A new distribution‐free k‐sample test: Analysis of kernel density functionals

ABSTRACTIn this article, we propose mixtures of skew Laplace normal (SLN) distributions to model both skewness and heavy-tailedness in the neous data set as an alternative to mixtures of skew Student-t-normal (STN) distributions. We give the expectation–maximization (EM) algorithm to obtain the maximum likelihood (ML) estimators for the parameters of interest. We also analyze the mixture regression model based on the SLN distribution and provide the ML estimators of the parameters using the EM algorithm. The performance of the proposed mixture model is illustrated by a simulation study and two real data examples.

Objective To investigate the clinical efficacy of laparoscopic splenectomy combined with pericardial devascularization in the treatment of cirrhotic patients with cirrhotic portal hypertension. Methods The retrospective and descriptive study was conducted. The clinicopathological data of 425 patients with cirrhotic portal hypertension who were admitted to Northern Jiangsu People′s Hospital Affiliated to Yangzhou University were collected. There were 289 males and 136 females, aged (53±11)years, with a range from 21 to 79 years. All the patients were allocated into 3 periods according to the operation time, including 100 patients of early period from February 2012 to March 2014, 156 patients of mature technology period from April 2014 to August 2016, and 169 patients of technology innovation period from september 2016 to December 2018. The patients of early period and mature technology period underwent laparoscopic splenectomy combined with pericardial devascularization, and the patients of technology innovation period underwent vagus nerve-preserving laparoscopic splenectomy combined with pericardial devascularization. Observation indicators: (1) surgical situations; (2) postoperative situations; (3) follow-up. Patients were followed up by outpatient examination to detect the upper digestive rebleeding, gastric retention, and diarrhea up to March 2019. Sequential therapy of endoscopic variceal ligation (EVL) was slectively performed on patients based on results of gastroscopy. Measurement data with normal distribution were represented as Mean±SD, and comparison between groups was analyzed using ANOVA, and paired comparison was analyzed using the t test. Measurement data with skewed distribution were represented as M (range), and comparison between groups was anlyzed using the Kruskal-Wallis rank sum test, and paired comparison was analyzed using the rank sum test. Count data were described as absolute numbers or percentages, and comparison between groups was analyzed using the chi-square test and Fisher exact probability. Results (1) Surgical situations: the operation time, volume of intraoperative blood loss, cases with intraoperative blood transfusion, cases with conversion to open surgery, and cases with emergency operation for bleeding were (187±46)minutes, 150 mL (range, 50-1 300 mL), 2, 2 , 1 for patients of early period, (164±22)minutes, 50 mL (range, 30-100 mL), 1, 1, 1 for patients of mature technology period, and (150±18)minutes, 50 mL (range, 10-300 mL), 0 , 0 , 0 for patients of technology innovation period, respectively. There were significant differences in the operation time and volume of intraoperative blood loss between the three groups (F=55.482, χ2=94.620, P 0.05). (2) Postoperative situations: 425 patients had oral aspirin enteric-coated tablets for prevention of thrombus, with no perioperative death. Duration of postoperative hospital stay, cases with portal vein thrombosis at postoperative 7 days, cases with pancreatic fistula, cases with pulmonary infection, and cases with abdominal infection were (11.0±2.9)days, 46, 2, 1, 0 for patients of early period, (9.9±1.7)days, 81, 3, 0, 0 for patients of mature technology period, and (8.8±1.3)days, 83, 2, 1, 1 for patients of technology innovation period, respectively. There was a significant difference in the duration of postoperative hospital stay between the three groups (F=39.836, P 0.05) and no significant difference in the cases with pancreatic fistula, cases with pulmonary infection, or cases with abdominal infection between the three groups (P>0.05). Patients with portal vein thrombosis at postoperative 7 days had oral aspirin enteric-coated tablets or warfarin for treatment. Patients with pancreatic fistula, pulmonary infection, and abdominal infection were cured and discharged after conservative treatment. (3) Follow-up: all the 425 patients were followed up for 1-72 months, with a median follow-up of 36 months. Of the 425 patients, 261 underwent postoperative sequential therapy of EVL, including 133 patients of mature technology period and 128 patients of technology innovation period. The incidence rate of upper digestive rebleeding was 3.83%(10/261) of the 261 patients undergoing postoperative sequential therapy of EVL and 17.68%(29/164) of 164 patients without postoperative sequential therapy of EVL, showing a significant difference between them (χ2=23.185, P<0.05). The incidence rates of gastric retention and diarrhea were 96.24%(128/133) and 61.65%(82/133) for 133 patients undergoing sequential therapy of EVL in mature technology period, and 1.56%(2/128) and 3.91%(5/128) for 128 patients undergoing sequential therapy of EVL in technology innovation period, showing significant differences between them (χ2=233.876, 97.883, P<0.05). Conclusions It is safe and feasible of laparoscopic splenectomy combined with pericardial devascularization for patients with cirrhotic portal hypertension, and intraoperative vagus nerve-preserving can reduce volume of intraoperative blood loss and incidence of postoperative complications. Key words: Liver cirrhosis; Portal hypertension; Splenectomy; Pericardial devascularization; Vagus nerve; Laparoscopy

