On the interval estimation of the parameters of a generalized time-dependent logistic model

This research was conducted to examine the effect of model choice on the epidemiologic interpretation of occupational cohort data. Three multiplicative models commonly employed in the analysis of occupational cohort studies--proportional hazards. Poisson, and logistic regression--were used to analyze data from an historical cohort study of workers exposed to formaldehyde. Samples were taken from this dataset to create a number of predetermined scenarios for comparing the models, varying study size, outcome frequency, strength of risk factors, and follow-up length. The Poisson and proportional hazards models yielded nearly identical relative risk estimates and confidence intervals in all situations except when confounding by age could not be closely controlled in the Poisson analysis. Logistic regression findings were more variable, with risk estimates differing most from the proportional hazards results when there was a common outcome or strong relative risk. The logistic model also provided less precise estimates than the other two. Thus, although logistic was the easiest model to implement, it should be used only in occupational cohort studies when the outcome is rare (5% or less), and the relative risk is less than approximately 2. Even then, the proportional hazards and Poisson models are better choices. Selecting between these two can be based on convenience in most circumstances.

High-resolution methods are generally defined to be high-performance methods for estimating and/or detecting the desired and/or undesired signal components present in a given set of data. The term “high-resolution” also implies a good ability to resolve very “similar” signal components. One of the most common problems in signal processing is known as frequency estimation. In frequency estimation, “high-resolution” often refers to a good ability to resolve two or more closely located frequencies in the given data. There are two groups of high-resolution methods. One is parametric methods, and the other non-parametric methods. The parametric high-resolution methods result from ingenious exploitations of known data structures. The non-parametric high-resolution methods maximize the output of some desired information with little knowledge of the data structure. The choice between parametric methods and non-parametric methods largely depends on one’s confidence in the assumed data model. In this chapter, we expose the readers to a range of existing parametric high-resolution methods. In Section 1.2, we present several frequency estimation techniques using algebraic principles. They are linear prediction, matrix pencil, and iterative quadratic maximum likelihood. The linear prediction method and the matrix pencil method can achieve near-optimal accuracy of estimation without the local convergence issues associated with the optimal methods. The computational complexities of the two methods are among the most efficient. The iterative quadratic maximum likelihood method is an approximation of the (exact) maximum likelihood method. Under some condition (e.g., high SNR), this approximation achieves the optimal accuracy. Concepts like forwardand-backward averaging, total least square, and (joint) singular value decomposition of orthonormal matrices will also be discussed. In Section 1.3, we present methods that exploit large sample theorems in statistics. In particular, we focus on data of multiple independent measurements. The key data structure is captured by the dominant (principal) subspace of the data matrix or the dominant eigenvectors of the data covariance matrix. The principal subspace is referred

In this thesis, we concentrate on the relationship of probability intervals and random sets. Furthermore, we are interested in solving uncertain linear programming problems with probability interval and random set parameters. We discover the conditions to verify when a given probability interval obtains the same information as a random set information. If these conditions are satisfied, we can transform a problem that contains both types of uncertainty into a problem which has only the random set information. In addition, we use an idea from decision making theory with random sets for solving this problem. If a probability interval does not satisfy these conditions, we can solve the problem for finding the optimistic and pessimistic expected recourse values. Finally, we present an algorithm for checking these conditions and constructing appropriate distributions for each of the optimistic and pessimistic approaches.

The determination of tolerance allocations among design parameters is an integral phase of product/process design. Such allocations are often necessary to achieve desired levels of product performance. We extend our prior research on tolerance allocation by developing both parametric and nonparametric methods for a multivariate set of performance measures that are functions of a common set of design parameters. The parametric method is novel and assumes full information about the probability distribution of design parameter processes. The proposed nonparametric method assumes that only partial information is available and significantly extends prior research by considering a more contemporary and realistic model for manufacturer costs. For both methods we derive economically based models that represent the costs, both internal (supplier) and external (manufacturer), of tolerance allocation under several different process scenarios. These scenarios are based on the manner of disposition of nonconforming product. For the parametric methods we derive tolerance allocation solutions that jointly minimize expected total cost of the supplier and manufacturer. For the nonparametric methods we derive solutions for tolerance allocation that jointly minimizes the maximum expected total cost. An example in the fabrication of a rubber tread compound is used to: (i) demonstrate the implementation of our proposed methodologies for tolerance allocation; (ii) illustrate and compare the nonparametric and parametric methods; land iii) assess the sensitivity of optimal tolerance allocations to changes in process model types, cost coefficient estimates, and manner of disposition of nonconforming product.

