Skew Estimation Research Articles

Estimation and Testing of Portfolio Value-at-Risk Based on L-Comoment Matrices

This study employs L-comoments introduced by Serfling and Xiao (2007) into portfolio Value-at-Risk estimation through two models: the Cornish-Fisher expansion (Draper and Tierney 1973) and modified VaR (Zangari 1996). Backtesting outcomes indicate that modified VaR outperforms and L-comoments give better estimates of portfolio skewness and excess kurtosis than do classical central moments in modeling heavy-tailed distributions.

Log-Pearson Type 3 Distribution and Its Application in Flood Frequency Analysis. III: Sample Skew and Weighted Skew Estimators

The accuracy of flood quantile estimates is constrained by the data available at a site. To improve the accuracy of quantile estimators, Bulletin 17B recommends combining the station skew with a regional skew using the inverse of their mean square errors (MSEs) as weights. While these weights can yield the minimum MSE skewness estimator, they do not provide the minimum MSE quantile estimators except when the true at-site skew is zero. In this paper, optimal weights which provide minimum MSE quantile estimators are derived. A Monte Carlo experiment illustrates the value of different weighting schemes and the value of using an informative regional skew. For reasonable values of the regional skew, the MSE of quantile estimators is reduced when the sample skew is combined with an informative regional skew. Modest improvements in the MSE of quantile estimates are obtained using optimal quantile weights rather than the MSE-skew weights. When the regional skew is actually very informative, there is a large loss ...

On the Impact of Mispointing Error and Hamming Filtering on Altimeter Waveform Retracking and Skewness Retrieval

Ground-based processing of radar altimeter signals has improved the accuracy of geophysical information retrieved from the shape of the waveforms over the ocean. Information about the nonlinear nature of ocean waves (wave skewness) can now be extracted (Gómez-Enri et al. 2006), but first estimates of wave skewness returned a large percentage of negative values, which have no physical meaning. Here, we investigate two possible causes of these negative skewness values using simulations of ocean waveforms for the Envisat RA-2 altimeter: the Hamming filter applied in the altimeter on-board processing and discrepancies between the real mispointing of the altimeter and the value assumed by the retracking algorithm. The Hamming filter strongly affects the retrieval of the parameters at low wave conditions, but it is not the responsible for the negative skewness. It is the second effect that plays a key role in the value of the skewness retrieved.

Measuring Global Ocean Wave Skewness by Retracking RA-2EnvisatWaveforms

For early satellite altimeters, the retrieval of geophysical information (e.g., range, significant wave height) from altimeter ocean waveforms was performed on board the satellite, but this was restricted by computational constraints that limited how much processing could be performed. Today, ground-based retracking of averaged waveforms transmitted to the earth is less restrictive, especially with respect to assumptions about the statistics of ocean waves. In this paper, a theoretical maximum likelihood estimation (MLE) ocean waveform retracker is applied tothe Envisat Radar Altimeter system (RA-2) 18-Hz averaged waveforms under both linear (Gaussian) and nonlinear ocean wave statistics assumptions, to determine whether ocean wave skewness can be sensibly retrieved from Envisat RA-2 waveforms. Results from the MLE retracker used in nonlinear mode provide the first estimates of global ocean wave skewness based on RA-2 Envisat averaged waveforms. These results show for the first time geographically coherent skewness fields and confirm the notion that large values of skewness occur primarily in regions of large significant wave height. Results from the MLE retracker run in linear and nonlinear modes are compared with each other and with the RA-2 Level 2 Sensor Geophysical Data Records (SGDR) products to evaluate the impact of retrieving skewness on other geophysical parameters. Good agreement is obtained between the linear and nonlinear MLE results for both significant wave height and epoch (range), except in areas of high-wave-height conditions.

Height and roughness distributions in thin films with Kardar–Parisi–Zhang scaling

