Large Observations Research Articles

Reliability Estimation of Scale Parameter in Type II Generalized Half-Logistic Distribution from Doubly Censored Samples Based on Monte Carlo Simulation

Objectives: This article deals with estimation of the reliability function for one-parameter Type II Generalized Half- Logistic distribution (Type II GHLD). Methods: The Maximum likelihood (ML) and Approximate Maximum likelihood (AML) methods provided by Jilani et.al. 1 . Findings: Comparisons between the estimators were made using Monte Carlo Simulation based on statistical indicter bias and mean squared error (MSE). We have generated 3000 random samples of size n=10(5)20 from a standard one-parameter Type II GHLD with = 0.5, 1.5 and 2.0. Each sample is then ordered and from this sample a doubly (including left and right) censored sample is considered, by censoring r smallest observations and s largest observations with all possible choices of r and s corresponding to this resultant sample we compute MLEs (using Newton-Raphson method), the LAMLE and unbiased LAMLE . Finally, the results are explained with tables. Novelty: This study has empirically proves that all the three reliability estimators have the same asymptotic variance. Hence, in this case, any one of the three estimators can be used but preferable estimator based unbiased estimator. Keywords: Maximum likelihood estimation, Approximate Maximum likelihood estimation, Bias, Mean squared error, Variances

O-311 Evaluating the Reproductive Potential of Azoospermic Men by Profiling the Genome of Surgically Retrieved Spermatozoa

Abstract Study question Can whole exome sequencing of surgically retrieved spermatozoa from azoospermic men pinpoint mutations related to the etiology of their infertility and ability to support pregnancy? Summary answer Identifying key germline mutations involved in spermatogenesis helps explain reproductive failure, regardless of the etiology of the azoospermia. What is known already Azoospermia accounts for approximately 15% of male factor infertility cases. Although it can be caused by pre-testicular factors, the most recognized forms are testicular and post-testicular. Post-testicular azoospermia is mainly attributed to a mechanical obstruction, whereas testicular azoospermia, the most challenging form, is characterized by scattered functional germinal epithelia that may fail to support the meiotic process during sperm development. To elucidate the etiology of this condition, genetic studies on somatic cells have been carried out. Here, we perform whole exome sequencing (WES) on surgically retrieved spermatozoa to preferentially detect germline mutations that may be passed on to offspring. Study design, size, duration Over 3 years, we recruited patients undergoing epididymal sperm aspiration for acquired obstructive azoospermia (OA; n = 19) or testicular biopsy for nonobstructive azoospermia (NOA; n = 11). Eight men were included as fertile controls. Copy number variants (CNVs) and gene mutation profiles were obtained through WES and compared between the OA and NOA cohorts, followed by sub-analyses within those two categories according to whether they generated a clinical pregnancy (fertile) or not (infertile), while controlling for maternal age. Participants/materials, setting, methods Spermatozoal DNA was extracted and amplified from the surgically retrieved specimens (concentration, 742±520 ng/ul; quality, 1.7±0.1 nm). CNVs and gene mutations were detected using CLC Genomic Server 9.0. Genes were considered duplicated or deleted when the read depth was >1.5 or < 0.5 times the median read depth in the control. Common mutations were compared between the OA and NOA cohorts, as well as according to the couples’ clinical outcomes. Female partners had negative infertility workups. Main results and the role of chance Of 30 men (paternal age, 42.3±7yrs), 19 OA men underwent epididymal sperm retrievals (concentration, 1.1±4x106/ml, 9±12% motility), while 11 NOA men underwent testicular biopsies (concentration, 0.03±0.4x106/ml, 0.5±1% motility). WES did not indicate a significant difference in sperm aneuploidy between the two etiologies (OA, 1.7%; NOA, 1.8%) compared to the control (1.1%). In OA patients, only 3 housekeeping-related genes were deleted, while in the NOA cohort, 5 genes involved in RNA transcription (POLR2L), apoptosis (AP5M1), and basic spermiogenic functions (AP1S2, AP1G2, APOE) were deleted. OA patients and their partners (maternal age, 36.8±4yrs) underwent 19 ICSI cycles resulting in a delivery rate of 47.4% (9/19). Those able to reproduce (n = 9) shared a mutation in ZNF749, specifically affecting sperm production. The infertile men (n = 10) all shared a PRB1 deletion, controlling essential DNA replication. NOA men and their partners (maternal age, 38.2±2yrs) underwent 11 ICSI cycles, yielding a delivery rate of 72.7% (8/11). The fertile men (n = 8) all shared a MPIG6B deletion, involved in stem cell lineage differentiation. All of their infertile counterparts (n = 3) presented gene deletions not only involved in spermato/spermio-genesis (n = 4) but, most importantly, also superimposed with those encoding early embryonic development (MBD5, CCAR1, PMEPA1, POLK, REC8, REPIN1, MAPRE3, ARL4C). Limitations, reasons for caution Although maternal age was controlled for, confounding factors related to the female partner cannot entirely be excluded. While men unable to reproduce shared common gene mutations providing information about their condition, these findings still need to be confirmed in larger observations. Wider implications of the findings By performing WES, we were able to identify specific mutations associated with compromised embryo developmental competence of surgically retrieved spermatozoa. DNA sequencing technologies help identify gametes capable of sustaining a pregnancy even in the most severe form of male infertility, laying the groundwork for precision medicine in this field. Trial registration number N/A