Hypothesis tests

If it hasn’t failed, does it work? On ‘the worst we can expect’ from observational trial results, with reference to airway management devices

The purposes of this study were to assess the trend of use of statistical methods including parametric and nonparametric methods and to evaluate the use of complex statistical methodology in recent periodontal studies. This study analyzed 123 articles published in the Journal of Periodontal & Implant Science (JPIS) between 2010 and 2014. Frequencies and percentages were calculated according to the number of statistical methods used, the type of statistical method applied, and the type of statistical software used. Most of the published articles considered (64.4%) used statistical methods. Since 2011, the percentage of JPIS articles using statistics has increased. On the basis of multiple counting, we found that the percentage of studies in JPIS using parametric methods was 61.1%. Further, complex statistical methods were applied in only 6 of the published studies (5.0%), and nonparametric statistical methods were applied in 77 of the published studies (38.9% of a total of 198 studies considered). We found an increasing trend towards the application of statistical methods and nonparametric methods in recent periodontal studies and thus, concluded that increased use of complex statistical methodology might be preferred by the researchers in the fields of study covered by JPIS.

Background: Considering that a major part of Iran is part of arid and semi-arid regions, obtaining stable genotypes with good yield stability is one of the ways to deal with drought stress.Due to the genotype environment interaction effect, however, it is difficult to identify cultivars and genotypes that have good stability and acceptable yields in various environmental conditions.Many methods are known to determine the genotype environment interaction effect to identify stable cultivars, which are divided into two univariate (parametric and non-parametric) and multivariate groups.Each of these methods shows different aspects of the stability of genotypes, and one method alone cannot investigate the yield of a genotype in different environments from different aspects of stability.This research aimed to select promising bread wheat genotypes with high yields and suitable stability in the water deficit conditions in the cold climate of Iran using various univariate and multivariate stability analysis methods.Methods: Fourteen wheat genotypes along with Mihan, Heydari, Zarineh, and Zare cultivars (18 genotypes) were investigated under water deficit conditions in a randomized complete block design (RCBD) with three replications in the research stations of Karaj, Mashhad, Miandoab, Arak, and Zanjan in crop years 2020-2022.The stability of genotypes was examined using some parametric and non-parametric univariate methods, AMMI multivariate analysis, and AMMI analysis parameters.Moreover, parametric and non-parametric univariate methods and AMMI stability parameters were integrated using the selection index ideal genotype (SIIG).Results: The location, genotype, year place, and genotype year place interaction effect at 1% and the genotype place interaction effect were significant at a 5% probability level.The main effect of the environment, the genotype environment the interaction effect, and the main effect of the genotype explained 43.61%, 22.92%, and 8.03% of the sum of squares of the experiment, respectively.In parametric methods, G17, G5, G13, and G1 genotypes based on the regression coefficient of Finley and Wilkinson, G9, G7, and G1 genotypes based on the variance of deviation from the regression line, G9, G1, G7, G17, and G4 genotypes based on Wrick's equivalence indices and Shokla stability variance, G9, G1, G17, G4, and G7 genotypes based on Plaisted and Peterson's method, G9, G1, G17, and G4 genotypes based on Plaisted's method, and G9, G1, G7, and G4 genotypes based on Kang's total rank method were known as stable genotypes.In non-parametric methods, G9, G15, and G7 genotypes based on Si(1) and Si(2), G9 and G1 genotypes based on Si(3) nd Si(6), G9, G1, and G7genotypes based on NP(1), G3, G9, G17, and G1 genotypes based on NP(2) statistics, and G9 and G1 genotypes based on NP(3) and NP(4) statistics were regarded as stable genotypes.In AMMI analysis, the first and second components showed the largest contribution (57.8%) in explaining the genotype environment interaction effect according to the significance of the six main components from the first to the sixth.Based on the AMMI1 biplot, G9 and G17 genotypes, and Zanjan1 and Arak2 environments were recognized as the most stable genotypes and environments due to higher than average grain

