Bartlett-corrected tests for normal linear models when the error covariance matrix is nonscaiar

This paper provides Bartlett corrections to improve likelihood ratio tests for heteroskedastic normal linear models when the error covariance matrix is nonscaiar and depends on a set of unknown parameters. The Bartlett corrections are simple enough to be used algebraically to obtain several closed-form expressions in special cases. The corrections have also advantages for numerical purposes because they involve only simple operations on matrices and vectors.     

Variance Estimation Based on Invariance Principles

Consistent variance estimators for certain stochastic processes are suggested using the fact that (weak or strong) invariance principles may be available. Convergence rates are also derived, the latter being essentially determined by the approximation rates in the corresponding invariance principles. As an application, a change point test in a simple AMOC renewal model is briefly discussed, where variance estimators possessing good enough convergence rates are required.     

Identifying rational distributed lag models using a joint test applied to the corner table

Often a distributed lag response pattern can be usefully represented in rational polynomial form. When the impulse response function decays, the corner table may be useful for model identification if appropriate statistical tests may be done. One or more joint tests are called for since use of the corner table involves studying groups of its elements. We consider an asymptotic x2 statistic that permits joint tests. We report simulation results showing that the distribution of this statistic follows the x ² distribution, for certain sample sizes and degrees of freedom, well enough to be useful in practice. With two data sets we illustrate how this statistic can be a useful aid when using the corner table.     

Modeling Efficiency of Foreign Aid Allocation in Malawi

ABSTRACT

The Open Aid Malawi initiative has collected an unprecedented database that identifies as much location-specific information as possible for each of over 2500 individual foreign aid donations to Malawi since 2003. The efficient use and distribution of such aid is important to donors and to Malawi citizens. However, because of individual donor goals and difficulty in tracking donor coordination it is difficult to determine whether aid allocation is efficient. We compare several Bayesian spatial generalized linear mixed models to relate aid allocation to various economic indicators within seven donation sectors. We find that the spatial gamma regression model best predicts current aid allocation. While we are cautious about making strong claims based on this exploratory study, we provide a methodology by which one could (i) evaluate the efficiency of aid allocation via a study of the locations of current aid allocation as compared to the need at those locations and (ii) come up with a strategy for efficient allocation of resources in conditions where there exists an ideal relationship between aid allocation and economic sectors.     

A weighted likelihood ratio of two related negative hypergeometric distributions

In this paper we consider some related negative hypergeometric distributions arising from the problem of sampling without replacement from an urn containing balls of different colours and in different proportions but stopping only after some specific number of balls of different colours have been obtained. With the aid of some simple recurrence relations and identities we obtain in the case of two colours the moments for the maximum negative hypergeometric distribution, the minimum negative hypergeometric distribution, the likelihood ratio negative hypergeometric distribution and consequently the likelihood proportional negative hypergeometric distribution. To the extent that the sampling scheme is applicable to modelling data as illustrated with a biological example and, in fact, many situations of estimating Bernoulli parameters for binary traits within a finite population, these are important first-step results.     

Dot Plots

Dot plots represent individual observations in a batch of data with symbols, usually circular dots. They have been used for more than 100 years to depict distributions in detail. Hand-drawn examples show their authors' efforts to arrange symbols so that they are as near as possible to their proper locations on a scale without overlapping enough to obscure each other. Recent computer programs that attempt to reproduce these historical plots have unfortunately resorted to simple histogram binning instead of using methods that follow the rules for the hand-drawn examples. This article introduces an algorithm that more accurately represents the dot plots cited in the literature.     

A unified sequential test procedure for simultaneous testing the equality of several binomial proportions to a specified standard

In this article, we propose a unified sequentially rejective test procedure for testing simultaneously the equality of several independent binomial proportions to a specified standard. The proposed test procedure is general enough to include some well-known multiple testing procedures such as the Ordinary Bonferroni procedure, Hochberg procedure and Rom procedure. It involves multiple tests of significance based on the simple binomial tests (exact or approximate) which can be easily found in many elementary standard statistics textbooks. Unlike the traditional Chi-square test of the overall hypothesis, the procedure can identify the subset of the binomial proportions, which are different from the prespecified standard with the control of the familywise type I error rate. Moreover, the power computation of the procedure is provided and the procedure is illustrated by two real examples from an ecological study and a carcinogenicity study.     