Comparing Outlier Detection Methods using Boxplot Generalized Extreme Studentized Deviate and Sequential Fences

Outliers identification is essential in data analysis since it can make wrong inferential statistics. This study aimed to compare the performance of Boxplot, Generalized Extreme Studentized Deviate (Generalized ESD), and Sequential Fences method in identifying outliers. A published dataset was used in the study. Based on preliminary outlier identification, the data did not contain outliers. Each outlier detection method's performance was evaluated by contaminating the original data with few outliers. The contaminations were conducted by replacing the two smallest and largest observations with outliers. The analysis was conducted using SAS version 9.2 for both original and contaminated data. We found that Sequential Fences have outstanding performance in identifying outliers compared to Boxplot and Generalized ESD.

On the generation of internal waves by river plumes in subcritical initial conditions

Internal waves (IWs) in the ocean span across a wide range of time and spatial scales and are now acknowledged as important sources of turbulence and mixing, with the largest observations having 200 m in amplitude and vertical velocities close to 0.5 m s−1. Their origin is mostly tidal, but an increasing number of non-tidal generation mechanisms have also been observed. For instance, river plumes provide horizontally propagating density fronts, which were observed to generate IWs when transitioning from supercritical to subcritical flow. In this study, satellite imagery and autonomous underwater measurements are combined with numerical modeling to investigate IW generation from an initial subcritical density front originating at the Douro River plume (western Iberian coast). These unprecedented results may have important implications in near-shore dynamics since that suggest that rivers of moderate flow may play an important role in IW generation between fresh riverine and coastal waters.

Flexible semiparametric generalized Pareto modeling of the entire range of rainfall amount

AbstractPrecipitation amounts at daily or hourly scales are skewed to the right, and heavy rainfall is poorly modeled by a simple gamma distribution. An important yet challenging topic in hydrometeorology is to find a probability distribution that is able to model well low, moderate, and heavy rainfall. To address this issue, we present a semiparametric distribution suitable for modeling the entire range of rainfall amount. This model is based on a recent parametric statistical model called the class of extended generalized Pareto distributions (EGPDs). The EGPD family is in compliance with extreme value theory for both small and large values, while it keeps a smooth transition between these tails and bypasses the hurdle of selecting thresholds to define extremes. In particular, return levels beyond the largest observation can be inferred. To add flexibility to this EGPD class, we propose to model the transition function in a nonparametric fashion. A fast and efficient nonparametric scheme based on Bernstein polynomial approximations is investigated. We perform simulation studies to assess the performance of our approach. It is compared to two parametric models: a parametric EGPD and the classical generalized Pareto distribution (GPD), the latter being only fitted to excesses above a high threshold. We also apply our semiparametric version of EGPD to a large network of 180 precipitation time series over France.

