A note on new confidence intervals for the difference between two proportions based on an Edgeworth expansion

Zhou and Qin [2004. New intervals for the difference between two independent binomial proportions. J. Statist. Plann. Inference 123, 97–115; 2005. A new confidence interval for the difference between two binomial proportions of paired data. J. Statist. Plann. Inference 128, 527–542] “new confidence intervals” for the difference between two treatment proportions exhibit a severe lack of invariance property that is a compelling reason not to use them.     

Utilization of higher order moments of scrambling variables in randomized response sampling

In this paper, a new estimator for estimating the proportion of a potentially sensitive attribute in survey sampling has been introduced. The proposed estimator makes use of higher order moments of the scrambling variable at the estimation stage. The proposed estimator has been found to be more efficient than the estimator due to Kuk [1990. Asking sensitive questions indirectly. Biomerika 77(2), 436–438] and Franklin [1989. A comparison of estimators for randomized response sampling with continuous distributions from a dichotomous population. Comm. Statist. Theory Methods 18, 489–505] type estimators in randomized response sampling. Recently, Guerriero and Sandri [2007. A note on the comparison of some randomized response procedures. J. Statist. Plann. Inference 137, 2184–2190] have shown that the family of randomized response models proposed by Kuk [1990. Asking sensitive questions indirectly. Biomerika 77(2), 436–438] is better than the Simmons’ family in terms of efficiency and protection.     

A theoretical analysis of the power of biased coin designs

Outlining some recently obtained results of Hu and Rosenberger [2003. Optimality, variability, power: evaluating response-adaptive randomization procedures for treatment comparisons. J. Amer. Statist. Assoc. 98, 671–678] and Chen [2006. The power of Efron's biased coin design. J. Statist. Plann. Inference 136, 1824–1835] on the relationship between sequential randomized designs and the power of the usual statistical procedures for testing the equivalence of two competing treatments, the aim of this paper is to provide theoretical proofs of the numerical results of Chen [2006. The power of Efron's biased coin design. J. Statist. Plann. Inference 136, 1824–1835]. Furthermore, we prove that the Adjustable Biased Coin Design [Baldi Antognini A., Giovagnoli, A., 2004. A new “biased coin design” for the sequential allocation of two treatments. J. Roy. Statist. Soc. Ser. C 53, 651–664] is uniformly more powerful than the other “coin” designs proposed in the literature for any sample size.     

A review of uniform cross-over designs

Uniform cross-over designs form an important family of experimental designs. They have been applied in many scientific disciplines including clinical trials, agricultural studies and psychological experiments. In this paper we consider the four types of uniform cross-over design, as given by Williams [1949. Experimental designs balanced for the estimation of residual effects of treatments. Aust. J. Sci. Res. 2, 149–168], Cheng and Wu [1980. Balanced repeated measurements designs. Ann. Statist. 8, 1272–1283. Corrigendum 11 (1983) 349], Bate and Jones [2006. The construction of nearly balanced and nearly strongly balanced uniform cross-over designs. J. Statist. Plann. Inference 136, 3248–3267] and Kunert [1983. Optimal design and refinement of the linear model with applications to repeated measurements designs. Ann. Statist. 11, 247–257]. The efficiency of these designs, existence criteria and methods of construction are described.     

Robust linear mixed models for Small Area Estimation

Hierarchical models are popular in many applied statistics fields including Small Area Estimation. One well known model employed in this particular field is the Fay–Herriot model, in which unobservable parameters are assumed to be Gaussian. In Hierarchical models assumptions about unobservable quantities are difficult to check. For a special case of the Fay–Herriot model, Sinharay and Stern [2003. Posterior predictive model checking in Hierarchical models. J. Statist. Plann. Inference 111, 209–221] showed that violations of the assumptions about the random effects are difficult to detect using posterior predictive checks. In this present paper we consider two extensions of the Fay–Herriot model in which the random effects are assumed to be distributed according to either an exponential power (EP) distribution or a skewed EP distribution. We aim to explore the robustness of the Fay–Herriot model for the estimation of individual area means as well as the empirical distribution function of their ‘ensemble’. Our findings, which are based on a simulation experiment, are largely consistent with those of Sinharay and Stern as far as the efficient estimation of individual small area parameters is concerned. However, when estimating the empirical distribution function of the ‘ensemble’ of small area parameters, results are more sensitive to the failure of distributional assumptions.     

On representing maximin efficient designs by Taylor series

This paper considers exponential and rational regression models that are nonlinear in some parameters. Recently, locally D-optimal designs for such models were investigated in [Melas, V. B., 2005. On the functional approach to optimal designs for nonlinear models. J. Statist. Plann. Inference 132, 93–116] based upon a functional approach. In this article a similar method is applied to construct maximin efficient D-optimal designs. This approach allows one to represent the support points of the designs by Taylor series, which gives us the opportunity to construct the designs by hand using tables of the coefficients of the series. Such tables are provided here for models with two nonlinear parameters. Furthermore, the recurrent formulas for constructing the tables for arbitrary numbers of parameters are introduced.     

