Effects Of Data Truncation Research Articles

Estimating Operational Risk Capital from Truncated Data with Constrained Optimization

In this presentation, the effect of data truncation on model stability is shown to be significant due to implied extrapolation into the region below threshold. Since the instability results from the absence of data below the truncation point, it can't be addressed by alternative fitting techniques. New information needs to be leveraged to resolve the problem. One source of information is the aggregated data of operational risk losses that fall below the truncation point, data which is often available but not used in modeling. The presentation demonstrates how to utilize this data to improve estimates of model distribution parameters and capital.

Firm Size and Growth Rate Variance: The Effects of Data Truncation

This paper discusses the effects of the existence of natural and/or exogenously imposed thresholds in firm size distributions on estimations of the relation between firm size and the variance in firm growth rates. We argue that these estimations are upwardly biased whenever the threshold operates on the same proxy that is used to calculate the growth rates. We show the potential impact of the bias on simulated data, suggest a methodology to improve these estimations, and present an empirical analysis on Dutch firms. The only stable relation that emerges is the negative relationship between firm size and growth rate variance.

On the Rate Distribution Analysis of Kinetic Data Using the Maximum Entropy Method: Applications to Myoglobin Relaxation on the Nanosecond and Femtosecond Timescales

We discuss the application of the maximum entropy method (MEM) to the extraction of rate distributions from kinetics experiments on the nanosecond to femtosecond time scale. We first present simulations to show the effects of data truncation (typical of nanosecond experiments) on rate distributions recovered by MEM. The stretched exponential decay is considered as an example to demonstrate that if the true distribution of rates for the underlying process includes faster time scales than are contained within the experimental data set, MEM can introduce unwarranted features that extend into the slower regions of rate space. This observation has relevance to the application of MEM to obtain rate distributions from kinetic experiments involving the relaxation of complex molecules like proteins, where features in the distribution are sometimes interpreted as static distributions of protein conformational substates. As an experimental example, we present an MEM analysis of the temperature dependence of the geminate rebinding kinetics of carbonmonoxy myoglobin near room temperature and find a barrier height of 18 kJ/mol. We also consider the application of MEM to ultrafast pump-probe transient absorption data, where one needs to take into account the possibility of nonmonotonicity in the kinetics and the finite pulse autocorrelation width that effectively convolves into the observed material responses. The MEM analyses of the femtosecond photophysics of Mb and MbNO, monitored at several wavelengths in the visible region, are presented as examples.

Time Dilation of BATSE Gamma‐Ray Bursts

We perform several nonparametric correlation tests on the BATSE 3B data to search for evidence of cosmological time dilation. These tests account for the effects of data truncation due to threshold effects in both limiting brightness and limiting duration, enabling us to utilize a larger number of bursts than in previous analyses. We find little significant evidence for correlation between various measures of peak intensity and duration, but the tests cannot conclusively rule out time dilation factors of 2 or less without more data. There is stronger evidence for a positive correlation between fluence and duration, which if confirmed would rule out simple no-evolution cosmological models unless there is a strong intrinsic correlation between the total radiant energy and the duration of bursts.

Incubation Period of Vertically Acquired AIDS in Europe Before Widespread Use of Prophylactic Therapies

European surveillance data on vertically acquired (VA) AIDS cases were used to investigate the incubation period of AIDS in the absence of widespread prophylactic treatment and to assess the uncertainty associated with parametric estimates based on retrospective data. Nonparametric and parametric analyses, taking into account the effects of data truncation, were based on a total of 792 children diagnosed with AIDS between July, 1982, and June, 1990, inclusive. Among HIV-infected children who develop AIDS within 8 years, the nonparametric estimate of the median age at diagnosis was 34 months. If 20% of children are assumed to develop AIDS by the age of 1 year (a plausible estimate on the basis of published cohort data), the estimated median among all maternally HIV-infected children is 4.4 years, with 26% of children expected to remain AIDS free by 8 years of age. Results from the parametric (double Weibull) model support the hypothesis of a bimodal distribution, with a subgroup of children progressing rapidly to AIDS at a median age of approximately 5 months. However, neither the relative size of this group nor the median age at which AIDS develops in the remaining children can yet be estimated with any reasonable precision.