An empirical saddlepoint approximation based method for smoothing survival functions under right censoring

AbstractThe Kaplan–Meier (KM) estimator is ubiquitously used for estimating survival functions, but it provides only a discrete approximation at the observation times and does not deliver a proper distribution if the largest observation is censored. Using KM as a starting point, we devise an empirical saddlepoint approximation‐based method for producing a smooth survival function that is unencumbered by choice of tuning parameters. The procedure inverts the moment generating function (MGF) defined through a Riemann–Stieltjes integral with respect to an underlying mixed probability measure consisting of the discrete KM mass function weights and an absolutely continuous exponential right‐tail completion. Uniform consistency, and weak and strong convergence results are established for the resulting MGF and its derivatives, thus validating their usage as inputs into the saddlepoint routines. Relevant asymptotic results are also derived for the density and distribution function estimates. The performance of the resulting survival approximations is examined in simulation studies, which demonstrate a favourable comparison with the log spline method (Kooperberg & Stone, 1992) in small sample settings. For smoothing survival functions we argue that the methodology has no immediate competitors in its class, and we illustrate its application on several real data sets. The Canadian Journal of Statistics 47: 238–261; 2019 © 2019 Statistical Society of Canada

Pathogenetically targeted method for conservative treatment of obesity and overweight correction

This review of literature presents modern pathogenetic treatment options for obesity and overweight correction including the optimization of the motor function, nutrition education, drug therapy, surgical techniques and psychotherapy. The need for a multidisciplinary approach to the development of combined treatment programs is underlined taking into account the multifactorial pathogenesis of obesity. A combination of optimal physical activity and diet therapy with active personal involvement in the process of recovery is accentuated among the priority areas of excess body weight correction, as well as the treatment and prevention of obesity. It is shown that the physical rehabilitation should focus on the individualization of the physical exertion, its adequate dosing and intensity control using heart rate monitors to ensure the safety and effectiveness of the training sessions. The article also presents data on the effectiveness of rational medical and other types of treatment of obesity when the adjustment of physical activities and nutrition is insufficient. In particular, the results of the world's largest observation program of safe weight loss for the treatment of patients with alimentary obesity held in Russia from 2012 to 2015 are described.

Does abiraterone withdrawal syndrome (AWS) exist also in metastatic castration-resistant prostate cancer (mCRPC) first-line setting?

344 Background: AWS is a recently phenomenon observed in mCRPC patients (pts) characterized by a PSA reduction with or without objective response after abiraterone acetate (AA) discontinuation. This syndrome has clinical features similar to antiandrogen withdrawal syndrome and was described in pts who treated with AA in the post-docetaxel setting. At the best of our knowledge, to date AWS was never described in chemo-naïve mCRPC pts. Methods: We retrospectively reviewed clinical records of mCRPC pts treated with first-line AA at our Institution. All pts were treated with AA 1,000 mg + prednisone (PDN) 10 mg po daily; the treatment was continued until progression disease (PD) which required an imaging confirmation too. After PD, we also discontinued the PDN administration. For each pt we recorded pre and post-AA clinical history, treatment details and outcomes. AWS was defined by PSA reduction ≥ 25% compared to the AA-end values observed in the first month after AA stop. Results: From September 2014, eight pts received first-line AA and, to date, 6 patients (75%) who discontinued the treatment due to PD are evaluable for AWS occurrence. We observed an AWS in 2/6 (33.3%). The first patient, a 76 year-old man, who experienced a PD after 12 wks AA treatment, had a 69% reduction in PSA with PSA dropping from 60 ng/mL to 19.47 ng/mL after about 30 days from the discontinuation. The second patient, 83 years old, treated with AA for 12 weeks, had a reduction in PSA from 112.2 ng/mL to 55 ng/mL at one-month (51% reduction) and to 35.36 ng/mL at two months (68.5% reduction) after AA and PDN discontinuation; after 9 wks the AWS is still ongoing. Conclusions: Notwithstanding the limits of the small sample size, our data shows for the first time that AWS can be observed also in mCRPC patients receiving AA as first-line treatment. Larger observations are needed to establish frequency and clinical role of this phenomenon. Although pathogenetic mechanisms and predictive factors are still unclear, AWS may represent a possibility to delay the second line start for mCRPC pts.