We study height and roughness distributions of films grown with discrete Kardar–Parisi–Zhang (KPZ) models in a small time regime which is expected to parallel the typical experimental conditions. Those distributions are measured with square windows of sizes 8 ⩽ r ⩽ 128 gliding through a much larger surface. Results for models with weak finite-size corrections indicate that the absolute value of the skewness and the value of the kurtosis of height distributions converge to 0.2 ⩽ ∣ S∣ ⩽ 0.3 and 0 ⩽ Q ⩽ 0.5, respectively. Despite the low accuracy of these results, they give additional support to a recent claim of KPZ scaling in oligomer films. However, there are significant finite-size effects in the scaled height distributions of models with large local slopes, such as ballistic deposition, which suggests that comparison of height distributions must not be used to rule out KPZ scaling. On the other hand, roughness distributions of the same models show good data collapse, with negligible dependence on time and window size. The estimates of skewness and kurtosis for roughness distributions are 1.7 ⩽ S ⩽ 2 and 3 ⩽ Q ⩽ 7. A stretched exponential tail was found, which seems to be a particular feature of KPZ systems in 2 + 1 dimensions. Moreover, the KPZ roughness distributions cannot be fitted by those of 1/ f α noise. This study suggests that the roughness distribution is the best option to test KPZ scaling in the growth regime, and provides quantitative data for future comparison with other models or experiments.

Spatiotemporal Modelling of Exposure to Airborne Pollutants

WM3-PD-05 Introduction: Health consequences of environmental pollution depend on the pollution source, its dispersion, and mobility. Given that humans move within their environment and between settings (home, work, leisure), exposure estimates should integrate pathways simultaneously through both space and time. Estimation of exposure is often difficult in environmental epidemiology studies. We present methods for estimating exposure that integrate across the space-time domain of human movement patterns while allowing for socioeconomic factors over the life course. Methods: We show how changes in residential locations of 541 women from Teesside interact with the changing industrial landscape over time to generate individual based exposure estimates. We obtained data on life-long residential, smoking, and socioeconomic history interview. We digitized maps of industrial land use from 1930 to 1990. We abstracted the positions of chimneys from 6 major polluting industries using them to create maps of indices of exposure. We combined the data on residential locations with exposure indices to derive cumulative life-time exposures. Results: Pollution sources and types changed considerably over the study period: For example the inverse distance weighting of exposure estimates for metal works had a maximum of 6885 in the 1930s and of 432 in the 1990s. Asbestos and chemical exposure estimates peaked in the 1960s, whereas values from waste incineration were highest in the 1990s. Women had been living an average of 56.4 (cases) and 55.3 years (controls) in the area. Given the average age of 65 years this indicated a stable population. However, they were mobile within the study area with an average of 6 moves. We observed greater mobility in high social classes in early life compared with more moves in low social classes in later life. This individual mobility led to highly skewed exposure estimates for some pollution types. Discussion: Exposure estimates varied greatly and were depending on personal factors such as changes in address and social class. There is a need to integrate the spatial and temporal information for individuals to obtain precise exposure estimates that are valid proxies of true exposure. Our results suggest that this is particularly important if the health outcomes under study are determined by cumulative exposure. This kind of approach is particularly important if pollution types and sources change dramatically over time as has been the case in many parts of the world.

Semi-Parametric Estimation in the Compositional Modeling of Multicomponent Systems from Raman Spectroscopic Data

Identification and quantification of molecular species are central applications of molecular spectroscopy. In complex multicomponent systems like tissue samples, linear parametric models are often used to estimate the relative concentrations of the biochemical components of the sample. In situations where not all of the components of the sample are known or modeled, such parametric models can suffer from omitted variable bias and result in skewed estimates of component concentrations. We propose a semi-parametric approach that tries to avoid this omitted variable bias by effectively including unknown covariates as a non-parametric term in the regression equation. Constituent concentrations estimated with such partial linear models should outperform strict parametric linear models when the user has limited information on the composition of a multi-constituent system.

Convex hull based skew estimation

Skew estimation and page segmentation are the two closely related processing stages for document image analysis. Skew estimation needs proper page segmentation, especially for document images with multiple skews that are common in scanned images from thick bound publications in 2-up style or postal envelopes with various printed labels. Even if only a single skew is concerned for a document image, the presence of minority regions of different skews or undefined skew such as noise may severely affect the estimation for the dominant skew. Page segmentation, on the other hand, may need to know the exact skew angle of a page in order to work properly. This paper presents a skew estimation method with built-in skew-independent segmentation functionality that is capable of handling document images with multiple regions of different skews. It is based on the convex hulls of the individual components (i.e. the smallest convex polygon that fully contains a component) and that of the component groups (i.e. the smallest convex polygon that fully contain all the components in a group) in a document image. The proposed method first extracts the convex hulls of the components, segments an image into groups of components according to both the spatial distances and size similarities among the convex hulls of the components. This process not only extracts the hints of the alignments of the text groups, but also separate noise or graphical components from that of the textual ones. To verify the proposed algorithms, the full sets of the real and the synthetic samples of the University of Washington English Document Image Database I (UW-I) are used. Quantitative and qualitative comparisons with some existing methods are also provided.

