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The basic formula to calculate sample variance is based on the sum of squared differences from mean. From computational perspective, mean calculation is nondesired as it can introduce computing errors. Previous researches have proposed to use weighted formula of the successive differences to calculate sample variance to avoid mean calculation. But their weighted formula is not in a unified format in the sense that it has to be represented as two formulas. This paper proposes a unified weight formula for sample variance calculation from weighted successive differences. A proof is provided to show that sample variance calculated using the proposed unified weighted formula is mathematically equivalent to the basic definition. [ABSTRACT FROM AUTHOR]

The most popular measure of variability of values in a sample is the variance – the average of the squares of observations deviated from the mean. That it is also an indicator of the deviations among observations themselves is not obvious from the popular formula of variance. In this note, we highlight the deviations among observations as the building block of variance in an amusingly instructive way. A simple algorithm has been presented to calculate sample variance. [ABSTRACT FROM PUBLISHER]

Gauss introduced the MLSq and Helmert completed its development whereas Bessel made important discoveries in astronomy and geodesy but was often extremely inattentive. Gauss' final condition of least variance led to effective estimators of the unknowns sought, jointly effective in case of the normal distribution of the observational errors. Gauss' memoire of 1823 leads to the principle of least squares much easier than generally thought. [ABSTRACT FROM AUTHOR]

The standard error of equating quantifies the variability in the estimation of an equating function. Because common items for deriving equated scores are treated as fixed, the only source of variability typically considered arises from the estimation of common-item parameters from responses of samples of examinees. Use of alternative, equally appropriate anchor sets results in different equating transformations, even when standard errors of common-item parameter estimates are negligible. A bootstrap approximation for quantifying the variability due to common-item selection is derived for a statewide assessment assuming random selection of common items from a large hypothetical item pool. The standard error of equating and the error due to common-item selection constitute only a small fraction of the variability for individual examinee scores. For group means, other sources of error shrink as sample size increases; unaffected by sample size, error due to common-item selection may become the dominant source of variability. [ABSTRACT FROM AUTHOR]

Inertial sensor errors include deterministic errors and stochastic errors. Deterministic errors can be calibrated in laboratory by simple computation technique. Stochastic errors can be determined during calibration by adopting special methods because of their random character. The simplest method to determine the stochastic errors for inertial sensors is the Allan variance. This kind of method needs large data to fully characterize the stochastic errors. The normal nonoverlapped Allan variance has quite poor estimation accuracy in long cluster time. The fully overlapping Allan variance and traditional total variance have better estimation accuracy in long cluster time but are quite time consuming for large data set. The not fully overlapping Allan variance and nonoverlapped total variance are suitable for large data set to improve the estimation accuracy in long cluster time with much less time, but their accuracy is still relatively poor in comparison with not fully overlapping total variance. Whereas the not fully overlapping total variance is relatively time consuming and, compared with Allan variance, there is a bias which is not easy to be corrected. This paper proposes a sliding average Allan variance that has comparable estimation accuracy with total variance. The data are not required to extend as the total variance; thus the calculation burden could be reduced greatly. Therefore, it is more suitable for large data set. In addition this method has no bias in comparison with Allan variance, which means no bias correction is required. This method is applied to 12-h static data of three gyroscopes from a position and orientation system with good performance. [ABSTRACT FROM PUBLISHER]

Accurate interval estimation of standardized hospital morbidity rates is essential for comparing health care utilization across geographical areas or different populations. There are typically repeated hospital admissions for individuals in the population in any specific time period; hence counts of admissions may not be well modelled by standard distributions for count data based on a Poisson assumption. This leads to empirical distributions of the counts with heavier tails than the Poisson. This paper complies and reviews various approaches for interval estimation of standardized hospital morbidity rates used at health agencies and examines their suitability under a broad range of conditions. The focus here is on approaches used for automated production of rates for developing atlases, using large-scale (e.g., country-wide) medical databases. We consider parametric models which incorporate such overdispersion, including the zero-inflated Poisson, negative binomial, zero-inflated negative binomial and Poisson-inverse-Gaussian distributions. Additionally, we consider the use of robust methods based on simple moment estimators for computing the mean and variance of the distribution of the counts, and Poisson-based methods currently utilized for some published rates when patient-level data are unavailable. A simulation study is conducted to compare the different approaches. Various confidence interval construction methods are also examined. Our results indicate that the moment approach as well as confidence intervals based on a log transformation of the rate provide more accurate inference for morbidity rates than the other methods. We recommend the use of the moment approach due to its simplicity of implementation. Some cautions regarding ad hoc approaches currently in use are also provided. [ABSTRACT FROM AUTHOR]

