On a general mixed priority queue with server discretion

We consider a single-server queueing system which attends to N priority classes that are classified into two distinct types: (i) urgent: classes which have preemptive resume priority over at least one lower priority class, and (ii) non-urgent: classes which only have non-preemptive priority among lower priority classes. While urgent customers have preemptive priority, the ultimate decision on whether to interrupt a current service is based on certain discretionary rules. An accumulating prioritization is also incorporated. The marginal waiting time distributions are obtained and numerical examples comparing the new model to other similar priority queueing systems are provided.     

General m-esttmators and applications to bounded influence estimation for non-linear regression

In this paper, we study the M-estimators in the case that λ_F:(β)=E_F:(φ(Z,β))=0 has more than one solution, We show that the numerical iterative procedures converge and that the resulting estimators are consistent and asymptotically normal. We apply them to the non-linear regression models, and then, we find an optimal M-estimate among those that have bounded gross error sensitivity.     

DRAM: Efficient adaptive MCMC

We propose to combine two quite powerful ideas that have recently appeared in the Markov chain Monte Carlo literature: adaptive Metropolis samplers and delayed rejection. The ergodicity of the resulting non-Markovian sampler is proved, and the efficiency of the combination is demonstrated with various examples. We present situations where the combination outperforms the original methods: adaptation clearly enhances efficiency of the delayed rejection algorithm in cases where good proposal distributions are not available. Similarly, delayed rejection provides a systematic remedy when the adaptation process has a slow start.     

Indexing the Federal Tax System: A Cost-of-Living Approach

In this article, we analyze the indexation of federal taxes, using an approach based on cost-of-living measurement. We use our Tax and Price Index methodology and data base to study an indexed system historically, comparing indexation with the Consumer Price Index (CPI) to actual tax policy, a tax system with constant parameters, and an “exact” indexing scheme. We reach three main conclusions: (a) The sequence of tax reductions implemented between 1967 and 1985 have fallen short of mimicking indexation, (b) wealthier households would have benefited relatively more than lower-income households from indexation, and (c) CPI indexation would not have completely eliminated bracket creep.     

Diagnostic checks for discrete data regression models using posterior predictive simulations

Model checking with discrete data regressions can be difficult because the usual methods such as residual plots have complicated reference distributions that depend on the parameters in the model. Posterior predictive checks have been proposed as a Bayesian way to average the results of goodness-of-fit tests in the presence of uncertainty in estimation of the parameters. We try this approach using a variety of discrepancy variables for generalized linear models fitted to a historical data set on behavioural learning. We then discuss the general applicability of our findings in the context of a recent applied example on which we have worked. We find that the following discrepancy variables work well, in the sense of being easy to interpret and sensitive to important model failures: structured displays of the entire data set, general discrepancy variables based on plots of binned or smoothed residuals versus predictors and specific discrepancy variables created on the basis of the particular concerns arising in an application. Plots of binned residuals are especially easy to use because their predictive distributions under the model are sufficiently simple that model checks can often be made implicitly. The following discrepancy variables did not work well: scatterplots of latent residuals defined from an underlying continuous model and quantile–quantile plots of these residuals.     

A comparison of random balance and two-stage group screening designs: A case study

In this paper we focus on the problem of supersaturated (fewer runs than factors) screening experiments. We consider two major types of designs which have been proposed in this situ¬ation: random balance and two-stage group screening. We discuss the relative merits and demerits of each strategy. In addition, we compare the performance of these strategies by means of a case study in which 100 factors are screened in 20,42,62, and 84 runs.     

Estimating the error variance in nonparametric regression by a covariate-matched u-statistic

For nonparametric regression models with fixed and random design, two classes of estimators for the error variance have been introduced: second sample moments based on residuals from a nonparametric fit, and difference-based estimators. The former are asymptotically optimal but require estimating the regression function; the latter are simple but have larger asymptotic variance. For nonparametric regression models with random covariates, we introduce a class of estimators for the error variance that are related to difference-based estimators: covariate-matched U-statistics. We give conditions on the random weights involved that lead to asymptotically optimal estimators of the error variance. Our explicit construction of the weights uses a kernel estimator for the covariate density.     

Estimating Parliamentary composition through electoral polls

Summary.  All electoral systems have an electoral formula that converts proportions of votes into Parliamentary seats. Pre-electoral polls usually focus on estimating proportions of votes and then apply the electoral formula to give a forecast of Parliamentary composition. We describe the problems that arise from this approach: there will typically be a bias in the forecast. We study the origin of the bias and some methods for evaluating and reducing it. We propose a bootstrap algorithm for computing confidence intervals for the allocation of seats. We show, by Monte Carlo simulation, the performance of the proposed methods using data from Spanish elections in previous years. We also propose graphical methods for visualizing how electoral formulae and Parliamentary forecasts work (or fail).     