Erratum to “Progressively Type-II right censored order statistics from discrete distributions” [J. Statist. Plann. Inference 138 (2008) 845–856]

In this note, we correct the proof of Representation 1 of Balakrishnan and Dembińska [2008. Progressively Type-II right censored order statistics from discrete distributions. J. Statist. Plann. Inference 138, 845–856] which relates the joint distribution of progressively Type-II right censored order statistics corresponding to an arbitrary population to progressively Type-II right censored order statistics from the standard uniform distribution.     

Stochastic comparisons and properties of conditional generalized order statistics

Generalized order statistics introduced by Kamps [1995. A concept of generalized order statistics. J. Statist. Plann. Inference 48, 1–23] provides a unified approach to a variety of models concerning ordered random variables. This paper carries out stochastic comparisons of conditional generalized order statistics in terms of the likelihood ratio order and the hazard rate order from two samples, and establishes some stochastic monotonicity properties. The main results strengthen and generalize the corresponding results established recently in the literature. Finally, some applications of the main results are given as well.     

The convolution theorem for estimating linear functionals in indirect nonparametric regression models

Nonparametric regression—directly or indirectly observed—is one of the important statistical models. On one hand it contains two infinite dimensional parameters (the regression function and the error density), and on the other it is of rather simple structure. Therefore, it may serve as an interesting paradigm for illustrating or developing abstract statistical theory for non-Euclidean parameters. In this paper estimation of a linear functional of the indirectly observed regression function is considered, when a deterministic design is used. It should be noted that any Fourier coefficient of an expansion of the regression function in an orthonormal basis is such a functional. Because the design is deterministic the observables are independent but not identically distributed. Local asymptotic normality is established and applied to prove Hájek's convolution theorem for this functional. Pertinent references are Beran [1977. Robust location estimates. Ann. Statist. 5, 431–444] and McNeney and Wellner [2000. Application of convolution theorems in semiparametric models with non-i.i.d. data. J. Statist. Plann. Inference 91, 441–480]. For purposes explained above, however, the paper is kept self-contained and full proofs are provided.     

Limit theory of generalized order statistics

Generalized order statistics (gos) were introduced by Kamps [1995. A Concept of Generalized Order Statistics. Teubner, Stuttgart] to unify several models of ordered random variables (rv's), e.g., (ordinary) order statistics (oos), records, sequential order statistics (sos). In a wide subclass of gos that includes oos and sos, the possible limit distribution functions (df's) of the maximum gos are obtained in Nasri-Roudsari [1996. Extreme value theory of generalized order statistics. J. Statist. Plann. Inference 55, 281–297]. In this paper, for this subclass, necessary and sufficient conditions of weak convergence, as well as the form of the possible limit df's of extreme, intermediate and central gos are derived. These results are extended to a wider subclass.     

Rank covariance matrix estimation of a partially known covariance matrix

Classical multivariate methods are often based on the sample covariance matrix, which is very sensitive to outlying observations. One alternative to the covariance matrix is the affine equivariant rank covariance matrix (RCM) that has been studied in Visuri et al. [2003. Affine equivariant multivariate rank methods. J. Statist. Plann. Inference 114, 161–185]. In this article we assume that the covariance matrix is partially known and study how to estimate the corresponding RCM. We use the properties that the RCM is affine equivariant and that the RCM is proportional to the inverse of the regular covariance matrix, and hence reduce the problem of estimating the original RCM to estimating marginal rank covariance matrices. This is a great computational advantage when the dimension of the original data vector is large.     

Controlling Bayes directional false discovery rate in random effects model

Starting with a decision theoretic formulation of simultaneous testing of null hypotheses against two-sided alternatives, a procedure controlling the Bayesian directional false discovery rate (BDFDR) is developed through controlling the posterior directional false discovery rate (PDFDR). This is an alternative to Lewis and Thayer [2004. A loss function related to the FDR for random effects multiple comparison. J. Statist. Plann. Inference 125, 49–58.] with a better control of the BDFDR. Moreover, it is optimum in the sense of being the non-randomized part of the procedure maximizing the posterior expectation of the directional per-comparison power rate given the data, while controlling the PDFDR. A corresponding empirical Bayes method is proposed in the context of one-way random effects model. Simulation study shows that the proposed Bayes and empirical Bayes methods perform much better from a Bayesian perspective than the procedures available in the literature.     

Lower bounds on expectations of positive L-statistics from without-replacement models

We consider samples drawn without replacement from finite populations. We establish optimal lower non-negative and upper non-positive bounds on the expectations of linear combinations of order statistics centered about the population mean in units generated by the population central absolute moments of various orders. We also specify the general results for important examples of sample extremes, Gini mean differences and sample range. The paper completes the results of Papadatos and Rychlik [2004. Bounds on expectations of L-statistics from without replacement samples. J. Statist. Plann. Inference 124, 317–336], where sharp negative lower and positive upper bounds on the expectations of the combinations were presented for the without-replacement samples.     