Optimal detection of a jump in the intensity of a Poisson process or in a density with likelihood ratio statistics

We consider the problem of detecting a ‘bump’ in the intensity of a Poisson process or in a density. We analyze two types of likelihood ratio‐based statistics, which allow for exact finite sample inference and asymptotically optimal detection: The maximum of the penalized square root of log likelihood ratios (‘penalized scan’) evaluated over a certain sparse set of intervals and a certain average of log likelihood ratios (‘condensed average likelihood ratio’). We show that penalizing the square root of the log likelihood ratio — rather than the log likelihood ratio itself — leads to a simple penalty term that yields optimal power. The thus derived penalty may prove useful for other problems that involve a Brownian bridge in the limit. The second key tool is an approximating set of intervals that is rich enough to allow for optimal detection, but which is also sparse enough to allow justifying the validity of the penalization scheme simply via the union bound. This results in a considerable simplification in the theoretical treatment compared with the usual approach for this type of penalization technique, which requires establishing an exponential inequality for the variation of the test statistic. Another advantage of using the sparse approximating set is that it allows fast computation in nearly linear time. We present a simulation study that illustrates the superior performance of the penalized scan and of the condensed average likelihood ratio compared with the standard scan statistic.     

A MODEL OF SYSTEMATIC SAMPLING WITH UNEQUAL PROBABILITIES

A new method is described of drawing, without replacement, two sample units per stratum from any population. The method is developed from a consideration of the asymptotic properties of systematic sampling with unequal probabilities, as the sizes of the population units tend to zero. The essential properties of this method are very easily analysed. They also converge, over a large number of strata, to those of systematic sampling from the same strata with their population units arranged in random order. In proving this, the assumption is made that the underlying population is of the type to which it is appropriate to apply ratio estimation. The sampling method described is, however, simple enough to commend itself as an alternative to systematic sampling when the underlying population is not of this type. Consideration is given to the case where the sizes of some of the population units exceed the skip interval.     

EVVMA and cusum control charts in the presence of correlation

The statistical properties of control charts are usually evaluated under the assumption that the observations from the process are independent. For many processes however, observations which are closely spaced in time will be correlated. This paper considers EWMA and CUSUM control charts for the process mean when the observations are from an AR(1) process with additional random error. This simple model may be a reasonable model for many processes encountered in practice. The ARL and steady state ARL of the EWMA and CUSUM charts are evaluated numerically using an integral equation approach and a Markov chain approach. The numerical results show that correlation can have a significant effect on the properties of these charts. Tables are given to aid in the design of these charts when the observations follow the assumed model.     

Why should clinicians care about Bayesian methods?

There is a growing awareness of Bayesian methods within the medical research community, and increasing discussion of their potential applications. This interest has, however, so far failed to convert into the routine use of such methods by working clinicians. I argue that attempts to encourage the use of Bayesian methods by highlighting the deficiencies of conventional (frequentist) inference have not succeeded because these deficiencies typically have minor practical consequences, while their more serious effects can usually be explained away by appeal to other statistical issues. As a result, Bayesian methods have not appeared to offer practical pay-offs big enough to justify the cost of acquiring the necessary expertise. In an attempt to remove this “cost–benefit” hurdle, I outline a simple Bayesian technique that can be used alongside frequentist methods to address an issue of routine practical concern to working clinicians: the credibility of new research findings.     

A simple algorithm for the adaptation of scores and power behavior of the corresponding rank test

The purpose of this paper is twofold:On one hand we want to give a very simple algorithm for evaluating a special rank estimator of the type given in Behnen, Neuhaus, and Ruymgaart (1983) for the approximate optimal choice of the scores-generating function of a two-sample linear rank test for the general testing problem H_o:F=G versus H₁:F ≤ G, F ≠ G, in order to demonstrate that the corresponding adaptive rank statistic is simple enough for practical applications. On the other hand we prove the asymptotic normality of the adaptive rank statistic under H (leading to approximate critical values) and demonstrate the adaptive behavior of the corresponding rank test by a Monte Carlo power simulation for sample sizes as low as m=10, n=10.     

Robust testing for stationarity of global surface temperature

Surface temperature is a major indicator of climate change. To test for the presence of an upward trend in surface-temperature (global warming), sophisticated statistical methods are typically used which depend on implausible and/or unverifiable assumptions, in particular on the availability of a very large number of measurements. In this paper, the validity of these methods is challenged. It is argued that the available series are simply not long enough to justify the use of methods which are based on asymptotic arguments, because only a small fraction of the information contained in the data is utilizable to distinguish between a trend and natural variability. Thus, a simple frequency-domain test is proposed for the case when all but a very small number of frequencies may be corrupted by transitory fluctuations. Simulations confirm its robustness against short-term autocorrelation. When applied to a global surface-temperature series, significance can be achieved with far fewer frequencies than required by conventional tests.     