최근 글로벌 금융시장은 COVID 충격이후 저금리와 양적완화로 인한 유동성 장세 및 변동성 증가로 주가가 높은 상관관계를 보이는 것으로 나타났다. 따라서 주가가 극단치 꼬리 의존성(tail dependence)을 가질 것으로 보아 이를 더 잘 설명하는 Copula 모형을 시장리스크 측정에 적용하였다. 실증분석 데이터는 벤치마크 시장포트폴리오로 미국 주식시장의 Vanguard S&P500 ETF와 GICKS의 글로벌 산업분류 표준에 의한 11개 산업의 Vanguard ETF 섹터를 분석에 사용하였으며, 분석기간은 2018년 1월 3일~2021년 3월 17일까지이다. 본 연구의 분석모형은 MSCI의 BARRA 산업요인모형(IFM)을 수정한 베타요인모형(BFM)을 최초로 적용하였으며, 공격적 베타와 방어적 베타의 최소분산 가중치를 Student’s t-Copula-VaR 및 ES를 산출하는 데 적용하였다. 분석 결과를 요약하면, BFM모형의 연간 수익률은 2.688%로서 공매도를 제약한 공격적 베타 41.72%와 방어적 베타 39.44%에 비해 현저히 낮았으며, 이 같은 결과는 공매도에 기인된 것으로 추정된다. 또한 모수적 및 비모수적 방법에 의한 VaR, Student’s t-VaR, 그리고 Student’s t-ES는 신뢰수준이 클수록 크며, BFM의 시장 리스크는 모수적 및 비모수적 방법에 관계없이 베타 투자전략에 비해 더 낮았다. 또한 Student’s t-Copula VaR 및 ES는 베타 투자전략에서 모수적 방법이 비모수적 방법보다 작고, 비모수적 방법의 시장 리스크는 공격적 베타 투자전략이 방어적 베타 투자전략 보다 더 큰 것으로 나타났다. 본 연구의 공헌도는 BFM을 시장 리스크 측정에 최초로 도입하였으며, 리스크 매니저가 모델 시장위험을 선제적으로 대응할 수 있는 방향성을 제시하였다. 또한 변동성 충격을 반영하기 위한 꼬리 의존성의 적용은 주변확률(Marginal) t-분포에 의한 통계량(, , )을 계산한 후 모수적(parametric) Student’s t-Copula VaR 및 ES에 대한 분석적(analytic)산출이 가능하도록 하였다. 본 연구의 한계점은 변동성 충격 시기 전·후의 시장 리스크의 차이점을 분석하지 못한 한계점이 존재한다. 추후 연구과제로는 이 같은 한계점을 극복하고 시변(time-varying)변동성이 고려된 동태적(dynamics) Copula를 적용하는 데 대한 연구가 필요하다.Recently, the global financial market has been shown to show a high correlation with the stock price, along with the increase in liquidity market and volatility due to low interest rates and quantitative easing after the COVID shock. Therefore, the Copula model, which explains this behavior better, was applied to the market risk measurement, considering that stock prices have extreme tail dependence of high kurtosis and thick skewness. For the empirical analysis data, the US stock market was analyzed, and the Vanguard S&P 500 ETF and the Vanguard ETF sector of 11 industries according to the global industry classification standard of GICKS were used for the analysis as the benchmark market portfolio. The analysis period is from January 3, 2018 to March 17, 2021. For the analysis model of this study, the beta factor model (BFM) modified from MSCI s BARRA industry factor model (IFM) was applied to this study for the first time, and the minimum variance weight calculated as a beta investment strategy divided into aggressive beta and defensive beta was applied to calculate Student s t-Copula-VaR and ES. To summarize the analysis results, VaR, Student’s t-VaR, and Student’s t-ES by parametric and non-parametric methods increased as the confidence level increased, and the market risk of BFM was lower than that of beta investment strategies regardless of parametric and non-parametric methods. Also, in Student s t-Copula VaR and ES, the parametric method was smaller than the non-parametric method in the beta investment strategy, and the market risk of the non-parametric method was greater in the aggressive beta investment strategy than the defensive beta investment strategy. The contribution of this study introduced BFM for the first time to calculate market risk, and suggested a direction for risk managers to preemptively respond to market risk in the model portfolio. In addition, in order to apply the tail dependence to reflect the volatility shock, statistics(,,) by marginal t-distribution were calculated, and then parametric Student s t-Copula VaR and ES were analyzed analytically. calculation was made possible. A limitation of this study is that it does not analyze the difference between the same portfolio rebalancing strategy and market risk analysis results before and after the volatility shock period. As a future research task, it is necessary to overcome this limitation and to apply a dynamics Copula that considers time-varying variability.

Investigated in this paper is the point estimation and confidence intervals of the treatment efficacy parameter and related secondary parameters in a two-stage adaptive trial. Based on the minimal sufficient statistics, several alternative estimators to the sample averages are proposed to reduce the bias and to improve the precision of estimation. Confidence intervals are constructed using Woodroofe's pivot method. Numerical studies are conducted to evaluate the bias and mean squared error of the estimators and the coverage probability of the confidence intervals.

For regression analysis of doubly truncated data, we propose two empirical likelihood (EL) inference approaches, called non-smooth EL and non-smooth Jackknife EL (JEL), to make inference about regression parameters based on the generalized estimating equations of existing weighted rank estimators. The limiting distributions of non-smooth log-EL and log-JEL ratios statistics are derived and non-smooth EL, and JEL confidence intervals for any specified component of regression parameters are obtained. We carry out extensive simulation studies to compare the proposed approaches with the random weighting (RW) approach. The simulation results demonstrate that the non-smooth EL and JEL confidence intervals have better performances than the RW confidence intervals based on coverage probability and average length of confidence intervals of regression parameters when the dependent variable is subject to the double truncation. A real data example is provided to illustrate the proposed approaches.