A Hierarchy of Data-Based ENSO Models

AbstractGlobal sea surface temperature (SST) evolution is analyzed by constructing predictive models that best describe the dataset’s statistics. These inverse models assume that the system’s variability is driven by spatially coherent, additive noise that is white in time and are constructed in the phase space of the dataset’s leading empirical orthogonal functions. Multiple linear regression has been widely used to obtain inverse stochastic models; it is generalized here in two ways. First, the dynamics is allowed to be nonlinear by using polynomial regression. Second, a multilevel extension of classic regression allows the additive noise to be correlated in time; to do so, the residual stochastic forcing at a given level is modeled as a function of variables at this level and the preceding ones. The number of variables, as well as the order of nonlinearity, is determined by optimizing model performance.The two-level linear and quadratic models have a better El Niño–Southern Oscillation (ENSO) hindcast skill than their one-level counterparts. Estimates of skewness and kurtosis of the models’ simulated Niño-3 index reveal that the quadratic model reproduces better the observed asymmetry between the positive El Niño and negative La Niña events. The benefits of the quadratic model are less clear in terms of its overall, cross-validated hindcast skill; this model outperforms, however, the linear one in predicting the magnitude of extreme SST anomalies.Seasonal ENSO dependence is captured by incorporating additive, as well as multiplicative forcing with a 12-month period into the first level of each model. The quasi-quadrennial ENSO oscillatory mode is robustly simulated by all models. The “spring barrier” of ENSO forecast skill is explained by Floquet and singular vector analysis, which show that the leading ENSO mode becomes strongly damped in summer, while nonnormal optimum growth has a strong peak in December.

On estimating clock skew for one-way measurements

Owning to the asymmetry of Internet paths, more and more studies have turned to the measurement of one-way metrics. Since the clocks at end systems often behave diversely, the synchronization between end hosts is what we care about all along. In this paper, we firstly propose a general model for clock skew estimation in one-way measurements, which turns the problem of clock skew estimation to the solution of n-dimension equation group, and give the equation group needed based on different presumptions. We then present Piece-wise Reliable Clock Skew Estimation Algorithm (PRCSEA), which introduces reliability test to estimation results and eliminates the extra presumptions needed by other algorithms, such as only one clock adjustment in the measurements. PRCSEA solves the skew estimation problem in a heuristic way, and it can handle many special cases affecting the estimation of clock skew, such as routing change, clock hiccup and network congestion. PRCSEA is the only algorithm that can handle clock drift to the best of our knowledge.

Limitations of a TCP model incorporating population heterogeneity

The variation between individuals in their dose-response characteristics complicates attempts to extract estimates of radiobiological parameters (e.g. α, β, etc) from fits to clinical dose-response data. The use of ‘population’ dose-response models that explicitly account for this variability is necessary to avoid obtaining skewed parameter estimates. In this work, we evaluated an example of a ‘population’ tumour control probability (TCP) model in terms of its ability to provide reliable parameter estimates. This was accomplished by performing fits of this population model to ‘pseudo’ data sets, which were generated with Monte Carlo techniques and based on preset values for the various radiobiological parameters. The fitting exercises illustrated considerable correlations between the model parameters. Especially significant was the large correlation observed between the parameter μ = α/σα used to characterize the level of population heterogeneity in radiosensitivity and the α/β parameter typically used to describe the response to fractionation. The results imply that fits to clinical data may not be able to distinguish between tumours exhibiting a high degree of heterogeneity and a strong β-mechanism and those containing little heterogeneity and having a weak β-mechanism. One implication is that basing the design of optimal fractionation regimes on such fitting results may be error-prone. If in vitro assays are to be used to independently determine biologically reasonable ranges for parameter values, an accurate knowledge of the relationship between in vitro and in vivo dose-response characteristics is required.