Increasing the Accuracy of Mapping Urban Forest Carbon Density by Combining Spatial Modeling and Spectral Unmixing Analysis

Accurately mapping urban vegetation carbon density is challenging because of complex landscapes and mixed pixels. In this study, a novel methodology was proposed that combines a linear spectral unmixing analysis (LSUA) with a linear stepwise regression (LSR), a logistic model-based stepwise regression (LMSR) and k-Nearest Neighbors (kNN), to map the forest carbon density of Shenzhen City of China, using Landsat 8 imagery and sample plot data collected in 2014. The independent variables that contributed to statistically significantly improving the fit of a model to data and reducing the sum of squared errors were first selected from a total of 284 spectral variables derived from the image bands. The vegetation fraction from LSUA was then added as an independent variable. The results obtained using cross-validation showed that: (1) Compared to the methods without the vegetation information, adding the vegetation fraction increased the accuracy of mapping carbon density by 1%–9.3%; (2) As the observed values increased, the LSR and kNN residuals showed overestimates and underestimates for the smaller and larger observations, respectively, while LMSR improved the systematical over and underestimations; (3) LSR resulted in illogically negative and unreasonably large estimates, while KNN produced the greatest values of root mean square error (RMSE). The results indicate that combining the spatial modeling method LMSR and the spectral unmixing analysis LUSA, coupled with Landsat imagery, is most promising for increasing the accuracy of urban forest carbon density maps. In addition, this method has considerable potential for accurate, rapid and nondestructive prediction of urban and peri-urban forest carbon stocks with an acceptable level of error and low cost.

Robust bias estimation for Kaplan–Meier survival estimator with jackknifing

For reducing bias of functionals of the Kaplan–Meier survival estimator, the jackknifing approach as proposed by Stute and Wang is a natural choice. We have extended their jackknifing approach to cover the case where the largest observation is censored by using different imputation approaches of the largest censored observations as proposed by Khan and Shaw. This modification to the existing formula reduces the number of conditions for creating jackknife bias estimates to one from the original two, and also avoids the problem in which the Kaplan–Meier estimator can be badly underestimated by the existing jackknife formula. Furthermore, we have studied broadly the behavior of the jackknife estimate of bias under varying configurations of censoring level, sample size, and distribution of censoring time and lifetime. This empirical research has explored some new findings about the robust calculation of bias particularly when censoring level is high—for example, the bias tends to zero as the censoring level tends to 100% although in the normal case the bias is zero as the censoring level is 0%.

Site monitoring of suction and temporary pore water pressure in an ancient landslide in the Three Gorges reservoir area, China

Rainfall is the main factor influencing the stability of landslides, but the precise mechanisms and processes are still poorly known. Unsaturated soil mechanics can be used to study how suction and temporary pore water pressure affect landslide stability. During rainfall, the groundwater level in the landslide will change, and the suction and temporary pore water pressure will also change with time and rainfall. Construction of a field observation well is an effective method of studying changes in suction. An observation well was constructed in an ancient landslide in the Three Gorges reservoir area in China. The well has a depth of 20 m, a diameter of 2 m, and is the largest observation well for monitoring of suction and temporary water pressure in the world. Suction, temporary water pressure, and rainfall were measured between October 2002 and December 2004; this is the longest observation period for this type of study. Analysis of the results shows that the distribution of suction is determined by the depth, soil materials, gradation, and structure of the landslide. The changes in suction are related to the intensity and duration time of rainfall, the season, and the climate. If the suction does not change promptly after rain, there is a time difference between the timing of rainfall and of suction change. The suction varied between 0 and 15 kPa. These conclusions form a basis for further scientific studies on how rainfall affects landslides.