Was the conservative majority predictable?

Canada's $41{\rm st}$ national general election saw the Conservative Party increase its seat count from 143 to 166, thus giving it a majority of the national parliament's 308 seats. By contrast, nearly all of the pre‐election seat count forecasts predicted a Conservative minority only. We examine the extent to which simple statistical models could or could not have predicted the Conservative majority prior to the election. We conclude that, by using data from the previous (2008) election appropriately, the Conservative majority should have been anticipated as the most likely outcome. The Canadian Journal of Statistics 39: 721–733; 2011. © 2011 Statistical Society of Canada     

Smooth estimation of a monotone density

We investigate the interplay of smoothness and monotonicity assumptions when estimating a density from a sample of observations. The nonparametric maximum likelihood estimator of a decreasing density on the positive half line attains a rate of convergence of [Formula: See Text] at a fixed point t if the density has a negative derivative at t. The same rate is obtained by a kernel estimator of bandwidth [Formula: See Text], but the limit distributions are different. If the density is both differentiable at t and known to be monotone, then a third estimator is obtained by isotonization of a kernel estimator. We show that this again attains the rate of convergence [Formula: See Text], and compare the limit distributions of the three types of estimators. It is shown that both isotonization and smoothing lead to a more concentrated limit distribution and we study the dependence on the proportionality constant in the bandwidth. We also show that isotonization does not change the limit behaviour of a kernel estimator with a bandwidth larger than [Formula: See Text], in the case that the density is known to have more than one derivative.     

中国房地产市场波动对宏观经济波动的影响研究

 房地产的波动会通过多种途径影响一国的宏观经济状况。为说明房地产市场的波动对我国宏观经济的影响,我们通过协整和VAR分析,实证了：①房地产价格波动对我国消费的影响,得出房价波动对社会消费品零售总额的波动有显著的负影响,且房价波动对消费波动的方差贡献最小都大于2.5%左右;②我国房地产投资波动对经济增长的影响,研究表明,房地产投资额的波动对GDP的增长率有显著的正影响,当房地产投资额的增长率上升1个百分点时,GDP增长率上涨0.181个百分点,且1个单位的房地产投资波动的冲击在第4个季度时达到最大,之后缓慢衰减,这说明房地产投资的波动对GDP有长期的影响;③我国房地产价格波动对通货膨胀的影响,计量结果表明,当房价的增长速度上升1个百分点时,通货膨胀率则上升0.118个百分点,且通货膨胀率对房价波动冲击的响应比较小,在第8个月达到最大,以后则开始衰减,而且达到的最大的影响以后,甚至出现负的、不稳定的影响。     

Dominance refinements of the Smirnov two-sample test

We prove the following conjecture of Narayana: there are no nontrivial dominance refinements of the Smirnov two-sample test if and only if the two sample sizes are relatively prime. We also count the number of natural significance levels of the Smirnov two-sample test in terms of the sample sizes and relate this to the Narayana conjecture. In particular, Smirnov tests with relatively prime sample sizes turn out to have many more natural significance levels than do Smirnov tests whose sample sizes are not relatively prime (for example, equal sample sizes).     

Information in Buffon experiments

Buffon needle experiments have long been used to estimate π. In this paper we analyse two Buffon grid types: grids consisting of a single bend in a segment, and star grids. We show that the simplest grids allow us to estimate π most efficiently. Our results build on earlier findings of Perlman and Wichura.     

Nonparametric Tests for Comparing Several Coefficients of Variation

We consider the problem of comparing (k + 1) coefficients of variation. We are interested in testing the null hypothesis that the coefficients of variation are equal against each of the alternatives: (a) some populations have different coefficients of variation and (b) the coefficients of variation are ordered. Three nonparametric test statistics are proposed and their asymptotic theory is developed. We compared the proposed tests together with another parametric test using two Monte Carlo studies to estimate their probabilities of Type I error and powers. An illustration of the proposed tests using a real data set is given.     

Comparison of non-parametric and semi-parametric tests in detecting long memory

The first two stages in modelling times series are hypothesis testing and estimation. For long memory time series, the second stage was studied in the paper published in [M. Boutahar et al., Estimation methods of the long memory parameter: monte Carlo analysis and application, J. Appl. Statist. 34(3), pp. 261–301.] in which we have presented some estimation methods of the long memory parameter. The present paper is intended for the first stage, and hence completes the former, by exploring some tests for detecting long memory in time series. We consider two kinds of tests: the non-parametric class and the semi-parametric one. We precise the limiting distribution of the non-parametric tests under the null of short memory and we show that they are consistent against the alternative of long memory. We perform also some Monte Carlo simulations to analyse the size distortion and the power of all proposed tests. We conclude that for large sample size, the two classes are equivalent but for small sample size the non-parametric class is better than the semi-parametric one.     