Purpose: To apply a statistical bootstrap analysis to assess the uncertainty in the dose–response relation for the endpoints pneumonitis and myelopathy reported in the QUANTEC review. Methods and Materials: The bootstrap method assesses the uncertainty of the estimated population-based dose-response relation due to sample variability, which reflects the uncertainty due to limited numbers of patients in the studies. A large number of bootstrap replicates of the original incidence data were produced by random sampling with replacement. The analysis requires only the dose, the number of patients, and the number of occurrences of the studied endpoint, for each study. Two dose–response models, a Poisson-based model and the Lyman model, were fitted to each bootstrap replicate using maximum likelihood. Results: The bootstrap analysis generates a family of curves representing the range of plausible dose–response relations, and the 95% bootstrap confidence intervals give an estimated upper and lower toxicity risk. The curve families for the 2 dose–response models overlap for doses included in the studies at hand but diverge beyond that, with the Lyman model suggesting a steeper slope. The resulting distributions of the model parameters indicate correlation and non-Gaussian distribution. For both data sets, the likelihood of the observed data was higher for the Lyman model in >90% of the bootstrap replicates. Conclusions: The bootstrap method provides a statistical analysis of the uncertainty in the estimated dose–response relation for myelopathy and pneumonitis. It suggests likely values of model parameter values, their confidence intervals, and how they interrelate for each model. Finally, it can be used to evaluate to what extent data supports one model over another. For both data sets considered here, the Lyman model was preferred over the Poisson-based model. [Copyright &y& Elsevier]

Procedures are described for estimating selection index accuracies for individual animals and expected genetic change from selection for the general case where indexes of EBVs predict an aggregate breeding objective of traits that may or may not have been measured. Index accuracies for the breeding objective are shown to take an important general form, being able to be expressed as the product of the accuracy of the index function of true breeding values and the accuracy with which that function predicts the breeding objective. When the accuracies of the individual EBVs of the index are known, prediction error variances (PEVs) and covariances (PECs) for the EBVs within animal are able to be well approximated, and index accuracies and expected genetic change from selection estimated with high accuracy. The procedures are suited to routine use in estimating index accuracies in genetic evaluation, and for providing important information, without additional modelling, on the directions in which a population will move under selection. [ABSTRACT FROM AUTHOR]

Cross-sectional evidence shows that loss of control (LOC) eating is a common and psychopathologically relevant experience in preadolescence. This study sought to investigate the natural course of preadolescent LOC eating in relation to psychopathology and body weight trajectory. A community sample of 55 children ages 8-13 years with LOC eating, defined as at least one episode of LOC eating within the past 3 months (LOC+), and 59 matched children without LOC history (LOC-), were assessed with the Eating Disorder Examination adapted for Children and self-report questionnaires every 6 months over a 2-year follow-up. Of the LOC+ children, 54.5% of children remitted from LOC eating, 3.6% showed persistent LOC eating, and 41.8% showed recurring LOC eating over the follow-up period. Of the LOC-children, 19% revealed an onset of LOC episodes, mostly with a low level of stability. Multilevel modeling showed that LOC eating predicted a partial binge eating disorder diagnosis and greater global eating disorder psychopathology, but not depressive symptoms or growth in body fatness. Between-person higher shape concern and weight-related teasing, as well as within-person decreases in shape concern and increases in depression, predicted a greater likelihood of subsequent LOC eating. The results indicate a moderate stability of LOC eating in preadolescent children, with prognostic significance for clinically relevant eating problems and eating disorder psychopathology. [ABSTRACT FROM AUTHOR]

It may not be an overstatement that one of the most widely reported measures of variation involves S, the sample variance, which is also well-known to be alternatively expressed in the form of an U statistic with a symmetric kernel of degree 2 whatever be the population distribution function. We propose a very general new approach to construct unbiased estimators of a population variance by U statistics with symmetric kernels of degree higher than two. Surprisingly, all such estimators ultimately reduce to S (Theorem 3.1). While Theorem 3.1 is interesting and novel in its own right, it leads to a newer interpretation of S that is much broader than what is known in the statistical literature including economics, actuarial mathematics, and mathematical finance. [ABSTRACT FROM AUTHOR]

The degree of return predictability is measured for 40 Bulgarian stocks, two Bulgarian stock market indices and 13 other South East European stock market indices using three finite-sample variance ratio tests. Daily data corrected for infrequent trading are used in a fixed-length rolling window to capture short-horizon predictability and rank Bulgarian stocks and South East European stock market indices by relative predictability. Overall, the degree of return predictability for both stocks and stock market price indices varies widely. For Bulgarian stocks, the degree of predictability is greater the less liquid is the market for a particular stock. For market indices, the degree of predictability is negatively related to capitalization, liquidity and market quality; small, new, relatively illiquid and less-developed stock markets are more predictable than large, liquid, developed markets. [ABSTRACT FROM PUBLISHER]