Fiducial line based skew estimation

Skew estimation for textual document images is a well-researched topic and numerals of methods have been reported in the literature. One of the major challenges is the presence of interfering non-textual objects of various types and quantities in the document images. Many existing methods require proper separation of the textual objects which are well aligned from the non-textual objects which are mostly nonaligned. Some comparative evaluation work on the existing methods chooses only the text zones of the test image database. Therefore, the object filtering or zoning stage is crucial to the skew detection stage. However, it is difficult if not impossible to design general-purpose filters that are able to discriminate noises from textual components. This paper presents a robust, general-purpose skew estimation method that does not need any filtering or zoning preprocessing. In fact, this method does apply filtering, but not on the input components at the beginning of the detection process, rather on the output spectrum at the end of the detection process. Therefore, the problem of finding a textual component filter has been transformed into finding a convolution filter on the output accumulator array. This method consists of three steps: (1) the calculation of the slopes of the virtual lines that pass through the centroids of all the unique pairs of the connected components in an image, and quantizes the arctangents of the slopes into a 1-D accumulator array that covers the range from - 90 ∘ to + 90 ∘ ; (2) a special convolution on the resultant histogram, after which there remain only the prominent peaks that possibly correspond to the skew angles of the image; (3) the verification of the detection result. Its computational complexity and detection precision are uncoupled, unlike those projection-profile-based or Hough-transform-based methods whose speeds drop when higher precision is in demand. Speedup measures on the baseline implementation are also presented. The University of Washington English Document Image Database I (UWDB-I) contains a large number of scanned document images with significant amount of non-textual objects. Therefore, it is a good image database for evaluating the proposed method.

Log Pearson type 3 quantile estimators with regional skew information and low outlier adjustments

The recently developed expected moments algorithm (EMA) [Cohn et al., 1997] does as well as maximum likelihood estimations at estimating log‐Pearson type 3 (LP3) flood quantiles using systematic and historical flood information. Needed extensions include use of a regional skewness estimator and its precision to be consistent with Bulletin 17B. Another issue addressed by Bulletin 17B is the treatment of low outliers. A Monte Carlo study compares the performance of Bulletin 17B using the entire sample with and without regional skew with estimators that use regional skew and censor low outliers, including an extended EMA estimator, the conditional probability adjustment (CPA) from Bulletin 17B, and an estimator that uses probability plot regression (PPR) to compute substitute values for low outliers. Estimators that neglect regional skew information do much worse than estimators that use an informative regional skewness estimator. For LP3 data the low outlier rejection procedure generally results in no loss of overall accuracy, and the differences between the MSEs of the estimators that used an informative regional skew are generally modest in the skewness range of real interest. Samples contaminated to model actual flood data demonstrate that estimators which give special treatment to low outliers significantly outperform estimators that make no such adjustment.

Labeled carbon dioxide (C18O2): an indicator gas for phase II in expirograms.

Carbon dioxide labeled with 18O (C18O2) was used as a tracer gas for single-breath measurements in six anesthetized, mechanically ventilated beagle dogs. C18O2 is taken up quasi-instantaneously in the gas-exchanging region of the lungs but much less so in the conducting airways. Its use allows a clear separation of phase II in an expirogram even from diseased individuals and excludes the influence of alveolar concentration differences. Phase II of a C18O2 expirogram mathematically corresponds to the cumulative distribution of bronchial pathways to be traversed completely in the course of exhalation. The derivative of this cumulative distribution with respect to respired volume was submitted to a power moment analysis to characterize volumetric mean (position), standard deviation (broadness), and skewness (asymmetry) of phase II. Position is an estimate of dead space volume, whereas broadness and skewness are measures of the range and asymmetry of functional airway pathway lengths. The effects of changing ventilatory patterns and of changes in airway size (via carbachol-induced bronchoconstriction) were studied. Increasing inspiratory or expiratory flow rates or tidal volume had only minor influence on position and shape of phase II. With the introduction of a postinspiratory breath hold, phase II was continually shifted toward the airway opening (maximum 45% at 16 s) and became steeper by up to 16%, whereas skewness showed a biphasic response with a moderate decrease at short breath holding and a significant increase at longer breath holds. Stepwise bronchoconstriction decreased position up to 45 +/- 2% and broadness of phase II up to 43 +/- 4%, whereas skewness was increased up to twofold at high-carbachol concentrations. Under all circumstances, position of phase II by power moment analysis and dead space volume by the Fowler technique agreed closely in our healthy dogs. Overall, power moment analysis provides a more comprehensive view on phase II of single-breath expirograms than conventional dead space volume determinations and may be useful for respiratory physiology studies as well as for the study of diseased lungs.