Nonlinear recursive estimation of volatility via estimating functions

For certain volatility models, the conditional moments that depend on the parameter are of interest. Following Godambe and Heyde (1987), the combined estimating function method has been used to study inference when the conditional mean and conditional variance are functions of the parameter of interest (See Ghahramani and Thavaneswaran [Combining Estimating Functions for Volatility. Journal of Statistical Planning and Inference, 2009, 139, 1449-1461] for details). However, for application purposes, the resulting estimates are nonlinear functions of the observations and no closed form expressions of the estimates are available. As an alternative, in this paper, a recursive estimation approach based on the combined estimating function is proposed and applied to various classes of time series models, including certain volatility models.     

New balanced sampling plans excluding adjacent units

Hedayat et al. [1988a. Sampling plans excluding contiguous units. J. Statist. Plann. Inference 19, 159–170; 1988b. Designs in survey sampling avoiding contiguous units. In: Krishnaiah, P.R., Rao, C.R. (Eds.). Handbook of Statistics, vol. 6. Elsevier, Amsterdam, pp. 575–583] first introduced balanced sampling designs for the exclusion of contiguous units. Sampling plans that excluded the selection of contiguous units within a given sample, while maintaining a constant second-order inclusion probability for non-contiguous units, were investigated for finite populations of N units arranged in a circular, one-dimensional ordering. There remain many open questions about the existence of such plans and their extension to plans excluding adjacent units. We present new generation techniques and new balanced sampling plans for the exclusion of adjacent units under finite, one-dimensional, circularly and linearly ordered populations.     

Some properties of the generalized TTT transform

Recently Li and Shaked [2007. A general family of univariate stochastic orders. J. Statist. Plann. Inference 137, 3601–3610] introduced the generalized total time on test (GTTT) transform with respect to a given function ?$?$. In this paper we study some properties of it which are related with stochastic orderings. A concept of Lehmann and Rojo [1992. Invariant directional orderings. Ann. Statist. 20, 2100–2110] is applied to a new setting and the GTTT transform is used to define invariance properties and distances of some stochastic orders. Iterations of the GTTT transforms are also studied and their relations with exponential mixtures of gamma distributions are established.     

Testing for coefficient stability of AR(1) model when the null is an integrated or a stationary process

In this paper, we propose a new test for coefficient stability of an AR(1) model against the random coefficient autoregressive model of order 1 neither assuming a stationary nor a non-stationary process under the null hypothesis of a constant coefficient. The proposed test is obtained as a modification of the locally best invariant (LBI) test by Lee [(1998). Coefficient constancy test in a random coefficient autoregressive model. J. Statist. Plann. Inference 74, 93–101]. We examine finite sample properties of the proposed test by Monte Carlo experiments comparing with other existing tests, in particular, the LBI test by McCabe and Tremayne [(1995). Testing a time series for difference stationary. Ann. Statist. 23 (3), 1015–1028], which is for the null of a unit root process against the alternative of a stochastic unit root process.     

Domains of study and poststratification

Sugden and Smith (2002. J. Statist. Plann. Inference 102, 25–38) investigated conditions under which exact linear unbiased estimators of linear estimands, and also exact quadratic unbiased estimators of quadratic estimands, could be constructed under the randomisation approach. In this paper the method is applied to domains of study and extended to poststratified estimators of finite population totals. The resulting estimators generalise some of those in Doss et al. (1979. J. Statist. Plann. Inference 3, 235–247). Some further properties of these estimators are explored.     

Tests for assessment of agreement using probability criteria

For the assessment of agreement using probability criteria, we obtain an exact test, and for sample sizes exceeding 30, we give a bootstrap-t$t$ test that is remarkably accurate. We show that for assessing agreement, the total deviation index approach of Lin [2000. Total deviation index for measuring individual agreement with applications in laboratory performance and bioequivalence. Statist. Med. 19, 255–270] is not consistent and may not preserve its asymptotic nominal level, and that the coverage probability approach of Lin et al. [2002. Statistical methods in assessing agreement: models, issues and tools. J. Amer. Statist. Assoc. 97, 257–270] is overly conservative for moderate sample sizes. We also show that the nearly unbiased test of Wang and Hwang [2001. A nearly unbiased test for individual bioequivalence problems using probability criteria. J. Statist. Plann. Inference 99, 41–58] may be liberal for large sample sizes, and suggest a minor modification that gives numerically equivalent approximation to the exact test for sample sizes 30 or less. We present a simple and accurate sample size formula for planning studies on assessing agreement, and illustrate our methodology with a real data set from the literature.     

Moment-based tail index estimation

A general method of tail index estimation for heavy-tailed time series, based on examining the growth rate of the logged sample second moment of the data was proposed and studied in Meerschaert and Scheffler (1998. A simple robust estimator for the thickness of heavy tails. J. Statist. Plann. Inference 71, 19–34) as well as Politis (2002. A new approach on estimation of the tail index. C. R. Acad. Sci. Paris, Ser. I 335, 279–282). To improve upon the basic estimator, we introduce a scale-invariant estimator that is computed over subsets of the whole data set. We show that the new estimator, under some stronger conditions on the data, has a polynomial rate of consistency for the tail index. Empirical studies explore how the new method compares with the Hill, Pickands, and DEdH estimators.