Parametric robustness of a statistic in a class of distributions implies that the distribution of the statistic is the same for any member of the class of distributions. The bivariate Wishart distribution, based on the class of bivariate elliptical distributions, involves three essential statistics, namely, two sample variances and the product moment correlation coefficient. The distribution of the product moment correlation coefficient is known to be robust in the class of bivariate elliptical distributions. In this paper, we prove that the distribution of the variance ratio is also robust in the class of bivariate elliptical distributions. [ABSTRACT FROM AUTHOR]

In this paper a goal programming technique of finding a compromise optimum allocation in stratified random sampling is suggested, which near about minimizes both the variance of the estimate and variance of the estimated variance. [ABSTRACT FROM AUTHOR]

We revisit fixed-width (= 2d) confidence interval procedures with a preassigned confidence coefficient (≥1 − α) for the mean μ of a normal distribution when its variance σ2is unknown. Had σ been known, the required optimal fixed sample size would beC ≡ a2σ2/d2wherea ≡ aαis the upper 50α% point ofN(0, 1). In his fundamental two-stage procedure, Stein (1945, 1949) estimatedCby replacing σ2with a sample variance from pilot data of sizem(≥2) andawithtm−1, α/2. Mukhopadhyay (1982) opened the possibility of incorporating less traditional estimators of σ2. We focus on estimating σ2by a statisticdefined viaGini's mean difference(GMD),mean absolute deviation(MAD), andrange. Such modifications are warranted especially when we suspect one or more outliers but normality of the data may not be questioned by a standard test for normality assumption. Obviously, then,tm−1, α/2must be replaced by the upper 50α% point corresponding to a pivotal distribution of the sample mean standardized appropriately byUm. This way, we explore the role of Mukhopadhyay (1982) two-stage confidence interval procedure when the requisite sample size is determined through GMD, MAD, or range. Associated exact and some asymptotic first-order properties are developed first. Next, we revisit Mukhopadhyay and Duggan (1997) updated two-stage methodology that was proposed when a known positive lower boundwas available for σ2in the present light. We highlight associated (i) first-order efficiency properties for all proposed fixed-width confidence interval procedures and (ii) second-order efficiency property of the GMD-based procedure. These are accompanied with extensive data analyses via simulations as well as real data. [ABSTRACT FROM PUBLISHER]

There are numerous statistical procedures for detecting items that function differently across subgroups of examinees that take a test or survey. However, in endeavouring to detect items that may function differentially, selection of the statistical method is only one of many important decisions. In this article, we discuss the important decisions that affect investigations of differential item functioning (DIF) such as choice of method, sample size, effect size criteria, conditioning variable, purification, DIF amplification, DIF cancellation, and research designs for evaluating DIF. Our review highlights the necessity of matching the DIF procedure to the nature of the data analysed, the need to include effect size criteria, the need to consider the direction and balance of items flagged for DIF, and the need to use replication to reduce Type I errors whenever possible. Directions for future research and practice in using DIF to enhance the validity of test scores are provided. [ABSTRACT FROM AUTHOR]

The paper considers a problem of estimating a finite population parameter T ( α, β, γ) in two-phase and successive sampling. Asymptotic optimum estimator (AOE) in a class is identified with its approximate variance formula. Several estimators of different parameters are identified as particular members of the class. In particular, we have focused on estimating the population coefficient of variation. The expressions for bias and variance are derived and compared theoretically. [ABSTRACT FROM AUTHOR]

Abstract: Traditional process control charts for a measurement standard deviation are based on the assumption of normality, which may not always be valid. Assuming that measurements follow a gamma distribution, we have obtained an approximate distribution of the sample variance, scaled appropriately. This approximate distribution, which happens to be another gamma model, is used to derive an interval estimate of the population standard deviation. Further, the above approximate gamma model for the sample variance can be used to develop a process control chart as demonstrated by a simulated data set. [Copyright &y& Elsevier]

We establish strong large deviation results for an arbitrary sequence of random variables under some assumptions on the normalized cumulant generating function. In other words, we give asymptotic expansions for the tail probabilities of the same kind as those obtained by Bahadur and Rao (Ann. Math. Stat. 31:1015-1027, ) for the sample mean. We consider both the case where the random variables are absolutely continuous and the case where they are lattice-valued. Our proofs make use of arguments of Chaganty and Sethuraman (Ann. Probab. 21:1671-1690, ) who also obtained strong large deviation results and local limit theorems. We illustrate our results with the kernel density estimator, the sample variance, the Wilcoxon signed-rank statistic and the Kendall tau statistic. [ABSTRACT FROM AUTHOR]

