scholarly journals Linear Regression Estimation Methods for Inferring Standard Values of Snow Load in Small Sample Situations

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Xudong Wang ◽  
Jitao Yao
Keyword(s):  
Linear Regression ◽  
Coefficient Of Variation ◽  
Small Sample ◽  
Point Estimation ◽  
Estimation Methods ◽  
Small Samples ◽  
Unbiased Estimation ◽  
Regression Estimation ◽  
Snow Load ◽  
Standard Values

The aim of this paper is to establish a new method for inferring standard values of snow load in small sample situations. Due to the incomplete meteorological data in some areas, it is often necessary to infer the standard values of snow load in the conditions of small samples in engineering, but the point estimation methods of classical statistics adopted till now do not take into account the influences of statistical uncertainty, and the inference results are always aggressive. In order to overcome the above shortcomings, according to the basic principle of optimal linear unbiased estimation and invariant estimation of the minimum type I distribution parameters and the tantile, using the least square method, the linear regression estimation methods for inferring standard values of snow load in small sample situations are proposed, which can take into account two cases such as parameter-free and known coefficient of variation, and the predicted formulas of snow load standard values are given, respectively. Through numerical integration and Monte Carlo numerical simulation, the numerical table of correlation coefficients is established, which is more convenient for the direct application of inferential formulas. According to the results of theoretical analysis and examples, when using the indirect point estimation methods to infer the standard values of snow load in the conditions of small samples, the inference results are always small. The linear regression estimation method is suitable for inferring standard values of snow load in the conditions of small samples, which can give more reasonable results. When using the linear regression estimation to infer standard values of snow load in practical application, even if the coefficient of variation is unknown, it can set the upper limit value of the coefficient of variation according to the experience; meanwhile, according to the parameter-free and known coefficient of variation, the estimation is carried out, respectively, and the smaller value of the two is taken as the final estimate. The method can be extended to the statistical inference of variable load standard values such as wind load and floor load.

Simulation evaluation of small samples based on grey estimation and improved bootstrap

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Wenguang Yang ◽  
Lianhai Lin ◽  
Hongkui Gao
Keyword(s):  
Similarity Measure ◽  
Bootstrap Method ◽  
Grey System Theory ◽  
Small Sample ◽  
Point Estimation ◽  
Small Samples ◽  
Content Type ◽  
Relational Similarity ◽  
Simulation Evaluation ◽  
Grey Relational

PurposeTo solve the problem of simulation evaluation with small samples, a fresh approach of grey estimation is presented based on classical statistical theory and grey system theory. The purpose of this paper is to make full use of the difference of data distribution and avoid the marginal data being ignored.Design/methodology/approachBased upon the grey distribution characteristics of small sample data, the definition about a new concept of grey relational similarity measure comes into being. At the same time, the concept of sample weight is proposed according to the grey relational similarity measure. Based on the new definition of grey weight, the grey point estimation and grey confidence interval are studied. Then the improved Bootstrap resampling is designed by uniform distribution and randomness as an important supplement of the grey estimation. In addition, the accuracy of grey bilateral and unilateral confidence intervals is introduced by using the new grey relational similarity measure approach.FindingsThe new small sample evaluation method can realize the effective expansion and enrichment of data and avoid the excessive concentration of data. This method is an organic fusion of grey estimation and improved Bootstrap method. Several examples are used to demonstrate the feasibility and validity of the proposed methods to illustrate the credibility of some simulation data, which has no need to know the probability distribution of small samples.Originality/valueThis research has completed the combination of grey estimation and improved Bootstrap, which makes more reasonable use of the value of different data than the unimproved method.

On Small Sample Properties of R2 in a Linear Regression Model with Multivariate t Errors and Proxy Variables

1993 ◽  
Vol 9 (3) ◽  
pp. 504-515 ◽  
Author(s):  
Kazuhiro Ohtani ◽  
Hikaru Hasegawa
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Important Variable ◽  
Small Sample ◽  
Small Samples ◽  
Coefficient Of Determination ◽  
Proxy Variables ◽  
Small Sample Properties ◽  
Multivariate T

In this paper we consider the small sample properties of the coefficient of determination in a linear regression model with multivariate t errors when proxy variables are used instead of unobservable regressors. The results show that if the unobservable variable is an important variable, the adjusted coefficient of determination can be more unreliable in small samples than the unadjusted coefficient of determination from both viewpoints of the bias and the MSE.

scholarly journals ImageJ software as an alternative method for estimating leaf area in oats

