Large Sample Variance Research Articles

Comparison of methods for analysis of extremes when records are fragmented: A case study using Amazon basin rainfall data

The analysis of annual extremes of hydrological and meteorological variables is frequently complicated by the presence of gaps in record, and when records are not only fragmented but also short, it is necessary to utilize to the full the information contained in them. One method is to abstract for statistical analysis all extreme events whose peaks exceed a pre-selected threshold value, but the threshold must be carefully chosen if clumps of peaks are to be avoided. A common alternative is a statistical analysis of maxima in years that are complete, possibly including in the analysis values from incomplete years according to some empirical rule. A plausible probability distribution has been proposed by [Jones, D.A., 1997. Plotting positions via maximum likelihood for a non-standard situation. Hydrol. Earth Syst. Sci. 1, 357-366] for the extremes observed in incomplete years, which takes into account not only the proportion of record that is missing within an incomplete year, but also the effect of seasonality. As part of a larger study on the hydrology of the Amazon basin, this paper uses 484 records with length not less than 12 years from an extensive network of 750 rain gauges, to compare the method proposed by Jones (termed the DAJ method) with the following alternative procedures: (i) using only complete years of record and (ii) including years with less than 20% missing record, as if they were complete. Using the large-sample variance calculated for the annual maximum one-day rainfall with 100-year return period (P-100), the method proposed by Jones is shown to give smaller standard errors than either of the alternatives. Using the number of years in each record to calculate weighted mean variances over the 484 records, the mean standard errors of Ploo obtained by methods (i) and (ii) were 1.25 and 1.06 times the mean standard error given by the DAJ method. The precision of estimates obtained by the latter method was therefore better than either alternative. (c) 2009 Elsevier B.V. All rights reserved. (Less)

Likelihood calculations to evaluate experimental designs to estimate genetic variances

Mixed model analyses via restricted maximum likelihood, fitting the so-called animal model, have become standard methodology for the estimation of genetic variances. Models involving multiple genetic variance components, due to different modes of gene action, are readily fitted. It is shown that likelihood-based calculations may provide insight into the quality of the resulting parameter estimates, and are directly applicable to the validation of experimental designs. This is illustrated for the example of a design suggested recently to estimate X-linked genetic variances. In particular, large sample variances and sampling correlations are demonstrated to provide an indication of 'problem' scenarios. Using simulation, it is shown that the profile likelihood function provides more appropriate estimates of confidence intervals than large sample variances. Examination of the likelihood function and its derivatives are recommended as part of the design stage of quantitative genetic experiments.

The Measure of Exogamous Marriage through Disagreement Scaling

In this paper we used the weighted kappa through disagreement scaling proposed by Cohen (1968) to measure the exogamous marriage. It is the interest of sociologist to investigate the trend of exogamous or mixed marriage between different ethnic groups, as the upward trend of mixed marriage can be view as degree of assimilation of particular ethnic groups. We are able to measure the strength of exogamous marriage directly. We found that the upward trend of mixed marriage among Americans of different ethnicity tend to increase from 1980 to 2000. We also used the estimated large sample variance of weighted kappa given by Fleiss et al. (1969) to build the Wald confidence interval and hence testing the null hypothesis of nonexistence of exogamous marriage.

Reliability studies of diagnostic tests are not using enough observers for robust estimation of interobserver agreement: a simulation study

Objective Any attempt to generalize the performance of a subjective diagnostic method should take into account the sample variation in both cases and readers. Most current measures of the performance of a test, especially the indices of reliability, only tackle the variation of cases, and hence are not suitable for generalizing results across the population of readers. We attempted to study the effect of readers' variation on two measures of multireader reliability: pair-wise agreement and Fleiss' kappa. Study Design and Setting We used a normal hierarchical model with a latent trait (signal) variable to simulate a binary decision-making task by different number of readers on an infinite sample of cases. Results It could be shown that both measures, especially Fleiss' kappa, have a large sample variance when estimated by a small number of readers, casting doubt on their accuracy given the number of readers typically used in current reliability studies. Conclusion The majority of the current agreement studies is likely limited by the number of readers and is unlikely to produce a reliable estimate of reader agreement.