The a priori determination of a proper sample size necessary to achieve some specified power is an important problem encountered frequently in practical studies. To establish the needed sample size for a two-sample t test, researchers may conduct the power analysis by specifying scientifically important values as the underlying population means while using a variance estimate obtained from related research or pilot study. In order to take account of the variability of sample variance, this article considers two approaches to sample size determinations. One provides the sample size required to guarantee with a given assurance probability that the actual power exceeds the planned power. The other gives the necessary sample size such that the expected power attains the designated power level. The suggested paradigm of adjusted sample variance combines the existing procedures into one unified framework. Numerical results are presented to illustrate the usefulness and advantages of the proposed approaches that accommodate the stochastic nature of the sample variance. More importantly, supplementary computer programs are developed to aid the usefulness and implementation of the suggested techniques. The exposition helps to clarify discrepancy in the previous demonstration and to extend the development of sample size methodology. [ABSTRACT FROM AUTHOR]

Abstract: Mass depletion–mass flux relationships usually applied to a groundwater plume were established at field scale for groundwater pumped from within the source zone of a dense non-aqueous phase liquid (DNAPL). These were used as part of multiple lines of evidence in establishing the DNAPL source mass and architecture. Simplified source mass-dissolved concentration models including those described by exponential, power, and error functions as well as a rational mass equation based on the equilibrium stream tube approach were fitted to data from 285days of source zone pumping (SZP) from a single well which removed 152kg of dissolved organics from a multi-component, reactive brominated solvent DNAPL. The total molar concentration of the source compound, tetrabromoethane and its daughter products was used as a single measure of contaminant concentration to relate to source mass. A partitioning inter-well tracer test (PITT) conducted prior to the SZP provided estimates of groundwater travel times, enabling parameterisation of the models. After accounting for capture of the down-gradient dissolved plume, all models provided a good fit to the observed data. It was shown that differentiation between models would only emerge after appreciably more pumping from the source zone. The model fits were not particularly sensitive to the exponent parameters and variance of groundwater travel time. In addition, the multi-component nature of the DNAPL did not seem to affect the utility of the models for the period examined. Estimates of the DNAPL mass prior to the start of SZP from the models were greatest where the log of the variance of travel time was used explicitly in the source depletion models (mean 295kg) compared to where the associated power exponent and variance was fitted freely (mean 258kg). The estimates of source mass were close to that of 220kg determined from the PITT. In addition to the PITT, multi-level groundwater sampling from within the source zone provided important supporting information for developing the conceptual model of the source zone. It is concluded that SZP may be an effective and relatively simple means for characterising DNAPL source zones. [Copyright &y& Elsevier]

Tian et al. (2007) introduced a so-called hidden sensitivity model for evaluating the association of two sensitive questions with binary outcomes. However, in practice, we sometimes need to assess the association between one sensitive binary variable (e.g., whether or not a drug user, the number of sex partner being ≤1 or >1, and so on) and one nonsensitive binary variable (e.g., good or poor health status, with or without cervical cancer, and so on). To address this issue, by sufficiently utilizing the information contained in the non-sensitive binary variable, in this paper, we propose a new survey scheme, called combination questionnaire design/model, which consists of a main questionnaire and a supplemental questionnaire. The introduction of the supplemental questionnaire which is indeed a design of direct questioning can effectively reduce the noncompliance behavior since more respondents will not be faced with the sensitive question. Likelihood-based inferences including maximum likelihood estimates via the expectation-maximization algorithm, asymptotic confidence intervals, and bootstrap confidence intervals of parameters of interest are derived. A likelihood ratio test is provided to test the association between the two binary random variables. Bayesian inferences are also discussed. Simulation studies are performed, and a cervical cancer data set in Atlanta is used to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]

We compare the observed probability distribution function (PDF) of the transmission in the H i Lyman α forest, measured from the Ultraviolet and Visual Echelle Spectrograph (UVES) ‘Large Programme’ sample at redshifts z = [2, 2.5, 3], to results from the gimic cosmological simulations. Our measured values for the mean transmission and its PDF are in good agreement with published results. Errors on statistics measured from high-resolution data are typically estimated using bootstrap or jackknife resampling techniques after splitting the spectra into chunks. We demonstrate that these methods tend to underestimate the sample variance unless the chunk size is much larger than is commonly the case. We therefore estimate the sample variance from the simulations. We conclude that observed and simulated transmission statistics are in good agreement; in particular, we do not require the temperature–density relation to be ‘inverted’. [ABSTRACT FROM PUBLISHER]

We used variance components to assess allocation of sampling effort in a hierarchically nested sampling design for ongoing monitoring of early life history stages of the federally endangered Devils Hole pupfish (DHP) ( Cyprinodon diabolis) . Sampling design for larval DHP included surveys (5 days each spring 2007-2009), events, and plots. Each survey was comprised of three counting events, where DHP larvae on nine plots were counted plot by plot. Statistical analysis of larval abundance included three components: (1) evaluation of power from various sample size combinations, (2) comparison of power in fixed and random plot designs, and (3) assessment of yearly differences in the power of the survey. Results indicated that increasing the sample size at the lowest level of sampling represented the most realistic option to increase the survey's power, fixed plot designs had greater power than random plot designs, and the power of the larval survey varied by year. This study provides an example of how monitoring efforts may benefit from coupling variance components estimation with power analysis to assess sampling design. [ABSTRACT FROM AUTHOR]