2021 ◽  
Vol 69 (3) ◽  
Author(s):  
Thomas Newton Martin ◽  
Glauber Monçon Fipke ◽  
José Eduardo Minussi Winck ◽  
José Abramo Marchese
Keyword(s):  
Standard Deviation ◽  
Linear Regression ◽  
Leaf Area ◽  
Coefficient Of Variation ◽  
Estimation Methods ◽  
Linear Regression Equation ◽  
Simple Linear Regression ◽  
Oat Cultivars ◽  
Highly Correlated ◽  
Imagej Software

The aim of this study was to compare two methods of estimating leaf area (leaf area meter LI-COR 3100 and ImageJ software) in oats. Renascem black oats and UTF Iguaçu white oats cultivars were evaluated. All the leaves of one plant per plot, with six repetitions, were evaluated every seven days to obtain five assessments for each cultivar. The leaves were identified and fixed on a white A4 sheet of paper with an indication of a known area (45 cm²), photographed and evaluated using a leaf area meter (LI-3100 - LI-COR). Leaf area was then estimated using ImageJ software. Estimates were obtained for standard deviation and coefficient of variation, and a simple linear regression equation was estimated based on the two estimation methods. Mean variances were tested using the ‘F’-test and the means compared by the ‘t’-test. There was no difference between the leaf areas found by both methods. In addition, they were highly correlated, and variances were homogeneous. We concluded that ImageJ software can be used instead of the leaf area meter on the two oat cultivars evaluated.

How to Correct for Chance Agreement in the Estimation of Sensitivity and Specificity of Diagnostic Tests

1994 ◽  
Vol 33 (02) ◽  
pp. 180-186 ◽  
Author(s):  
H. Brenner ◽  
O. Gefeller
Keyword(s):  
Sensitivity And Specificity ◽  
Disease Status ◽  
Disease Prevalence ◽  
Small Sample ◽  
Small Samples ◽  
Interval Estimate ◽  
Traditional Concept ◽  
Interval Estimates ◽  
Major Disadvantage ◽  
Test Result

Abstract:The traditional concept of describing the validity of a diagnostic test neglects the presence of chance agreement between test result and true (disease) status. Sensitivity and specificity, as the fundamental measures of validity, can thus only be considered in conjunction with each other to provide an appropriate basis for the evaluation of the capacity of the test to discriminate truly diseased from truly undiseased subjects. In this paper, chance-corrected analogues of sensitivity and specificity are presented as supplemental measures of validity, which pay attention to the problem of chance agreement and offer the opportunity to be interpreted separately. While recent proposals of chance-correction techniques, suggested by several authors in this context, lead to measures which are dependent on disease prevalence, our method does not share this major disadvantage. We discuss the extension of the conventional ROC-curve approach to chance-corrected measures of sensitivity and specificity. Furthermore, point and asymptotic interval estimates of the parameters of interest are derived under different sampling frameworks for validation studies. The small sample behavior of the estimates is investigated in a simulation study, leading to a logarithmic modification of the interval estimate in order to hold the nominal confidence level for small samples.

scholarly journals Biased and unbiased estimation of the average length of stay in intensive care units in the Covid-19 pandemic

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Nathanael Lapidus ◽  
Xianlong Zhou ◽  
Fabrice Carrat ◽  
Bruno Riou ◽  
Yan Zhao ◽  
...  
Keyword(s):  
Intensive Care ◽  
Length Of Stay ◽  
Average Length ◽  
Parametric Method ◽  
Estimation Methods ◽  
Unbiased Estimation ◽  
Bed Occupancy ◽  
Average Length Of Stay ◽  
Discharged Patients ◽  
First Admission

Abstract Background The average length of stay (LOS) in the intensive care unit (ICU_ALOS) is a helpful parameter summarizing critical bed occupancy. During the outbreak of a novel virus, estimating early a reliable ICU_ALOS estimate of infected patients is critical to accurately parameterize models examining mitigation and preparedness scenarios. Methods Two estimation methods of ICU_ALOS were compared: the average LOS of already discharged patients at the date of estimation (DPE), and a standard parametric method used for analyzing time-to-event data which fits a given distribution to observed data and includes the censored stays of patients still treated in the ICU at the date of estimation (CPE). Methods were compared on a series of all COVID-19 consecutive cases (n = 59) admitted in an ICU devoted to such patients. At the last follow-up date, 99 days after the first admission, all patients but one had been discharged. A simulation study investigated the generalizability of the methods' patterns. CPE and DPE estimates were also compared to COVID-19 estimates reported to date. Results LOS ≥ 30 days concerned 14 out of the 59 patients (24%), including 8 of the 21 deaths observed. Two months after the first admission, 38 (64%) patients had been discharged, with corresponding DPE and CPE estimates of ICU_ALOS (95% CI) at 13.0 days (10.4–15.6) and 23.1 days (18.1–29.7), respectively. Series' true ICU_ALOS was greater than 21 days, well above reported estimates to date. Conclusions Discharges of short stays are more likely observed earlier during the course of an outbreak. Cautious unbiased ICU_ALOS estimates suggest parameterizing a higher burden of ICU bed occupancy than that adopted to date in COVID-19 forecasting models. Funding Support by the National Natural Science Foundation of China (81900097 to Dr. Zhou) and the Emergency Response Project of Hubei Science and Technology Department (2020FCA023 to Pr. Zhao).