A Paper City: On History, Maps, and Map Collections in 18th and 19th Century Paris

ABSTRACTThis essay considers how maps became implicated in historical inquiry, with particular reference to the city of Paris. Three interrelated episodes are discussed, from the early eighteenth century to the mid-nineteenth century, each associated with specific mapmakers and collectors whose activities shaped the early development of map history. These episodes reveal how maps were historicized in different ways in this period, initially as images created in the present to reveal the past and eventually as objects of historical interest in their own right. It is further argued that this intellectual shift was associated with a growing awareness, especially among state officials, that the study and collection of historic maps had important geopolitical implications. In tracing this story across three episodes in a single urban setting, the essay seeks to make larger observations about the relationship between the map as a visual representation, the map collection as an urban ‘assemblage’ of geographical information, and the city as a physical environment.

An Estimator of Heavy Tail Index through the Generalized Jackknife Methodology

In practice, sometimes the data can be divided into several blocks but only a few of the largest observations within each block are available to estimate the heavy tail index. To address this problem, we propose a new class of estimators through the Generalized Jackknife methodology based on Qi’s estimator (2010). These estimators are proved to be asymptotically normal under suitable conditions. Compared to Hill’s estimator and Qi’s estimator, our new estimator has better asymptotic efficiency in terms of the minimum mean squared error, for a wide range of the second order shape parameters. For the finite samples, our new estimator still compares favorably to Hill’s estimator and Qi’s estimator, providing stable sample paths as a function of the number of dividing the sample into blocks, smaller estimation bias, and MSE.

Multivariate extreme value analysis and its relevance in a metallographical application

Motivated from extreme value (EV) analysis for large non-metallic inclusions in engineering steels and a real data set, the benefit of choosing a multivariate EV approach is discussed. An extensive simulation study shows that the common univariate setup may lead to a high proportion of mis-specifications of the true EV distribution, as well as that the statistical analysis is considerably improved when being based on the respective data of r largest observations, with r appropriately chosen. Results for several underlying distributions and various values of r are presented along with effects on estimators for the parameters of the generalized EV family of distributions.

A new bounded log-linear regression model

In this paper we introduce a new regression model in which the response variable is bounded by two unknown parameters. A special case is a bounded alternative to the four parameter logistic model. The four parameter model which has unbounded responses is widely used, for instance, in bioassays, nutrition, genetics, calibration and agriculture. In reality, the responses are often bounded although the bounds may be unknown, and in that situation, our model reflects the data-generating mechanism better. Complications arise for the new model, however, because the likelihood function is unbounded, and the global maximizers are not consistent estimators of unknown parameters. Although the two sample extremes, the smallest and the largest observations, are consistent estimators for the two unknown boundaries, they have a slow convergence rate and are asymptotically biased. Improved estimators are developed by correcting for the asymptotic biases of the two sample extremes in the one sample case; but even these consistent estimators do not obtain the optimal convergence rate. To obtain efficient estimation, we suggest using the local maximizers of the likelihood function, i.e., the solution to the likelihood equations. We prove that, with probability approaching one as the sample size goes to infinity, there exists a solution to the likelihood equation that is consistent at the rate of the square root of the sample size and it is asymptotically normally distributed.

Intersatellite Differences of HIRS Longwave Channels Between NOAA-14 and NOAA-15 and Between NOAA-17 and METOP-A