We consider the estimation of dynamic panel data models in the presence of incidental parameters in both dimensions: individual fixed-effects and time fixed-effects, as well as incidental parameters in the variances. We adopt the factor analytical approach by estimating the sample variance of individual effects rather than the effects themselves. In the presence of cross-sectional heteroskedasticity, the factor method estimates the average of the cross-sectional variances instead of the individual variances. The method thereby eliminates the incidental-parameter problem in the means and in the variances over the cross-sectional dimension. We further show that estimating the time effects and heteroskedasticities in the time dimension does not lead to the incidental-parameter bias even when T and N are comparable. Moreover, efficient and robust estimation is obtained by jointly estimating heteroskedasticities. [ABSTRACT FROM AUTHOR]

Abstract: Wine derives its economic value to a large extent from geographical origin, which has a significant impact on the quality of the wine. According to the food legislation, wines can be without geographical origin (table wine) and wines with origin. Wines with origin must have characteristics which are essential due to its region of production and must be produced, processed and prepared, exclusively within that region. The development of fast and reliable analytical methods for the assessment of claims of origin is very important. The current official method is based on the measurement of stable isotope ratios of water and alcohol in wine, which are influenced by climatic factors. The results in this paper are based on 5220 Italian wine samples collected in the period 2000–2010. We evaluate the univariate approach underlying the official method to assess claims of origin and propose several new methods to get better geographical discrimination between samples. It is shown that multivariate methods are superior to univariate approaches in that they show increased sensitivity and specificity. In cases where data are non-normally distributed, an approach based on mixture modelling provides additional improvements. [Copyright &y& Elsevier]

Abstract: Objectives: The aims of this study were to compare the effect of sample volume (SV) size settings and sampling method on measurement variability and peak systolic (s′), and early (e′) and late (a′) diastolic longitudinal myocardial velocities using color tissue Doppler imaging (cTDI) in cats. Animals: Twenty cats with normal echocardiograms and 20 cats with hypertrophic cardiomyopathy. Methods: We quantified and compared empirical variance and average absolute values of s′, e′ and a′ for three cardiac cycles using eight different SV settings (length 1,2,3 and 5 mm; width 1 and 2 mm) and three methods of sampling (end-diastolic sampling with manual tracking of the SV, end-systolic sampling without tracking, and random-frame sampling without tracking). Results: No significant difference in empirical variance could be demonstrated between most of the tested SVs. However, the two settings with a length of 1 mm resulted in a significantly higher variance compared with all settings where the SV length exceeded 2 mm (p < 0.001). There was an overall significant effect of sampling method on the variability of measurements (p = 0.003) and manual tracking obtained the lowest variance. No difference in average values of s′, e′ or a′ could be found between any of the SV settings or sampling methods. Conclusion: Within the tested range of SV settings, an SV length of 1 mm resulted in higher measurement variability compared with an SV length of 3 and 5 mm, and should therefore be avoided. Manual tracking of the sample volume is recommended. [Copyright &y& Elsevier]

ABSTRACT We use N-body/photometric galaxy simulations to examine the impact of sample variance of spectroscopic redshift samples on the accuracy of photometric redshift (photo- z) determination and calibration of photo- z errors. We estimate the biases in the cosmological parameter constraints from weak lensing and derive requirements on the spectroscopic follow-up for three different photo- z algorithms chosen to broadly span the range of algorithms available. We find that sample variance is much more relevant for the photo- z error calibration than for photo- z training, implying that follow-up requirements are similar for different algorithms. We demonstrate that the spectroscopic sample can be used for training of photo- zs and error calibration without incurring additional bias in the cosmological parameters. We provide a guide for observing proposals for the spectroscopic follow-up to ensure that redshift calibration biases do not dominate the cosmological parameter error budget. For example, assuming optimistically (pessimistically) that the weak lensing shear measurements from the Dark Energy Survey could obtain 1σ constraints on the dark energy equation of state w of 0.035 (0.055), implies a follow-up requirement of 150 (40) patches of sky with a telescope such as Magellan, assuming a 1/8 deg2 effective field of view and 400 galaxies per patch. Assuming (optimistically) a VIMOS-VLT Deep Survey-like spectroscopic completeness with purely random failures, this could be accomplished with about 75 (20) nights of observation. For more realistic assumptions regarding spectroscopic completeness, or with the presence of other sources of systematics not considered here, further degradations to dark energy constraints are possible. We test several approaches for making the requirements less stringent. For example, if the redshift distribution of the overall sample can be estimated by some other technique, e.g. cross-correlation, then follow-up requirements could be reduced by an order of magnitude. [ABSTRACT FROM AUTHOR]

The authors discuss issues related to variation as it applies to research results. They state that the existence of variance between groups allows researchers to estimate the likelihood that groups were drawn from the same population. They mention that since there will be variation in the values find in replicate measurements, taking several samples is necessary to obtain a more representative of the picture of that particular unit as a whole.