Estimation of the Mean of Truncated Exponential Distribution

Problem statement: In this study, the researcher considers the problem of estimation of the mean of the truncated exponential distribution. Approach: This study contracted with maximum likelihood and unique minimum variance unbiased estimators and gives a modification for the maximum likelihood estimator, asymptotic variances and asymptotic confidence intervals for the estimators. The properties of these estimators in small, moderate and large samples were investigated via asymptotic theory and computer simulation. Results: It turns out that the modified maximum likelihood estimator was more efficient than the others and exists with probability 1. Conclusion: The modified maximum likelihood estimator was always exist, fast and straightforward to compute and more likely to yield feasible values than the unique minimum variance unbiased estimator. Its variance was well approximated by the large sample variance of the other estimators.

SEMIPARAMETRIC ESTIMATION OF THE ERROR DISTRIBUTION IN MULTIVARIATE REGRESSION USING COPULAS

SummaryA semiparametric method is developed to estimate the dependence parameter and the joint distribution of the error term in the multivariate linear regression model. The nonparametric part of the method treats the marginal distributions of the error term as unknown, and estimates them using suitable empirical distribution functions. Then the dependence parameter is estimated by either maximizing a pseudolikelihood or solving an estimating equation. It is shown that this estimator is asymptotically normal, and a consistent estimator of its large sample variance is given. A simulation study shows that the proposed semiparametric method is better than the parametric ones available when the error distribution is unknown, which is almost always the case in practice. It turns out that there is no loss of asymptotic efficiency as a result of the estimation of regression parameters. An empirical example on portfolio management is used to illustrate the method.

Estimating the error distribution in multivariate heteroscedastic time-series models

A semiparametric method is studied for estimating the dependence parameter and the joint distribution of the error term in a class of multivariate time-series models when the marginal distributions of the errors are unknown. This method is a natural extension of Genest, C., Ghoudi, K., Rivest, L.-P. [1995. A semiparametric estimation procedure of dependence parameters in multivariate families of distributions. Biometrika 82, 543–552.] for independent and identically distributed observations. The proposed method first obtains n -consistent estimates of the parameters of each univariate marginal time series, and computes the corresponding residuals. These are then used to estimate the joint distribution of the multivariate error terms, which is specified using a copula. Our developments and proofs make use of, and build upon, recent results of Koul and Ling [2006. Fitting an error distribution in some heteroscedastic time series model. Ann. Statist. 34, 994–1012.] and Koul [2002.Weighted empirical processes in dynamic nonlinear models, Lecture Notes in Statistics, vol. 166. Springer, New York.] for these models. The rigorous proofs provided here also lay the foundation and collect together the technical arguments that would be useful for other potential extensions of this semiparametric approach. It is shown that the proposed estimator of the dependence parameter of the multivariate error term is asymptotically normal, and a consistent estimator of its large sample variance is also given so that confidence intervals may be constructed. A large-scale simulation study was carried out to compare the estimators particularly when the error distributions are unknown, which is almost always the case in practice. In this simulation study, our proposed semiparametric method performed better than the well-known parametric methods. An example on exchange rates is used to illustrate the method.

Empirical Bias Bandwidth Choice for Local Polynomial Matching Estimators

This paper addresses the choice of an optimal smoothing parameter for local polynomial matching. A version of Empirical Bias Bandwidth Selection (EBBS) proposed by Ruppert (1997) is applied to account for the MSE computation of the matching estimator. Thereby, an estimator for the large sample variance of the local polynomial matching estimator is also provided. A Monte Carlo study indicates better small sample performance of nonparametric matching estimators when the bandwidth choice is based on EBBS in comparison to cross-validation. Furthermore, the method is applied to estimate the treatment efiect on the treated (TT) of the National Supported Work (NSW) Demonstration.