Tolerance Limits Based on the Multivariate MaxMin Chart

In a previous paper, we have showed how to obtain sequences of number proved random. With this aim, we used sequences of noises y_n such that the conditional probabilities have Lipschitz coefficients not too large. We transformed them using Fibonacci congruences. Then, we obtained sequences x_n which admit the IID model for correct model. This method consisted to value the work of Marsaglia in order to build his CD-ROM. But we did not use Rap Music (as Marsaglia), but texts files. This method also uses an extractor and at the same time the notion of correct models. In this paper, we apply this method to numbers provided by machines or chips. Unfortunately, it is less sure than they have Lipschtiz coefficient not too large. But we can solve this problem: it suffices to use the Central Limit Theorem. We do it modulo 1. In this case, we use a new limit theorem, the XOR Limit theorem : asymptotic distribution of sum of random vectors modulo 1 are asymptotically independent. Then Lipschtiz coefficient of associated sequences are not too large and we can obtain IID sequences by using Fibonacci congruences.     

On stochastic processes for quantitative trait locus mapping under selective genotyping

We consider the likelihood ratio test (LRT) process related to the test of the absence of QTL (a QTL denotes a quantitative trait locus, i.e. a gene with quantitative effect on a trait) on the interval [0, T] representing a chromosome. The originality of this study is that we are under selective genotyping: only the individuals with extreme phenotypes are genotyped. We give the asymptotic distribution of this LRT process under the null hypothesis that there is no QTL on [0, T] and under local alternatives with a QTL at t^☆ on [0, T]. We show that the LRT process is asymptotically the square of a ‘non-linear interpolated and normalized Gaussian process’. We have an easy formula in order to compute the supremum of the square of this interpolated process. We prove that we have to genotype symmetrically and that the threshold is exactly the same as in the situation where all the individuals are genotyped.     

Profile Hellinger distance estimation

The successful application of the Hellinger distance approach to fully parametric models is well known. The corresponding optimal estimators, known as minimum Hellinger distance (MHD) estimators, are efficient and have excellent robustness properties [Beran R. Minimum Hellinger distance estimators for parametric models. Ann Statist. 1977;5:445–463]. This combination of efficiency and robustness makes MHD estimators appealing in practice. However, their application to semiparametric statistical models, which have a nuisance parameter (typically of infinite dimension), has not been fully studied. In this paper, we investigate a methodology to extend the MHD approach to general semiparametric models. We introduce the profile Hellinger distance and use it to construct a minimum profile Hellinger distance estimator of the finite-dimensional parameter of interest. This approach is analogous in some sense to the profile likelihood approach. We investigate the asymptotic properties such as the asymptotic normality, efficiency, and adaptivity of the proposed estimator. We also investigate its robustness properties. We present its small-sample properties using a Monte Carlo study.     

Statistical Issues in Fisheries' Stock Assessments*

Decisions concerning the management of fisheries are founded on confidence statements for interest parameters such as biomass and exploitation rate, derived from complex structural models that describe the dynamics of fisheries. We identify four generic statistical issues and focus on how they impact on the reliability of those confidence statements: (a) parameters for which the data have little or no information; (b) competing structural relationships; (c) weighting of observations; and (d) alternative methods for computing confidence statements. Our purpose is to give an exposition of how these issues impact on fisheries' analyses, with the intent of stimulating thought on more effective alternatives. We describe the fisheries' management context and use two specific studies to illustrate how these generic statistical issues impact on fisheries assessment results. It is demonstrated that these statistical issues can have a profound impact on fishery management decisions and that established approaches to handle them have not been fully developed.     

A new procedure for variance estimation in simple random sampling using auxiliary information

In this article we have envisaged an efficient generalized class of estimators for finite population variance of the study variable in simple random sampling using information on an auxiliary variable. Asymptotic expressions of the bias and mean square error of the proposed class of estimators have been obtained. Asymptotic optimum estimator in the proposed class of estimators has been identified with its mean square error formula. We have shown that the proposed class of estimators is more efficient than the usual unbiased, difference, Das and Tripathi (Sankhya C 40:139–148, 1978), Isaki (J. Am. Stat. Assoc. 78:117–123, 1983), Singh et al. (Curr. Sci. 57:1331–1334, 1988), Upadhyaya and Singh (Vikram Math. J. 19:14–17, 1999b), Kadilar and Cingi (Appl. Math. Comput. 173:2, 1047–1059, 2006a) and other estimators/classes of estimators. In the support of the theoretically results we have given an empirical study.