Intersatellite differences of the High-Resolution Infrared Radiation Sounder (HIRS) longwave channels (channels 1-12) between National Oceanic and Atmospheric Administration 14 (NOAA-14) and NOAA-15 and between NOAA-17 and METOP-A are examined. Two sets of colocated data are incorporated in the examination. One data set is obtained during periods when equator crossing times of two satellites are very close to each other, and the data set is referred to as global simultaneous nadir overpass observation (SNO). The other data set is based on multiyear polar SNOs. The examination shows that intersatellite differences (ISDs) of temperature-sounding channels from lower stratosphere to lower troposphere, i.e., channels 3-7, are correlated with their corresponding lapse rate factors. Many of the channels also vary with respect to channel brightness temperatures; however, for the upper tropospheric temperature channel (channel 4), the patterns of ISDs from low latitudes and high latitudes are very different due to the fact that the latitudinal variation of brightness temperature does not necessarily follow the latitudinal variation of the temperature lapse rate. The differences between observations in low latitudes and high latitudes form “fork” patterns in scatter plots of ISDs with respect to brightness temperatures. A comparison of ISDs derived from short-term global SNOs and those derived from multiyear polar SNOs reveals the advantage and the limitation of the two data sets. The multiyear polar SNO generally provides larger observation ranges of brightness temperatures in channels 1-4. The global SNO extends the brightness temperature observations to the warm sides for channels 5-12 and captures the occurrences of larger ISDs for most longwave channels.

Smallest Pareto confidence regions and applications

Available joint confidence sets for the parameters of the Pareto model are not the regions with minimum area. In order to determine the smallest joint confidence region among all those which are based on the minimal sufficient statistic, a computational procedure is proposed which is applicable even when some of the smallest and largest observations have been discarded or censored; i.e., both single (right or left) and double censoring are allowed. The smallest Pareto region is determined by using iterative linear interpolation, as well as numerical integration and optimization methods. A few iterations are often enough to achieve the optimal solution. The reduction in area of the smallest confidence regions with respect to the existing sets is substantial in most situations, and enormous in some cases. Applications of the present approach include uses in estimation and hypothesis testing. In particular, it permits to construct confidence intervals for functions of the Pareto parameters, as well as pointwise and simultaneous confidence bands for the Pareto distribution function. Data sets concerning component lifetimes, fire claims and business failures are studied for illustrative and comparative purposes.

Semi-Parametric Probability-Weighted Moments Estimation Revisited

In this paper, for heavy-tailed models and through the use of probability weighted moments based on the largest observations, we deal essentially with the semi-parametric estimation of the Value-at-Risk at a level p, the size of the loss occurred with a small probability p, as well as the dual problem of estimation of the probability of exceedance of a high level x. These estimation procedures depend crucially on the estimation of the extreme value index, the primary parameter in Statistics of Extremes, also done on the basis of the same weighted moments. Under regular variation conditions on the right-tail of the underlying distribution function F, we prove the consistency and asymptotic normality of the estimators under consideration in this paper, through the usual link of their asymptotic behaviour to the one of the extreme value index estimator they are based on. The performance of these estimators, for finite samples, is illustrated through Monte-Carlo simulations. An adaptive choice of thresholds is put forward. Applications to a real data set in the field of insurance as well as to simulated data are also provided.

Minimizing the area of a Pareto confidence region

A constrained optimization problem is formulated and solved in order to determine the smallest confidence region for the parameters of the Pareto distribution in a proposed family of sets. The objective function is the area of the region, whereas the constraints are related to the required confidence level. Explicit expressions for the area and confidence level of a given region are first deduced. An efficient procedure based on minimizing the corresponding Lagrangian function is then presented to solve the nonlinear programming problem. The process is valid when some of the smallest and largest observations have been discarded or censored, i.e., both single (right or left) and double censoring are allowed. The optimal Pareto confidence region is derived by simultaneously solving three (four) nonlinear equations in the right (double) censoring case. In most practical situations, Newton’s method with the balanced set as the starting point only needs a few iterations to find the global solution. In general, the reduction in area of the optimal Pareto region with respect to the balanced set is considerable if the sample size, n, is small or moderately large, which is usual in practice. This reduction is sometimes impressive when n is quite small and the censoring degree is fairly high. Two numerical examples regarding component lifetimes and fire claims are included for illustrative and comparative purposes.

Semi-parametric tail inference through probability-weighted moments

In this paper, for heavy-tailed models, and working with the sample of the k largest observations, we present probability weighted moments (PWM) estimators for the first order tail parameters. Under regular variation conditions on the right-tail of the underlying distribution function F we prove the consistency and asymptotic normality of these estimators. Their performance, for finite sample sizes, is illustrated through a small-scale Monte Carlo simulation.