Estimation of the mean error in atomic positions from the overall values of R indices

The theoretical overall values of different types of R indices have been evaluated as a function of the mean coordinate error (i.e. (Izlrl)) for the atoms in a model and the fractional contribution of the known atoms to the local mean intensity (i.e. o-~). The effect of data truncation due to unobserved reflections has also been taken into account. Results for centrosymmetric and non-centrosymmetric crystals containing similar atoms have been obtained in the form of compact tables. Results in these tables can be used to obtain the mean coordinate error (IArl) for any model from the overall values of the R indices.

Measurability of Bijvoet differences in triclinic, monoclinic and orthorhombic crystals

Theoretical expressions for the measurability of Bijvoet differences have been derived for triclinic, monoclinic and orthorhombic crystals containing p (= 1 or 2) anomalous scatterers and many normal scatterers per asymmetric unit. Results for the many- atom cases (i.e. P = MN and MC cases) in space group P1 are also obtained. The theory takes into consideration the effect of data truncation due to unobserved reflections. The measurability values for the various cases are given in the form of compact tables as functions of the relevant parameters k and σ21. The theoretical results are also used to discuss briefly the following aspects. (i) The effect of k and σ21 on the measurability. (ii) Measurability to be expected in the heavy-atom derivatives of proteins with Cu Kα radiation. (iii) A comparison of the measurabilities in Sm derivatives of a protein for Cu Kα and for a wavelength (λ = 1.8448 Å) at which the anomalous scattering effect has been observed to be the largest. It is also found that in the case of the heavy-atom derivatives of proteins measurability is strongly influenced by variation in σ21.

The effect of data truncation on the measurability of Bijvoet differences; erratum

In Table 2 of Parthasarathy & Ponnuswamy [Acta Cryst. (1981), A37, 153-162], for every value of k, the row against yt = 0.3 for P = 1 and the row against yt = 0.3 for P = MC are to be interchanged. All relevant information is given in the Abstract.

The effect of data truncation on the measurability of Bijvoet differences

Theoretical expressions for the complementary cumulative function of the Bijvoet ratio X applicable to a truncated data set are worked out for a non-centrosymmetric crystal containing P anomalous scatterers in the unit cell [P = 1 and many (MN and MC cases)] besides a large number of normal scatterers. These expressions contain the truncation limit yt as a parameter of the distribution. The results obtained are used to discuss the effect of data truncation arising from the non-observability of extremely weak reflections on the measurability of Bijvoet differences.

Multiple scattering effects in the fourier transform deconvolution procedure for leed analysis

A direct Fourier transform deconvolution procedure based on the Southwell relaxation scheme is outlined. The technique is fully tested using low energy electron diffraction (LEED) intensity ( I– V) spectra calculated from single scattering theory which shows, in this simple case, that the method is both rapid and accurate and does not suffer from the effects of data truncation. The deliberate introduction of errors in the inner potential and surface Debye temperature is also satisfactorily accounted for. However, the use of I– V spectra calculated from multiple scattering theory produces grossly misleading results. It is concluded that the procedure is not applicable to the evaluation of experimental data.

Surface structure determination via a transform-deconvolution method

A fast direct-transform method for the determination of surface structures from low-energy-electron diffraction (LEED) intensity data is presented. Basic principles of a proper transform construction and its applications are discussed and demonstrated. The effects of data truncation is studied and a deconvolution procedure for extraction of accurate structural information from the transform is described. Results of a complete surface structure determination of Ni(100) by application of the method to experimental data are discussed.

Firm Size and Rate of Growth

Firm Size and Rate of Growth