Regression Analysis Based Variance Estimation of Gaussian Distribution for Histogram Matching

There have been a significant number of recent papers about hyperspectral imaging, which propose various methods for estimating the number of materials/endmembers in hyperspectral images. This is sometimes called the “intrinsic” dimension (ID) of the image. Estimation of the error variance in each spectral band is a critical first step in ID estimation. The estimated error variances can then be used to preprocess (e.g., whiten) the data, prior to ID estimation. A range of variance estimation methods have been advocated in the literature. We investigate the impact of five variance estimation methods (three using spatial information and two using spectral information) on five ID estimation methods, with the aid of four different, but semirealistic, sets of simulated hyperspectral images. Our findings are as follows: first, for all four sets, the two spectral variance estimation methods significantly outperform the three spatial methods; second, when used with the spectral variance estimation methods, two of the ID estimation methods (called random matrix theory and NWHFC) consistently outperform the other three ID estimation methods; third, the better spectral variance estimation method sometimes gives negative variance estimates; fourth, we introduce a simple correction that guarantees positivity; and fifth, we give a fast algorithm for its computation.

Local Differential Privacy (LDP) provides a formal guarantee of privacy that enables the collection and analysis of sensitive data without revealing any individual's data. While LDP methods have been extensively studied, there is a lack of a systematic and empirical comparison of LDP methods for descriptive statistics. In this paper, we first provide a systematization of LDP methods for descriptive statistics, comparing their properties and requirements. We demonstrate that several mean estimation methods based on sampling from a Bernoulli distribution are equivalent in the one-dimensional case and introduce methods for variance estimation. We then empirically compare methods for mean, variance, and frequency estimation. Finally, we provide recommendations for the use of LDP methods for descriptive statistics and discuss their limitations and open questions.

It is quite essential to estimate serum bilirubin in neonates with jaundice. The early prediction of jaundice is usually by observing the yellowish colour of the skin. Various methods of estimation of bilirubin have been developed and used for assessing the risk of jaundice.
 Jaundice is the common neonatal problem, that with the timely diagnosis, effective treatment and proper counselling to the mother can decrease the neonatal morbidity. Proper neonatal examination, breastfeeding advice to the mother, identifying the high risk groups, proper history elicitation, quick diagnosis and early intervention can reduce the incidence of jaundice and also prevent long term complications. The main goal is to prevent the risk of severe hyperbilirubinemia and for prevention of kernicterus. Hence there is a need for a sensitive, rapid and a reliable method for the assessment of serum bilirubin. These methods include both invasive and non-invasive analysis. Invasive methods involve estimation of serum bilirubin by obtaining a plasma or serum sample and non-invasive include the assessment of bilirubin using various instruments without the requirement of blood sample from the neonate.
 As the invasive method of bilirubin estimation needs more time for analysis to yield a result, many non invasive methods are being studied to find an effective tool which can give fast and accurate results ,thus making it an effective screening tool. This review article throws light on the different methods of estimating bilirubin levels in a neonate.

The design of complex engineering systems often relies on simulation-based models, which inherently introduce uncertainty. Consequently, effective system design necessitates the incorporation of robust design principles and metrics to manage the uncertainties. From a decision-based design perspective, metrics such as the Design Capability Index (DCI) and Error Margin Index (EMI) are employed in problem formulations to address this challenge. These metrics typically utilize Taylor series-based approximations to estimate variance. However, due to the structural limitations of the Taylor series expansion, these formulations may mislead designers toward local minima rather than guide them toward actual robust solutions. In this paper, we propose an alternative formulation of the Design Capability Index (DCI) and Error Margin Index (EMI) that leverages the multiple-point variance estimation method. This approach employs a weighted average of multiple points to assess variance estimations around the nominal design, ensuring that the solution is not confined to a local optimum by estimating the correct variance at the local optimum. The proposed alternative metrics are incorporated into the robust Concept Exploration Framework (rCEF) to find robust solutions for complex engineering systems. A machine learning-based visualization tool, the interpretable Self-Organizing Maps (iSOM), is used to visualize and explore the high-dimensional robust solution space generated using the updated rCEF. Two examples are used to evaluate the proposed formulation: (i) a polynomial function to examine the effect of the alternative variance estimation method on EMI and DCI metrics, and (ii) a comprehensive hot rod rolling problem, considering model parameters and model structure uncertainty.