Semiparametric Estimation of Animal Abundance Using Capture–Recapture Data from Open Populations

A semiparametric partially linear model for the size of an open population is proposed and inference is conducted using weighted martingale estimating equations. This extends a previous nonparametric approach to modeling capture-recapture data for open populations with frequent capture occasions. Analytic expressions for the large sample variances are derived and these are confirmed in a simulation study. The method is illustrated on monthly penguin banding data collected over 6 years.

Measuring Agreement for Ordered Ratings in 3 x 3 Tables

When two raters consider a qualitative variable ordered according to three categories, the qualitative agreement is commonly assessed with a symmetrically weighted kappa statistic. However, these statistics can present paradoxes, since they may be insensitive to variations of either complete agreements or disagreements. Agreement may be summarized by the relative amounts of complete agreements, partial and maximal disagreements beyond chance. Fixing the marginal totals and the trace, we computed symmetrically weighted kappa statistics and we developed a new statistic for qualitative agreements. Data sets from the literature were used to illustrate the methods. We show that agreement may be better assessed with the unweighted kappa index, kappa(c), and a new statistic zeta, which assesses the excess of maximal disagreements with respect to the partial ones, and does not depend on a particular weighting system. When zeta is equal to zero, maximal and partial disagreements beyond chance are equal. With its estimated large sample variance, we compared the values of two contingency tables. The (kappa(c), zeta) pair is sensitive to variations in agreements and/or disagreements and enables locating the difference between two qualitative agreements. The qualitative agreement is better with increasing values of kappa(c) and zeta.

Large Sample Properties of Matching Estimators for Average Treatment Effects

Matching estimators for average treatment effects are widely used in evaluation research despite the fact that their large sample properties have not been established in many cases. The absence of formal results in this area may be partly due to the fact that standard asymptotic expansions do not apply to matching estimators with a fixed number of matches because such estimators are highly nonsmooth functionals of the data. In this article we develop new methods for analyzing the large sample properties of matching estimators and establish a number of new results. We focus on matching with replacement with a fixed number of matches. First, we show that matching estimators are not N 1/2 -consistent in general and describe conditions under which matching estimators do attain N 1/2 -consistency. Second, we show that even in settings where matching estimators are N 1/2 -consistent, simple matching estimators with a fixed number of matches do not attain the semiparametric efficiency bound. Third, we provide a consistent estimator for the large sample variance that does not require consistent nonparametric estimation of unknown functions. Software for implementing these methods is available in Matlab, Stata, and R.

On the use of the sample partial autocorrelation for order determination in a pure autoregressive process: a Monte Carlo study and empirical example

Sample partial autocorrelations are one of the main statistical tools of time series analysis. They are especially useful in identifying the order of an AR(p) process. In this note, we show via a simulation experiment that normalizing each sample partial autocorrelation with Anderson's (1993a) means and variances, instead of the large-sample moments, can yield asymptotic distributions that are better approximated by the N(0,1) distribution. The important implication of this result is that the true order of a pure autoregressive process can be incorrectly identified due to use of the large-sample mean and variance of sample partial autocorrelations. An empirical example given in Box and Jenkins (1976) is used to highlight this problem.

Maximum Likelihood Estimation of Two Inversely Related Poisson Rate Parameters with Misclassified Data

SYNOPTIC ABSTRACTWe derive maximum likelihood estimators (MLEs) for two inversely related Poisson rate parameters when data is subject to misclassification. We assume a cheap error-prone device is used to search a large area and an expensive error-free search method is utilized on a smaller area. This double sample allows identification of all unknown parameters. Additionally, we derive large sample variance approximations for the rate parameter estimators, give asymptotic confidence intervals for the rate parameters, and study these confidence intervals via a Monte Carlo simulation. We then apply the newly derived estimator and confidence intervals to a real data problem.

