one-at-a-time or jackknife procedure, repeats the whole LDA procedure as many times as there are objects, and each time one object alone is the evaluation set. 

Although this approach is still used, it is undesirable for statistical reasons error calculations underestimate the true uncertainty associated with the equations (17, 21). A better approach is to use the equations developed for one set of lakes to infer chemistry values from counts of taxa from a second set of lakes (i.e., cross-validation). The extra time and effort required to develop the additional data for the test set is a major limitation to this approach. Computer-intensive techniques, such as jackknifing or bootstrapping, can produce error estimates from the original training set (53), without having to collect data for additional lakes. 

Jackknifing involves removing one sample from the calibration set, deriving the inference equations based on the remaining set of lakes (i.e., n — 1), and then using the new inference equation to derive an inferred value for the one sample that was removed (i.e., providing an independent error estimate). These steps are repeated until all samples have been left out once from the calibration process and used to calculate a new inferred value. The set of new inferred values is then used in conjunction with the... 

Table 6.3. LOADINGS WITH JACKKNIFE ESTIMATES OF STANDARD DEVIATION AND CROSS-VALIDATION cvd-sd FROM PCA OF THE BHT 920 EXAMPLE...

Two non-parametric methods for hypothesis testing with PCA and PLS are cross-validation and the jackknife estimate of variance. Both methods are described in some detail in the sections describing the PCA and PLS algorithms. Cross-validation is used to assess the predictive property of a PCA or a PLS model. The distribution function of the cross-validation test-statistic cvd-sd under the null-hypothesis is not well known. However, for PLS, the distribution of cvd-sd has been empirically determined by computer simulation technique [24] for some particular types of experimental designs. In particular, the discriminant analysis (or ANOVA-like) PLS analysis has been investigated in some detail as well as the situation with Y one-dimensional. This simulation study is referred to for detailed information. However, some tables of the critical values of cvd-sd at the 5 % level are given in Appendix C. 

The jackknife estimate of variance can be used to assess the significance of the weight and loading coefficients in a PLS model. This is a valuable source of information in case interpretation of the parameters is warranted. The weights with jackknifed standard deviations from the BHT example are given in Table 6.5. The weights of the first PLS dimension suggest that the behavioural effect of these doses of BHT is to suppress most aspects of a rat s... 

Table 6.5. WEIGHTS AND JACKKNIFE ESTIMATES OF STANDARD DEVIATION FOR THE FIRST TWO PLS DIMENSIONS OF THE BHT 920 DATA...

A second possibility is to use some estimate of the variance of the loadings. This can be done by the jackknife method due to Quenouille and Tukey (see [37]) or by Efron s bootstrap method [38] (the colourful terminology stems from the expressions jack of all trades and master of none and lifting yourself up by your own bootstraps ). The use of the bootstrap to estimate the variance of the loadings in PCA has been described [39] and will not be elaborated upon further. The jackknife method is used partly because it is a natural side-product of the cross-validation and therefore computationally non-demanding and partly because the jackknife estimate of variance is used later on in conjunction with PLS. 

The jackknife method is based on an idea similar to cross-validation. The calculation of the statistical model is repeated g times holding out 1/gth of the data each time. In the end, each element has been held out once and once only (exactly as in cross-validation). Thus, a number of estimates of each parameter is obtained, one for each calculation round. It has been proposed that the quantity... 

For a more realistic estimate of the future error one splits the total data set into a training and a prediction part. With the training set the discriminant functions are calculated and with the objects of the prediction or validation set, the error rate is then calculated. If one has insufficient samples for this splitting, other methods of cross-validation are useful, especially the holdout method of LACHENBRUCH [1975] which is also called jackknifing or leaving one out . The last name explains the procedure For every class of objects the discriminant function is developed using all the class mem-... 

Jackknifing Characters are randomly sampled without replacement, leading to new data set smaller than original one. Jackknifing of taxa is sometimes done instead of characters 15,16... 

Efron B (1981) Nonparametric estimates of standard error The jackknife, the bootstrap and other methods. Biometrika 68 589-599... 

To derive these equations, log P (hydrophobic parameter), MR (molar refrac-tivity index), and MV (molar volume) were calculated using software freely available on the internet (wwwlogP.com, www.daylight.com). The first-order valence molecular connectivity index of substituents was calculated as suggested by Kier and Hall [46,47]. In these equations, is cross-vahdated obtained by the leave-one-out jackknife procedure. Its value higher than 0.6 defines the good predictive ability of the equation. The different indicator variables in these equations were defined as follows. 

Jackknife estimate of the bias. For the estimate discussed above, consider the jackknifed samples obtained by deleting one point from an original sample, — Let F k) be the estimated free energy obtained with the Mi jackknifed sample so that... 

Fig. 6. Repacking of the influenza HA2 hydrophobic core. Left. A ribbon trace of HA2 residues 38 to 127, including the helices that make up the core of the stalk in the native HA structure (see Fig. 3). Middle A hypothetical structure obtained by fusing the base of the coiled coil from the native HA structure with the top of the extended coiled coil from the low pH-converted HA structure. This panel helps distinguish the two major components of the HA conformational change on low pH treatment the existence of such an intermediate structure has not been shovm experimentally for influenza and may exist only transiently if at all. This extended structure, known as a prehairpin intermediate, has been detected indirectly in other virus envelope proteins (reviewed in Chan and Kim, 1998). Right Residues 38 to 127 from low pH-converted HA2 (Bullough et al, 1994). Hydrophobic residues that stabilize the jackknifed structure are indicated in one protomer as gray space-filling atoms. The amino (N) and carboxy (C) termini of a protomer within each trimer structure are indicated.

Alley EA, Pollock JE. Transient neurologic syndrome in a patient receiving hypobaric lidocaine in the prone jackknife position. Anesth Analg 2002 95(3) 757-9. 

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