Assessing the effect of the amount of financial aids to Piedmont firms using the generalized propensity score

Regional and national development policies play an important role to support local enterprises in Italy. The amount of financial aid may be a key feature for firms’ employment policies. We study the impact on employment of the amount of financial aid attributed to enterprises located in Piedmont, a region in northern Italy, analysing small-sized firms and medium- or large-sized firms separately. We apply generalized propensity score methods under the unconfoundedness assumption that adjusting for differences in a set of observed pre-treatment variables removes all biases in comparisons by different amounts of financial aid. We find that the estimated effects are increasing with amount of financial aid for both small-sized and medium- or large-sized firms, whereas the marginal effects of additional incentives are decreasing with amount of financial aid for small-sized firms, and have an inverse J-shape for medium- or large-sized firms.     

The Loss of Efficiency Estimating Linear Functions under Restrictions

This article is motivated by the problem of estimating contrast in a one-way ANOVA model with restrictions in the parameter vector. We prove that when the restrictions are given by a tree order or a simple order the MLE of some contrast has greater MSE than the unrestricted estimator. A similar behaviour of the MLE is exhibited in a general restricted setting given by a multivariate normal distribution with mean vector constrained to belong to a circular cone. The approach we use focuses on the central direction of the cones. These directions appear to have the greater MSE when the dimension of the restricted cone is big enough.     

Ratio estimator for the population mean using ranked set sampling

We adapt the ratio estimation using ranked set sampling, suggested by Samawi and Muttlak (Biometr J 38:753–764, 1996), to the ratio estimator for the population mean, based on Prasad (Commun Stat Theory Methods 18:379–392, 1989), in simple random sampling. Theoretically, we show that the proposed ratio estimator for the population mean is more efficient than the ratio estimator, in Prasad (1989), in all conditions. In addition, we support this theoretical result with the aid of a numerical example.      

ANOVA Problems with Simple Numbers

This article shows how to construct simple numerical exercises in balanced and unequally replicated one-way analysis of variance (ANOVA) (and experimental design) such that the estimated effects and residual standard deviations are preassigned whole numbers. Methods for generating single samples and simple linear regressions with exact estimates are already available (see Edwards 1959, Searle and Firey 1980, Posten 1982, and Read and Riley 1983). In this article the basic method of Read and Riley is extended to one-way ANOVA. For small numbers of treatments and replications and small residual standard deviations, tables of basic data are supplied that greatly expedite the construction of ANOVA layouts; the same methods may easily be applied, and the tables extended, to generate exercises involving larger numbers if required. The sets of estimated effects are essentially arbitrary, and so the significance or insignificance of main effects, or of contrasts thereof, can be illustrated by data sets designed for the purpose. This facility is a new and helpful aid to instruction.     

The RL2 chart versus the np chart for detecting upward shifts in fraction defective

The use of the np chart for monitoring fraction-defective is well-established, but there are a number of relatively simple alternatives based on run-lengths of conforming items. Here, the RL₂ chart, based on the moving sum of two successive conforming run-lengths, is investigated in order to provide SPC practitioners with clear-cut guidance on the comparative performance of these competing charts. Both sampling inspection and 100% inspection are considered here, and it is shown that the RL₂ chart can often be considerably more efficient than the np chart, but the comparative performance depends on the false-alarm rate used for the comparison. Graphs to aid parameter-choice for the RL₂ chart are also provided.     

A litter-based approach to risk assessment in developmental toxicity studies via a power family of completely monotone functions

Summary.  A new class of distributions for exchangeable binary data is proposed that originates from modelling the joint success probabilities of all orders by a power family of completely monotone functions. The distribution proposed allows flexible modelling of the dose–response relationship for both the marginal response probability and the pairwise odds ratio and is especially well suited for a litter-based approach to risk assessment. Specifically, the risk of at least one adverse response within a litter takes on a simple form under the distribution proposed and can be reduced further to a generalized linear model if a complementary log–log-link function is used. Existing distributions such as the beta–binomial or folded logistic functions have a tendency to assign too much probability to zero, leading to an underestimation of the risk that at least one foetus is affected and an overestimation of the safe dose. The distribution proposed does not suffer from this problem. With the aid of symbolic differentiation, the distribution proposed can be fitted easily and quickly via the method of scoring. The usefulness of the class of distributions proposed and its superiority over existing distributions are demonstrated in a series of examples involving developmental toxicology and teratology data.     

Multivariate Bayesian variable selection and prediction

The multivariate regression model is considered with p regressors. A latent vector with p binary entries serves to identify one of two types of regression coefficients: those close to 0 and those not. Specializing our general distributional setting to the linear model with Gaussian errors and using natural conjugate prior distributions, we derive the marginal posterior distribution of the binary latent vector. Fast algorithms aid its direct computation, and in high dimensions these are supplemented by a Markov chain Monte Carlo approach to sampling from the known posterior distribution. Problems with hundreds of regressor variables become quite feasible. We give a simple method of assigning the hyperparameters of the prior distribution. The posterior predictive distribution is derived and the approach illustrated on compositional analysis of data involving three sugars with 160 near infrared absorbances as regressors.