Gene-gene interaction plays an important role in the etiology of complex diseases, which may exist without a genetic main effect. Most current statistical approaches, however, focus on assessing an interaction effect in the presence of the gene's main effects. It would be very helpful to develop methods that can detect not only the gene's main effects but also gene-gene interaction effects regardless of the existence of the gene's main effects while adjusting for confounding factors. In addition, when a disease variant is rare or when the sample size is quite limited, the statistical asymptotic properties are not applicable; therefore, approaches based on a reasonable and applicable computational framework would be practical and frequently applied. In this study, we have developed an extended support vector machine (SVM) method and an SVM-based pedigree-based generalized multifactor dimensionality reduction (PGMDR) method to study interactions in the presence or absence of main effects of genes with an adjustment for covariates using limited samples of families. A new test statistic is proposed for classifying the affected and the unaffected in the SVM-based PGMDR approach to improve performance in detecting gene-gene interactions. Simulation studies under various scenarios have been performed to compare the performances of the proposed and the original methods. The proposed and original approaches have been applied to a real data example for illustration and comparison. Both the simulation and real data studies show that the proposed SVM and SVM-based PGMDR methods have great prediction accuracies, consistencies, and power in detecting gene-gene interactions.

Extension of SO-PLS to multi-way arrays: SO-N-PLS

Clustered data are common in biomedical research. Observations in the same cluster are often more similar to each other than to observations from other clusters. The intraclass correlation coefficient (ICC), first introduced by R. A. Fisher, is frequently used to measure this degree of similarity. However, the ICC is sensitive to extreme values and skewed distributions, and depends on the scale of the data. It is also not applicable to ordered categorical data. We define the rank ICC as a natural extension of Fisher's ICC to the rank scale, and describe its corresponding population parameter. The rank ICC is simply interpreted as the rank correlation between a random pair of observations from the same cluster. We also extend the definition when the underlying distribution has more than two hierarchies. We describe estimation and inference procedures, show the asymptotic properties of our estimator, conduct simulations to evaluate its performance, and illustrate our method in three real data examples with skewed data, count data, and three-level ordered categorical data.

ABSTRACTThe paper presents 3D diffraction imaging based on the spectral decomposition of a different combination of selective or partial images. These images are obtained by the pre‐stack asymmetric migration procedure, which is weighted data summation. Spectral decomposition is done in the Fourier domain with respect to spatial dip and azimuth angles. Numerical examples with the application of different workflows for the synthetic and real data examples demonstrate detailed reliable reconstruction of the fractured zones and reliable reconstruction of fracture orientation on synthetic and real 3D data examples.