On more robust estimation of skewness and kurtosis

For both the academic and the financial communities it is a familiar stylized fact that stock market returns have negative skewness and severe excess kurtosis. This stylized fact has been supported by a vast collection of empirical studies. Given that the conventional measures of skewness and kurtosis are computed as an average and that averages are not robust, we ask: “How useful are the measures of skewness and kurtosis used in previous empirical studies?” To answer this question, we provide a survey of robust measures of skewness and kurtosis from the statistics literature and carry out extensive Monte Carlo simulations that compare the conventional measures with the robust measures of our survey. An application of the robust measures to daily S&P500 index data indicates that the stylized facts might have been accepted too readily. We suggest that looking beyond the standard skewness and kurtosis measures can provide deeper and more accurate insight into market returns behavior.

Regression Residuals, Moments, and Their Use in Tests for Normality

In linear regression the unknown true errors are often estimated by the ordinary least squares residuals. These estimates suffer from shrinkage and superimposed normality effects and may give a misleading impression of the true error distribution. A new method, RMOLS, is proposed to improve the estimation of moments by suitably rescaling the moment estimators obtained from least squares residuals. These RMOLS moments give better estimates of skewness and kurtosis coefficients and better power for one class of tests for normality. These properties are demonstrated by a Monte Carlo study under a variety of random error distributions.

Cross correlations among estimators of shape

The regional variability of shape parameters (such as κ for the GEV distribution) may be described by generalized least squares (GLS) regression models that allow shape parameters to be estimated from basin characteristics recognizing the sampling uncertainty in available shape estimators. Implementation of such GLS models requires estimates of the cross‐site correlation of the shape parameter estimators for every pair of sites. Monte Carlo experiments provided the information needed to identify simple power approximations of the relationships between the cross correlation of estimators of skewness γ from [log] Pearson type 3 (P3) data and of the shape parameter κ of both generalized Pareto (GP) and generalized extreme value (GEV) distributions, as functions of the intersite correlation of concurrent flows.

Testing the distribution of error components in panel data models

We propose tests for normality of the error components in panel data models, using estimates of skewness and kurtosis in the components.

A Maastrichtian palaeomagnetic pole for the Pacific plate from a skewness analysis of marine magnetic anomaly 32

The asymmetry (skewness) of marine magnetic anomaly 32 (72.1–73.3 Ma) on the Pacific plate has been analysed in order to estimate a new palaeomagnetic pole. Apparent effective remanent inclinations of the seafloor magnetization were calculated from skewness estimates of 108 crossings of anomaly 32 distributed over the entire Pacific plate and spanning a great-circle distance of ∼12 000 km. The data were inverted to obtain a palaeomagnetic pole at 72.1°N, 26.8°E with a 95 per cent confidence ellipse having a 4.0° major semi-axis oriented 98° clockwise of north and a 1.8° minor semi-axis; the anomalous skewness is 14.2° ± 3.7°. The possible dependence of anomalous skewness on spreading rate was investigated with two empirical models and found to have a negligible effect on our palaeopole analysis over the range of relevant spreading half-rates, ∼25 to ∼90 mm yr−1. The new pole is consistent with the northward motion for the Pacific plate indicated by coeval palaeocolatitude and palaeoequatorial data, but differs significantly from, and lies to the northeast of, coeval seamount poles. We attribute the difference to unmodelled errors in the seamount poles, mainly in the declinations. Comparison with the northward motion inferred from dated volcanoes along the Hawaiian–Emperor seamount chain indicates 13° of southward motion of the Hawaiian hotspot since 73 Ma. When the pole is reconstructed with the Pacific plate relative to the Pacific hotspots, it differs by 14°–18° from the position of the pole relative to the Indo–Atlantic hotspots. This has several possible explanations including bias in one or more of the palaeomagnetic poles, motion between the Pacific and Indo–Atlantic hotspots, and errors in plate reconstructions relative to the hotspots.

The “normality” of El Niño

The amplitude of the El Niño‐Southern Oscillation (ENSO) would be normally distributed if the coupled Pacific ocean‐atmosphere were a linear system forced by Gaussian weather noise. Moment estimates of skewness and kurtosis demonstrate that this is not the case for monthly mean anomalies in Pacific sea surface temperatures during 1950–97. The noted predominance of El Niño events compared to La Niña events is related to the high skewness in the eastern Pacific. Skewness and kurtosis both exhibit an intriguing geographical variation from positive in the eastern to negative in the western Pacific. We have also examined Niño‐3 indices generated by three climate models having widely different complexity. These exhibit a wide range of skewness and kurtosis values rather different from those found for the observations. Skewness and kurtosis can be used to diagnose non‐linear processes and provide powerful tools for validating models, and for testing observed sea‐surface temperatures for the presence of possible climate change.