A main benefit from taking a systematic sample is the ease of implementation when field sampling. However, it is not uncommon for a researcher to sample only one primary sampling unit (PSU) but to assume that the secondary sampling units (SSUs) were selected by simple random sampling to obtain a variance estimate. To obtain an unbiased estimator of variance for conventional or adaptive systematic sampling, it is necessary to sample > 1 PSUs, and this can marginally increase cost and complicate implementation. We show that it is possible to obtain an unbiased estimate of variance if the researcher takes only a single PSU and one or more SSUs. Although this is no longer a true systematic sample, such a design retains much of the simplicity of sampling a single PSU and allows for a valid variance estimate. This paper introduces three new sampling strategies stemming from systematic adaptive cluster sampling and the Raj estimator. The new sampling designs will be referred to as partial systematic adaptive cluster sampling. The sampling strategies are investigated in a simulation study that utilizes distance traveled as a measure of cost when comparing sampling strategies. When only a single PSU can be sampled because of cost or logistics concerns, we recommend also sampling one or more SSUs to obtain an unbiased estimate of variance. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The linearity (or lack thereof) of association between sample mean and sample variance is explored in this note with the intent of providing new insights. Of particular interest is a well-known inequality involving the measures of skewness and kurtosis that is derived as a consequence of an identity involving the correlation between sample mean and sample variance. The nature of association between the two is explored further by means of the conditional expectation of the sample variance given the mean. We present several characterization results where the specific relationship of this conditional expectation and sample mean uniquely determines the parent population. The note is presented at a level accessible to graduate or upper-level undergraduate students with several illustrative examples included as teaching aid. [ABSTRACT FROM AUTHOR]

Designing double sampling plan requires identification of sample sizes and acceptance numbers. In this paper a genetic algorithm has been designed for the selection of optimal acceptance numbers and sample sizes for the specified producer's risk and consumer's risk. Implementation of the algorithm has been illustrated numerically for different choices of quantities involved in a double sampling plan. [ABSTRACT FROM AUTHOR]

Particle size analyses of a raw material are commonplace in the mineral processing industry. Knowledge of particle size distributions is crucial in planning milling operations to enable an optimum degree of liberation of valuable mineral phases, to minimize plant losses due to an excess of oversize or undersize material or to attain a size distribution that fits a contractual specification. The problem addressed in the present paper is how to test the equality of two or more underlying size distributions. A distinguishing feature of these size distributions is that they are not based on counts of individual particles. Rather, they are mass size distributions giving the fractions of the total mass of a sampled material lying in each of a number of size intervals. As such, the data are compositional in nature, using the terminology of Aitchison [1] that is, multivariate vectors the components of which add to 100%. In the literature, various versions of Hotelling's T 2 have been used to compare matched pairs of such compositional data. In this paper, we propose a robust test procedure based on ranks as a competitor to Hotelling's T 2. In contrast to the latter statistic, the power of the rank test is not unduly affected by the presence of outliers or of zeros among the data. [ABSTRACT FROM AUTHOR]

DECORATE (Diverse Ensemble Creation by Oppositional Relabeling of Artificial Training Examples) is a classifier combination technique to construct a set of diverse base classifiers using additional artificially generated training instances. The predictions from the base classifiers are then integrated into one by the mean combination rule. In order to gain more insight about its effectiveness and advantages, this paper utilizes a large experiment to study the bias–variance analysis of DECORATE as well as some other widely used ensemble methods (such as bagging, AdaBoost, random forest) at different training sample sizes. The experimental results yield the following conclusions. For small training sets, DECORATE has a dominant advantage over its rivals and its success is attributed to the larger bias reduction achieved by it than the other algorithms. With increase in training data, AdaBoost benefits most and the bias reduced by it gradually turns to be significant while its variance reduction is also medium. Thus, AdaBoost performs best with large training samples. Moreover, random forest behaves always second best regardless of small or large training sets and it is seen to mainly decrease variance while maintaining low bias. Bagging seems to be an intermediate one since it reduces variance primarily. [ABSTRACT FROM AUTHOR]

Abstract: The Student–Teacher Relationship Scale (STRS) is widely used to examine teachers'' relationships with young students in terms of closeness, conflict, and dependency. This study aimed to verify the dimensional structure of the STRS with confirmatory factor analysis, test its measurement invariance across child gender and age, improve its measurement of the dependency construct, and extend its age range. Teachers completed a slightly adapted STRS for a Dutch sample of 2335 children aged 3 to 12. Overall, the 3-factor model showed an acceptable fit. Results indicated metric invariance across gender and age up to 8years. Scalar invariance generally did not hold. Lack of metric invariance at ages 8 to 12 primarily involved Conflict items, whereas scale differences across gender and age primarily involved Closeness items. The adapted Dependency scale showed strong invariance and higher internal consistencies than the original scale for this Dutch sample. Importantly, the revealed non-invariance for gender and age did not influence mean group comparisons. [Copyright &y& Elsevier]