scholarly journals Inference for the Exponential Distribution under Generalized Progressively Hybrid Censored Data from Partially Accelerated Life Tests with a Time Transformation Function

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1510
Author(s):  
Alaa H. Abdel-Hamid ◽  
Atef F. Hashem
Keyword(s):  
Exponential Distribution ◽  
Failure Rate ◽  
Censored Data ◽  
Sufficient Conditions ◽  
Transformation Function ◽  
Point Estimation ◽  
Estimation Methods ◽  
Time Transformation ◽  
Monte Carlo Simulation Study ◽  
Accelerated Life

In this article, the tampered failure rate model is used in partially accelerated life testing. A non-decreasing time function, often called a ‘‘time transformation function", is proposed to tamper the failure rate under design conditions. Different types of the proposed function, which have sufficient conditions in order to be accelerating functions, are investigated. A baseline failure rate of the exponential distribution is considered. Some point estimation methods, as well as approximate confidence intervals, for the parameters involved are discussed based on generalized progressively hybrid censored data. The determination of the optimal stress change time is discussed under two different criteria of optimality. A real dataset is employed to explain the theoretical outcomes discussed in this article. Finally, a Monte Carlo simulation study is carried out to examine the performance of the estimation methods and the optimality criteria.

scholarly journals G-computation and machine learning for estimating the causal effects of binary exposure statuses on binary outcomes

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Florent Le Borgne ◽  
Arthur Chatton ◽  
Maxime Léger ◽  
Rémi Lenain ◽  
Yohann Foucher
Keyword(s):  
Machine Learning ◽  
Support Vector Machine ◽  
Statistical Power ◽  
Small Sample ◽  
Causal Effects ◽  
Small Samples ◽  
Support Vector ◽  
Sample Sizes ◽  
Super Learner ◽  
Small Sample Sizes

AbstractIn clinical research, there is a growing interest in the use of propensity score-based methods to estimate causal effects. G-computation is an alternative because of its high statistical power. Machine learning is also increasingly used because of its possible robustness to model misspecification. In this paper, we aimed to propose an approach that combines machine learning and G-computation when both the outcome and the exposure status are binary and is able to deal with small samples. We evaluated the performances of several methods, including penalized logistic regressions, a neural network, a support vector machine, boosted classification and regression trees, and a super learner through simulations. We proposed six different scenarios characterised by various sample sizes, numbers of covariates and relationships between covariates, exposure statuses, and outcomes. We have also illustrated the application of these methods, in which they were used to estimate the efficacy of barbiturates prescribed during the first 24 h of an episode of intracranial hypertension. In the context of GC, for estimating the individual outcome probabilities in two counterfactual worlds, we reported that the super learner tended to outperform the other approaches in terms of both bias and variance, especially for small sample sizes. The support vector machine performed well, but its mean bias was slightly higher than that of the super learner. In the investigated scenarios, G-computation associated with the super learner was a performant method for drawing causal inferences, even from small sample sizes.

Fuzzy C-Regression Models

2013 ◽  
Vol 278-280 ◽  
pp. 1323-1326
Author(s):  
Yan Hua Yu ◽  
Li Xia Song ◽  
Kun Lun Zhang
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Linear Models ◽  
Least Squares Method ◽  
Least Square Method ◽  
Least Square ◽  
Estimation Methods ◽  
Statistical Regression ◽  
Fuzzy Linear Regression ◽  
Fuzzy Degree

Fuzzy linear regression has been extensively studied since its inception symbolized by the work of Tanaka et al. in 1982. As one of the main estimation methods, fuzzy least squares approach is appealing because it corresponds, to some extent, to the well known statistical regression analysis. In this article, a restricted least squares method is proposed to fit fuzzy linear models with crisp inputs and symmetric fuzzy output. The paper puts forward a kind of fuzzy linear regression model based on structured element, This model has precise input data and fuzzy output data, Gives the regression coefficient and the fuzzy degree function determination method by using the least square method, studies the imitation degree question between the observed value and the forecast value.

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