A century ago, when Student’s t-statistic was introduced, no one ever imagined its increasing applicability in the modern era. It finds applications in highly multiple hypothesis testing, feature selection and ranking, high dimensional signal detection, etc. Student’s t-statistic is constructed based on the empirical distribution function (EDF). An alternative choice to the EDF is the kernel density estimate (KDE), which is a smoothed version of the EDF. The novelty of the work consists of an alternative to Student’s t-test that uses the KDE technique and exploration of the usefulness of KDE based t-test in the context of its application to large-scale simultaneous hypothesis testing. An optimal bandwidth parameter for the KDE approach is derived by minimizing the asymptotic error between the true p-value and its asymptotic estimate based on normal approximation. If the KDE-based approach is used for large-scale simultaneous testing, then it is interesting to consider, when does the method fail to manage the error rate? We show that the suggested KDE-based method can control false discovery rate (FDR) if total number tests diverge at a smaller order of magnitude than N3/2, where N is the total sample size. We compare our method to several possible alternatives with respect to FDR. We show in simulations that our method produces a lower proportion of false discoveries than its competitors. That is, our method better controls the false discovery rate than its competitors. Through these empirical studies, it is shown that the proposed method can be successfully applied in practice. The usefulness of the proposed methods is further illustrated through a gene expression data example.

ABSTRACTA mixture model is proposed to analyze a bivariate interval censored data with cure rates. There exist two types of association related with bivariate failure times and bivariate cure rates, respectively. A correlation coefficient is adopted for the association of bivariate cure rates and a copula function is applied for bivariate survival times. The conditional expectation of unknown quantities attributable to interval censored data and cure rates are calculated in the E-step in ES (Expectation-Solving algorithm) and the marginal estimates and the association measures are estimated in the S-step through a two-stage procedure. A simulation study is performed to evaluate the suggested method and a real data from HIV patients is analyzed as a real data example.

The issue of multicollinearity has long been acknowledged in statistical modelling; however, it is often untreated in the most of published papers. Indeed, the use of methods for multicollinearity correction is still scarce. One important reason is that despite many proposed methods, little is known about their strength or performance. We compare the statistical properties and performance of four main techniques to correct multicollinearity, i.e., Ridge Regression (R-R), Principal Components Regression (PC-R), Partial Least Squares Regression (PLS-R), and Lasso Regression (L-R), in both a simulation study and two real data examples used for modelling volumes of heart and Thyroid as a function of clinical and anthropometric parameters. We find that when the statistical approaches were used to address different levels of collinearity, we observed that R-R, PC-R and PLS-R appeared to have a somewhat similar behavior, with a slight advantage for the PLS-R. Indeed, in all implemented cases, the PLS-R always provided the smallest value of root mean square error (RMSE). When the degree of collinearity was moderate, low or very low, the L-R method had also somewhat similar performance to other methods. Furthermore, correction methods allowed us to provide stable and trustworthy parameter estimates for predictors in the modelling of heart and Thyroid volumes. Therefore, this work will contribute to highlighting performances of methods used only for situations ranging from low to very high multicollinearity.

Most deconvolution algorithms try to transform the seismic wavelet into spikes by designing inverse filters that remove an estimated seismic wavelet from seismic data. We assume that seismic trace subtle discontinuities are associated with acoustic impedance contrasts and can be characterized by wavelet transform spectral ridges, also called modulus maxima lines (WTMML), allowing us to improve seismic resolution by using the wavelet transform. Specifically, we apply the complex Morlet continuous wavelet transform (CWT) to each seismic trace and compute the WTMMLs. Then, we reconstruct the seismic trace with the inverse continuous wavelet transform from the computed WTMMLs with a broader band complex Morlet wavelet than that used in the forward CWT. Because the reconstruction process preserves amplitude and phase along different scales, or frequencies, the result looks like a deconvolution method. Considering this high-resolution seismic representation as a reflectivity approximation, we estimate the relative acoustic impedance (RAI) by filtering and trace integrating it. Conventional deconvolution algorithms assume the seismic wavelet to be stochastic, while the CWT is implicitly time varying such that it can be applied to both depth and time-domain data. Using synthetic and real seismic data, we evaluated the effectiveness of the methodology on detecting seismic events associated with acoustic impedance changes. In the real data examples, time and in-depth RAI results, show good correlation with real P-impedance band-pass data computed using more rigorous commercial inversion software packages that require well logs and low-frequency velocity model information.