Abstract: This paper presents “contribution to sample variance plot”, a natural extension of the “contribution to the sample mean plot”, which is a graphical tool for global sensitivity analysis originally proposed by Sinclair. These graphical tools have a great potential to display graphically sensitivity information given a generic input sample and its related model realizations. The contribution to the sample variance can be obtained at no extra computational cost, i.e. from the same points used for deriving the contribution to the sample mean and/or scatter-plots. The proposed approach effectively instructs the analyst on how to achieve a targeted reduction of the variance, by operating on the extremes of the input parameters'' ranges. The approach is tested against a known benchmark for sensitivity studies, the Ishigami test function, and a numerical model simulating the behaviour of a water hammer effect in a piping system. [Copyright &y& Elsevier]

Randomized graph sampling (RGS) is an approach for sampling populations associated with or describable as graphs, when the structure of the graph is known and the parameter of interest is the total weight of the graph. RGS is related to, but distinct from, other graph-based approaches such as snowball and network sampling. Graph elements are clustered into walks that reflect the structure of the graph, as well as operational constraints on sampling. The basic estimator in RGS can be constructed as a Horvitz-Thompson estimator. I prove it to be design-unbiased, and also show design-unbiasedness of an estimator of the sample variance when walks are sampled with replacement. Covariates can be employed for variance reduction either through improved assignment of selection probabilities to walks in the design step, or through the use of alternative estimators during analysis. The approach is illustrated with a trail maintenance example, which demonstrates that complicated approaches to assignment of selection probabilities can be counterproductive. I describe conditions under which RGS may be efficient in practice, and suggest possible applications. [ABSTRACT FROM AUTHOR]

Let be a U-statistic based on a kernel function h(x 1, x 2) and independent and identically distributed samples {X n ; n ≥ 1}. The author obtained a weak invariance principle and a strong functional limit theorem for the products of when may be infinite. Moreover, the author also applies the results to the sample variance and the Gini's mean difference, and obtain the limiting properties of their products. [ABSTRACT FROM AUTHOR]

The article presents a study related to peak alignment method to deal with variations in case of two-dimensional gas chromatography time-of-flight mass spectrometry (MS) in metabolite profiling in metabolomics. It is mentioned that the method performs better than other existing method mentioning data generated from the plasma of a rat. The developed model-based peak alignment method is state to process both homogeneous and heterogeneous experimental data.

For estimating the population variance of variable under study, a generalized difference-cum-ratio type estimator has been proposed. Expressions for bias and mean square error have been obtained using random sampling at both the phases. The expressions have also been derived using simple random sampling at both the phases as a special case. Then the comparison has been made with the regression-type estimator and sample variance. Results have also been illustrated numerically and graphically. [ABSTRACT FROM AUTHOR]

In this paper, a new approach to independent component analysis (ICA) for three-way data is considered. The rotational freedom of the three-mode component analysis (Tucker3) model is exploited to implement ICA in one mode of the data. The performance of the proposed approach is evaluated by means of numerical experiments. An illustration with real data from atmospheric science is presented, where the first mode is spatial location, the second is time and the third is a set of different meteorological variables representing geopotential heights at various vertical pressure levels. The results show that the three-mode decomposition finds spatial patterns of climate anomalies which can be interpreted in a meteorological sense and as such gives an insightful low-dimensional representation of the data. [ABSTRACT FROM AUTHOR]

The article focuses on the statistical approach in determining the relationships between categorical dependent and different variables. It mentions the significance of categorical dependent variables as well as censored data in conducting veterinary-related studies and in determining the prognostic indicators. The random sampling noncensored observations and linear relationships are also detailed.

Classification performance of an ensemble method can be deciphered by studying the bias and variance contribution to its classification error. Statistically, the bias and variance of a single classifier is controlled by the size of the training set and the complexity of the classifier. It has been both theoretically and empirically established that the classification performance (hence bias and variance) of a single classifier can be improved partially by using a suitable ensemble method of the classifier and resampling the original training set. In this paper, we have empirically examined the bias-variance decomposition of three different types of ensemble methods with different training sample sizes consisting of 10% to maximum 63% of the observations from the original training sample. First ensemble is bagging, second one is a boosting type ensemble named adaboost and the last one is a bagging type hybrid ensemble method, called bundling. All the ensembles are trained on training samples constructed with small subsampling ratios (SSR) 0.10, 0.20, 0.30, 0.40, 0.50 and bootstrapping. The experiments are all done on 20 UCI Machine Learning repository datasets and designed to find out the optimal training sample size (smaller than the original training sample) for each ensemble and then find out the optimal ensemble with smaller trianing sets with respect to the bias-variance performance. The bias-variance decomposition of bundling shows that this ensemble method with small subsamples has significantly lower bias and variance than subsampled and bootstrapped version of bagging and adaboost. [ABSTRACT FROM AUTHOR]