In this paper, we study the effects of using smoothed variance estimates in place of the sample variances on the performance of stochastic kriging (SK). Different variance estimation methods are investigated and it is shown through numerical examples that such a replacement leads to improved predictive performance of SK. An SK-based dual metamodeling approach is further proposed to obtain an efficient simulation budget allocation rule and consequently more accurate prediction results.

An improved method for estimating capillary pressure from 3D microtomography images and its application to the study of disconnected nonwetting phase

This paper deals with various methods of estimation used for estimating the parameters of lifetime distributions. The distributions considered are exponential, Weibull, Rayleigh, lognormal and gamma and the method used are: method of moments, maximum likelihood, probability weighted moments, least squares and relative least squares. To compare the efficiency between the different methods of estimation, we used the total deviation, mean squared error and probability plot correlation coefficients. In order to study numerically, the execution of the different methods of estimation and goodness of fit analysis, their statistical properties have been simulated for different sample sizes. The graphs of bias designed for different methods of estimation have also been plotted against various sample sizes.

SummaryConsistency and optimality of block bootstrap schemes for distribution and variance estimation of smooth functionals of dependent data have been thoroughly investigated by Hall, Horowitz & Jing (), among others. However, for nonsmooth functionals, such as quantiles, much less is known. Existing results, due to Sun & Lahiri (), regarding strong consistency for distribution and variance estimation via the moving block bootstrap (MBB) require that b→∞, where b=⌊n/ℓ⌋ is the number of resampled blocks to be pasted together to form the bootstrap data series, n is the available sample size, and ℓ is the block length. Here we show that, in fact, weak consistency holds for any b such that 1≤b=O(n/ℓ). In other words we show that a hybrid between the subsampling bootstrap (b=1) and MBB is consistent. Empirical results illustrate the performance of hybrid block bootstrap estimators for varying numbers of blocks.

An important issue in statistical inference for semiparametric models is how to provide reliable and consistent variance estimation. Brown and Wang (2005. Standard errors and covariance matrices for smoothed rank estimators. Biometrika 92: , 732-746) proposed a variance estimation procedure based on an induced smoothing for non-smooth estimating functions. Herein a Monte Carlo version is developed that does not require any explicit form for the estimating function itself, as long as numerical evaluation can be carried out. A general convergence theory is established, showing that any one-step iteration leads to a consistent variance estimator and continuation of the iterations converges at an exponential rate. The method is demonstrated through the Buckley-James estimator and the weighted log-rank estimators for censored linear regression, and rank estimation for multiple event times data.

ABSTRACTThis article considers the problem of variance estimation of a U-statistic. Following the proposal of a linearly extrapolated variance estimator in Wang and Chen (2015), we consider a second-order extrapolation technique and devise a variance estimator that is nearly second-order unbiased. Simulation studies confirm that the second-order extrapolated variance estimator has smaller bias than the linearly extrapolated variance estimator and the jackknife variance estimator across a wide selection of distributions. In addition, the proposal also yields a smaller mean squared error than its counterparts. In the end, we discuss the advantages of the proposed variance estimator in regression analysis and model selection.

Iterative GMM for partially linear single-index models with partly endogenous regressors

Mark rate, or the proportion of the population with unique, identifiable marks, must be determined in order to estimate population size from photographic identification data. In this study we address field sampling protocols and estimation methods for robust estimation of mark rate and its uncertainty in cetacean populations. We present two alternatives for estimating the variance of mark rate: (1) a variance estimator for clusters of unequal sizes (SRCS) and (2) a hierarchical Bayesian model (SRCS‐Bayes), and compare them to the simple random sampling (SRS) variance estimator. We tested these variance estimators using a simulation to see how they perform at varying mark rates, number of groups sampled, photos per group, and mean group sizes. The hierarchical Bayesian model outperformed the frequentist variance estimators, with the true mark rate of the population held in its 95% HDI 91.9% of the time (compared with coverage of 79% for the SRS method and 76.3% for the SRCS‐Cochran method). The simulation results suggest that, ideally, mark rate and its precision should be quantified using hierarchical Bayesian modeling, and researchers should attempt to sample as many unique groups as possible to improve accuracy and precision.