This chapter is a catalogue of R functions commonly used to get confidence intervals for usual parameters: mean, proportion, variance, median and correlation. We also present a catalogue of R functions to perform standard hypothesis testing. Furthermore, a few practical worksheets will help the reader understand how to interpret confidence intervals, as well as the various errors related to hypothesis testing.KeywordsConfidence IntervalBody Mass IndexAlternative HypothesisCumulative Distribution FunctionRisk LevelThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

BackgroundThis study was conducted to explore the association between oral leukoplakia (OL) and the risk of upper gastrointestinal cancer death in the Linxian General Population Trial Cohort.MethodsA prospective cohort study of the Linxian General Population Trial Cohort was performed. Participants with OL were treated as an exposed group, and the remainder was selected as a control group. All subjects were followed monthly by village health workers and reviewed quarterly by the Linxian Cancer Registry. Hazard ratios (HRs) and 95% confidence interval (CIs) were evaluated using proportional hazard and proportional subdistribution hazard models, respectively.ResultsOver a median of 27 years of observation, 29 476 subjects were followed‐up. A total of 17 473 deaths occurred, including 2345 esophageal squamous cell carcinoma (ESCC), 1139 gastric cardia carcinoma, and 506 gastric non‐cardia carcinoma deaths. Significant increased ESCC mortality was observed in subjects with OL (exposed 9.66% vs. unexposed 7.39%; P < 0.0001). Furthermore, subjects with OL had a 22% higher risk of death from ESCC (HR 1.22, 95% CI 1.10–1.34; P = 0.0001) after adjusted covariates. In subjects aged ≤52 at the baseline, OL was significantly associated with an elevated risk of ESCC mortality (HR 1.32, 95% CI 1.13–1.54; P = 0.0005). No significant associations were observed for gastric cardia carcinoma and non‐cardia carcinoma mortality.ConclusionsOL may increase the risk of ESCC mortality, especially in the younger population. These associations should be investigated in further studies.

The Quality Assurance and Laboratory Standards Committee of the American Society for Veterinary Clinical Pathology and the guidelines of the Clinical and Laboratory Standards Institute provide a framework for establishing reference intervals of physiological parameters in reputedly healthy individuals, humans, and terrestrial animals, respectively. This framework was applied for the first time to the Pacific cupped oyster, Crassostrea gigas. Reference intervals (RIs) would, first, be of interest for research purposes, including pathophysiology studies. RI determination is the first step before considering the use of RIs for field applications by farmers and marine shellfish health services. The purpose of this study was to propose reference intervals of feeding and respiration parameters, the clearance rate (CR), and oxygen consumption rate (OCR), in a reference population of hatchery-reared diploid Pacific oysters. A de novo, a priori, and a direct approach were applied. The reference values acquired from 214 healthy diploid C gigas (total wet weight 6.23-83.64g, DW 0.06-1.87g) were analyzed using a non-parametric statistical method. Reference intervals were proposed for CR, 0.7-4.1L/h/g dry flesh weight (DW), and OCR, 0.4-1.3mg O2/h/g DW in C gigas in a seawater at a temperature of 22℃ and a salinity of 32‰. Animals were fed 30-40 cells/µL of Isochrysis affinis galbana. The confidence intervals at 90% of the upper limits of the two parameters were found to be higher than those of the Clinical and Laboratory Standards Institute (CLSI) recommendations. Obtaining reference intervals is an important step and must be completed by proposed decision limits to facilitate the early detection of health disorders in C gigas.

Annual maxima (AM) and partial duration (PD) flood series are modelled by parametric and non-parametric methods. In PD analysis the number of threshold exceedances is assumed to be Poisson distributed; the peak exceedances are described by the generalized Pareto (GP) and non-parametric (NP) distributions. The generalized extreme value (GEV) and non-parametric (NP) distributions are used to describe the AM series. L-moments are employed for parameter estimation for GEV and GP distributions. Analysis of data from the provinces of Quebec and Ontario, Canada, shows that both AM and PD series can be inferred as being unimodal and bimodal, both of which can be described by the NP method. Also, this method is found not to be sensitive to the choice of threshold level; however, it was also observed that parametric methods cannot detect biomodality, give different quantile estimates for AM and PD data and PD estimates are sensitive to the selection of threshold level. Therefore, the NP method is more advantageous than the parametric methods in flood frequency analysis for both AM and PD series. © 1998 John Wiley & Sons, Ltd.