The authors deal with the problem of comparing receiver operating characteristic (ROC) curves from independent samples. From a nonparametric approach, they propose and study three different statistics. Their asymptotic distributions are obtained and a resample plan is considered. In order to study the statistical power of the introduced statistics, a simulation study is carried out. The (observed) results suggest that, for the considered models, the new statistics are more powerful than the usually employed ones (the Venkatraman test and the usual area under the ROC curve criterion) in non-uniform dominance situations and quite good otherwise. [ABSTRACT FROM AUTHOR]

The article presents a study which examines the impact of snow depth variability at the plot scale in Rio Ésera Valley in Pyrenees mountains in Spain on the representativeness of depth samples. The study analyzes the spatial distribution of snow by conducting a snow depth sampling between January and April 2009 in 15 plots. It is found out that increasing the number of the snow depth measurements can improve the representativeness of snow depth sampling in a given plot.

In this article, we consider bootstrapping the Lasso estimator of the regression parameter in a multiple linear regression model. It is known that the standard bootstrap method fails to be consistent. Here, we propose a modified bootstrap method, and show that it provides valid approximation to the distribution of the Lasso estimator, for all possible values of the unknown regression parameter vector, including the case where some of the components are zero. Further, we establish consistency of the modified bootstrap method for estimating the asymptotic bias and variance of the Lasso estimator. We also show that the residual bootstrap can be used to consistently estimate the distribution and variance of the adaptive Lasso estimator. Using the former result, we formulate a novel data-based method for choosing the optimal penalizing parameter for the Lasso using the modified bootstrap. A numerical study is performed to investigate the finite sample performance of the modified bootstrap. The methodology proposed in the article is illustrated with a real data example. [ABSTRACT FROM AUTHOR]

To identify a target, the moving noncoherent colocated multiple-input multiple-output (MIMO) radar system takes advantage of multiple antennas in transmission and reception which are close in space. In this paper, we study the estimation performance and the resolution limit for this scheme in which each array geometry is described by the sample-variance of the sensor distribution. So, our analysis encompasses any sensor distributions, including varying intersensors distances or/and lacunar (missing sensors) configuration. As in the space-time MIMO model considered here the radar is moving, the target Doppler frequency cannot be assumed invariant to the target position/angle. The first part of this paper derives and analyzes closed form (nonmatrix) expressions of the deterministic Cramér-Rao lower bound (CRB) for the direction and the velocity of a moving target contaminated by a structured noise (clutter echoes) and a background noise, including the cases of the clutter-free environment and the high signal-to-noise ratio (SNR) regime. The analysis of the proposed expressions of the CRB allows to better understand the characterization of the target. In particular, we prove the coupling between the direction parameter and the velocity of the target is linear with the radar velocity. In the second part, we focus our study on the analytical (closed form) derivation and the analysis of the angular resolution limit (ARL). Based on the resolution of an equation involving the CRB, the ARL can be interpreted as the minimal separation to resolve two closely spaced targets. Consequently, the ARL is a key quantity to evaluate the performance of a radar system. We show that the ARL is in fact quasi-invariant to the movement of the MIMO radar. [ABSTRACT FROM PUBLISHER]

Based on the odds ratio representation of a joint density, we propose a unified framework to study parameter identifiability in biased sampling designs. It is shown that most of these designs encountered in practice can be reformulated within the proposed framework and, as a result, the question of parameter identifiability can be largely clarified. Estimation of the identifiable parameters is considered and traditional results on the equivalence of the prospective and retrospective likelihoods are extended. Information contained in data on certain identifiable parameters is often very limited. Such parameters can be poorly estimated by the likelihood approach with practically attainable sample sizes, which can substantially affect the estimates of parameters of primary interest. A partially penalized likelihood approach is proposed to address this. Simulation results suggest that the proposed approach has good performance. [ABSTRACT FROM PUBLISHER]

For the univariate case, the R chart and the S2 chart are the most common charts used for monitoring the process dispersion. With the usual sample size of 4 and 5, the R chart is slightly inferior to the S2 chart in terms of efficiency in detecting process shifts. In this article, we show that for the multivariate case, the chart based on the standardized sample ranges, we call the RMAX chart, is substantially inferior in terms of efficiency in detecting shifts in the covariance matrix than the VMAX chart, which is based on the standardized sample variances. The user's familiarity with sample ranges is a point in favor of the RMAX chart. An example is presented to illustrate the application of the proposed chart. [ABSTRACT FROM AUTHOR]