Chapter 12 - Specific Methods

In this paper we propose a longitudinal credit rating model which accounts for the serial correlation in the ratings. We achieve this by imposing an autoregressive structure of order one on the errors of a multivariate ordinal regression model. The longitudinal structure of the model improves significantly both the goodness-of-fit and predictive performance compared to static models. By modeling the joint distribution of the ratings over time, the framework allows us to obtain predictions conditional on the past rating history of a firm, which clearly out-perform the unconditional predictions both in- and out-of-sample. This shows the importance of incorporating past rating information in the prediction. Another upside lies in the framework’s ability to deal with missing rating observations. A real data example is provided by using a sample of US publicly traded corporates rated by S&P for the years 1985–2016. The determinants of corporate credit ratings are pre-selected using the ordinal version of the least absolute shrinkage and selection operator (LASSO). Additionally, as a model extension we allow the regression coefficients of the selected variables to vary over time in the longitudinal model. This allows us to gain a better understanding of the drivers and evolution of the rating behavior over the sample period. Finally, based on the longitudinal model with LASSO selected variables, we find evidence that S&P exhibits procyclical aspects in their rating behavior. • A credit rating model accounting for the serial correlation in the ratings. • A variable selection exercise is performed using ordinal LASSO. • Predictions conditional on the past rating history of a firm. • Longitudinal structure improves goodness-of-fit and predictive performance. • Real data example of US corporates rated by S&P for the years 1985–2016.

When analyzing functional MRI data, several thresholding procedures are available to account for the huge number of volume units or features that are tested simultaneously. The main focus of these methods is to prevent an inflation of false positives. However, this comes with a serious decrease in power and leads to a problematic imbalance between type I and type II errors.In this paper, we show how estimating the number of activated peaks or clusters enables one to estimate post-hoc how powerful the selection procedure performs. This procedure can be used in real studies as a diagnostics tool, and raises awareness on how much activation is potentially missed.The method is evaluated and illustrated using simulations and a real data example. Our real data example illustrates the lack of power in current fMRI research.

Analysis of variance.

In the early stage of acoustic full-waveform inversion (AFWI), it is important to exploit the long-wavelength features of the gradient and suppress its short-wavelength features to update the background velocity. However, due to strong near-offset PP reflections and multiples within the pressure data, conventional AFWI sometimes primarily reconstructs the short-wavelength features of a given model and fails to converge on a reliable subsurface P-wave velocity model. Therefore, this study, we propose the usage of pseudo-horizontal particle acceleration (pseudo-ax) data for AFWI, rather than the original pressure data. Because the amplitudes of PP reflections are implicitly weighted according to the reflection angle in pseudo-ax data, the near-offset PP reflections and multiples of the pseudo-ax data are much weaker than those of the pressure data. As a result, AFWI using pseudo-ax data focuses on reconstructing the longer-wavelength features of a given model in the early iterations, and then gradually reconstructs short-wavelength features as the inversion process continues. Using synthetic and real data examples for the Volve oilfield in the North Sea, we examined the effects and feasibility of this strategy. In the synthetic data example, the proposed strategy rapidly reduced far-offset data misfits related to long-wavelength feature updates and achieved smaller model misfits than the conventional strategy. The real data example showed that the velocity model reconstructed using the proposed strategy flattened some of the reflectors at the angle-domain common-image gathers (ADCIGs) better than the velocity model obtained using the conventional strategy. These findings demonstrate that our strategy converges closer to the real P-wave velocity model than the conventional strategy by building a hierarchical velocity model from long- to short-wavelength structures.