Attributable fraction estimation from complex sample survey data

Background The currently available various methods of estimation of total iron binding capacity (TIBC) show marked variation in reference range. Although serum transferrin (TF) level is a sensitive indicator of iron status, its measurement requires immunoassay equipment which may not be available in many routine biochemistry laboratories. So, this study was planned to find the most appropriate method to estimate TIBC.Objectives This study aimed to compare different methods of TIBC estimation and to corelate the TIBC values obtained by different methods with serum TF concentration.Material and Methods This analytical cross-sectional study was performed in the clinical chemistry laboratory of the Biochemistry Department of Medical College Baroda & SSG Hospital, Vadodara, Gujarat, on 250 leftover serum samples destined to be discarded. In all these samples, serum TIBC was estimated by direct method, indirect method, as well as calculated method (iron + unsaturated iron binding capacity [UIBC]) along with the measurement of serum TF level.Statistical Analysis Among the different methods, repeated analysis of variance (ANOVA) analysis and Bland–Altman plot were used to find out significance of difference. Correlation coefficients were found between different methods of TIBC estimation and serum TF levels.Results The means of TIBC by calculated, indirect, and direct methods were 344.51, 342.23, and 378.24 µg/dL, respectively. The mean of serum TF was 295.3 mg/dL. There was statistically significant difference between TIBC by direct and indirect methods and between direct and calculated methods. There was a strong positive correlation between TIBC by direct method and serum TF (r = 0.888,p < 0.0001), but there was moderate correlation between TIBC by indirect method and serum TF (r = 0.748,p < 0.04), and between TIBC by calculated method and serum TF (r = 0.725,p < 0.05).Conclusion Among different methods of estimation of TIBC, direct method is more reliable in reference to serum TF levels.

ABSTRACTAn objective analysis is one of the main components of data assimilation. By combining observations with the output of a predictive model we combine the best features of each source of information: the complete spatial and temporal coverage provided by models, with a close representation of the truth provided by observations. The process of combining observations with a model output is called an analysis. To produce an analysis requires the knowledge of observation and model errors, as well as its spatial correlation. This paper is devoted to the development of methods of estimation of these error variances and the characteristic length-scale of the model error correlation for its operational use in the Canadian objective analysis system. We first argue in favor of using compact support correlation functions, and then introduce three estimation methods: the Hollingsworth–Lönnberg (HL) method in local and global form, the maximum likelihood method (ML), and the diagnostic method. We perform one-dimensional (1D) simulation studies where the error variance and true correlation length are known, and perform an estimation of both error variances and correlation length where both are non-uniform. We show that a local version of the HL method can capture accurately the error variances and correlation length at each observation site, provided that spatial variability is not too strong. However, the operational objective analysis requires only a single and globally valid correlation length. We examine whether any statistics of the local HL correlation lengths could be a useful estimate, or whether other global estimation methods such as by the global HL, ML, or should be used. We found in both 1D simulation and using real data that the ML method is able to capture physically significant aspects of the correlation length, while most other estimates give unphysical and larger length-scale values.Implications: This paper describes a proposed improvement of the objective analysis of surface pollutants at Environment and Climate Change Canada (formerly known as Environment Canada). Objective analyses are essentially surface maps of air pollutants that are obtained by combining observations with an air quality model output, and are thought to provide a complete and more accurate representation of the air quality. The highlight of this study is an analysis of methods to estimate the model (or background) error correlation length-scale. The error statistics are an important and critical component to the analysis scheme.