A Study on Two Group Comparison in Gene Expression Data

Tusher, Tibshirani and Chu (2001) suggested SAM (Significance Analysis of Microarrays) to compare two groups under different conditions for each gene, using microarray data. They used two sample t-statistic adding fudge factor in the denominator to prevent the value of statistic from being inflated by large sample variance, which might result in significant difference despite of a small value in the numerator. This paper aims at finding robust fudge factor and replacing it in two-sample t-statistic used in SAM, which we call Modified SAM (MSAM). Using the simulated data and data used in Dudoit et al.(2002), it is shown that MSAM find significant genes better and has less error rate than SAM.

Interpreting the Observed Clustering of Red Galaxies atz∼ 3

Daddi et al. have recently reported strong clustering of a population of red galaxies at z � 3 in the Hubble Deep Field-South. Fitting the observed angular clustering with a power law of index � 0.8, they infer a comoving correlation length r0 � 8 h � 1 Mpc; for a standard cosmology, this r0 would imply that the red galaxies reside in rare, M � 10 13 h � 1 Mhalos, with each halo hosting � 100 galaxies to match the number density of the pop- ulation. Using the framework of the halo occupation distribution (HOD) in a CDM universe, we show that the Daddi et al. data can be adequately reproduced by less surprising models, e.g., models with galaxies residing in halos of mass M > Mmin ¼ 6:3;10 11 h � 1 Mand a mean occupation Navg(M) ¼ 1:4(M =Mmin) 0:45 above this cutoff. The resultant correlation functions do not follow a strict power law, showing instead a clear transition from the one-halo-dominated regime, where the two galaxies of each pair reside in the same dark matter halo, to the two-halo-dominated regime, where the two galaxies of each pair are from different halos. The observed high- amplitude data points lie in the one-halo-dominated regime, so these HOD models are able to explain the observations despite having smaller correlation lengths, r0 � 5 h � 1 Mpc. HOD parameters are only loosely constrained by the current data because of large sample variance and the lack of clustering information on scales that probe the two-halo regime. If our explanation of the data is correct, then future observations covering a larger area should show that the large-scale correlations lie below a � � 1:8 extrapolation of the small-scale points. Our models of the current data suggest that the red galaxies are somewhat more strongly clustered than UV-selected Lyman break galaxies and have a greater tendency to reside in small groups. Subject heading gs: galaxies: halos — galaxies: high-redshift — large-scale structure of universe

Variability in Respiratory Protection and the Assigned Protection Factor

The workplace protection factor (WPF) for a given respirator wearer shows substantial variability from wearing to wearing; this variability is commonly assumed to be lognormal in nature. Further, when multiple WPFs are measured for each of multiple wearers, the aggregated WPFs appear to follow a lognormal distribution. However, the analysis typically applied to WPF data does not apportion variability within versus between wearers. We present an analytical framework based on a normal random effects model of log-transformed penetration P values (P = 1/WPF). Data from seven studies of negative-pressure air-purifying half-mask respirators, and from two studies of hemlet-and-visor type powered air-purifying respirators were analyzed by the method of maximum likelihood in the context of the model. More specifically, analyses were performed for log-transformed P values and for logit-transformed P values. Parameter estimates included within-wearer and between-wearer variance components. In general, the within-wearer component dominated the between-wearer component. We also propose a method for establishing an assigned protection factor, APF, that properly accounts for these variance components. Our method provides an APF satisfying two criteria: (1) for a given wearer, an acceptable WPF distribution has no more than 5% of WPFs below the APF value; and (2) for a wearer population, no more than 5% of wearers have unacceptable WPF distributions. The method incorporates an one-sided confidence limit to account for sampling variability. Alternative confidence limits were computed based on large sample variance estimates of random effects model parameters versus a bootstrap method. In general, there was good agreement between the APF values based on log-transformed versus logit-transformed P data, and between APF values based on the large sample variance estimates versus the bootstrap method. Based on large sample variance estimates for the logit-transformed P data from the seven half-mask studies, estimated APFs ranged from 1.4 to 250, with 5/7 studies yielding an APF ≤ 5.3. Given these results and related considerations, we recommend that the current half-mask APF be reduced from 10 to 5.

On the optimum number of levels in the one-way model with random effects

The optimal number of levels is studied for the one-way random model with normally distributed effects. The optimum criteria used are based on the variances of the traditional analysis of variance estimators of the variance components. Exact solutions are compared to earlier results based on lower bounds of the sampling variances. Comparisons are also made to the large-sample variances of the estimates based on restricted maximum likelihood.

Optimal blind nonlinear least-squares carrier phase and frequency offset estimation for general qam modulations

This paper introduces a family of blind feedforward nonlinear least-squares (NLS) estimators for joint estimation of the carrier phase and frequency offset of general quadrature amplitude modulated (QAM) transmissions. As an extension of the Viterbi and Viterbi (1983) estimator, a constellation-dependent optimal matched nonlinear estimator is derived such that its asymptotic (large sample) variance is minimized. A class of conventional monomial estimators is also proposed. The asymptotic performance of these estimators is established in closed-form expression and compared with the Cramer-Rao lower bound. A practical implementation of the optimal matched estimator, which is a computationally efficient approximation of the latter and exhibits negligible performance loss, is also derived. Finally, computer simulations are presented to corroborate the theoretical performance analysis and indicate that the proposed optimal matched nonlinear estimator improves significantly the performance of the classic fourth-power estimator.

Conceptualizing Interrater Agreement as Testing the Existence of Extra Variation in the Multinomial Model

The existence of extra variation has long been of interest to many researchers. In some studies, it may be a nuisance variable that needs to be accounted for. In other cases, it is the parameter of interest, such as agreement among raters in a study. In this article, I demonstrate how the goodness-of-fit (GOF) procedure and a test statistic based on a large-sample variance from Bartfay and Donner (2001a) can be applied to assess whether there is agreement, as an example of extra variation, between 2 raters. Using a Monte Carlo simulation study, I compare the properties of these 2 procedures to the likelihood ratio test. The results show that the GOF procedure possesses satisfactory Type I error rate and power. I illustrate these methods using a published data set on assessing the agreement between two reviewers on accepting manuscripts for publication.

Advanced formulation of base pair changes in the stem regions of ribosomal RNAs; its application to mitochondrial rRNAs for resolving the phylogeny of animals

The ribosomal RNAs (rRNAs) of animal mitochondria, especially those of arthropod mitochondria, have a higher content of G:U and U:G base pairs in their stem regions than the nuclear rRNAs. Thus, the theoretical formulation of base pair changes is extended to incorporate the faster base pair changes A:U↔G:U↔G:C and U:A↔U:G↔C:G into the previous formulation of the slower base pair changes between A:U, G:C, C:G and U:A. The relative base pair change probability containing the faster and slower base pair changes is theoretically derived to estimate the divergence time of rRNAs under the influence of selection for these base pairs. Using the cartilaginous fish–teleost fish divergence and the crustacean–insect divergence as calibration points, the present method successfully predicts the divergence times of the main branches of animals: Deuterostomia and Protostomia diverged 9.2×10 8 years ago, the divergence of Echinodermata, Hemichordata and Cephalochordata succeedingly occurred during the period from 8×10 8 to 6×10 8 years ago, while Arthropoda, Annelida and Mollusca diverged almost concomitantly about 7×10 8 years ago. The dating for the divergence of Platyhelminthes and Cnidaria is traced back to 1.2×10 9 years ago. This result is consistent with the fossil records in the Stirling Range Formation of southwestern Australia, the Ediacara and Avalon faunas and the Cambrian Burgess Shale. Thus, the present method may be useful for estimating the divergence times of animals ranging from 10 8 to 10 9 years ago, resolving the difficult problems, e.g. deviation from rate constancy and large sampling variances, in the usual methods of treating apparent change rates between individual bases and/or base pairs.