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For testing goodness of fit, we consider a class of U-statistics of overlapping spacings of order two, and investigate their asymptotic properties. The standard U-statistic theory is not directly applicable here as the overlapping spacings form a dependent random sequence. The asymptotic distribution of the statistics under the null hypothesis and under a sequence of local alternatives are derived. In terms of the Pitman ARE, the U-statistic based on Gini's mean square difference of overlapping spacings is found to be the asymptotically locally most powerful. Interestingly, this test has the same efficacy as the Greenwood test based on overlapping spacings. • For testing goodness of fit, we consider U-statistics of overlapping spacings. • We derive asymptotic distribution of statistics for a sequence of local alternatives. • The asymptotically locally most powerful test is obtained in terms of the Pitman ARE. [ABSTRACT FROM AUTHOR]

We derive Poisson limit theorems for the multinomial Cressie–Read goodness-of-fit statistics and some of their modifications under the assumption that as the sample size n goes to infinity, the number of groups m n increases with the sample size. Our results extend the Poisson limit theorems for the Pearson chi-square statistic reported in Rempała and Wesołowski (2016). • Multinomial goodness-of-fit (GOF) tests in genomic studies depend on sequencing depth • As a result, number of different groups (transcripts) may change with sample size • Limit theorem for Cressie-Read (CR) GOF statistics is proved here for such settings • We show that properly normalized CR statistics follow Poisson distribution • This result generalizes the one already known for the Pearson statistic • Some examples in testing hypothesis are presented [ABSTRACT FROM AUTHOR]

The problem of fitting two concentric objects (circles and ellipses) to noisy data plays a vital role in many fields. In this paper, statistical methodologies are deployed by additionally assuming that the angular differences between successively measured data points are known, which is known as Berman's model. The heteroscedasticity between covariates is also assumed here, and hence, several estimators for the problem of fitting concentric circles and ellipses are developed and their statistical properties are established. Unlike concentric circles, the problem of fitting concentric ellipses turns out to be nonlinear even with Berman's assumption, and as such, iterative algorithms are implemented. Extensive numerical experiments were conducted to validate our results. • Fitting two concentric objects to noisy data plays a vital role in many fields. • The statistical properties of the three developed estimators have been established. • Numerically stable algorithm for fitting concentric ellipses has been proposed. [ABSTRACT FROM AUTHOR]

We introduce a density basis of the trigonometric polynomials that is suitable to mixture modelling. Statistical and geometric properties are derived, suggesting it as a circular analogue to the Bernstein polynomial densities. Nonparametric priors are constructed using this basis and a simulation study shows that the use of the resulting Bayes estimator may provide gains over comparable circular density estimators previously suggested in the literature. From a theoretical point of view, we propose a general prior specification framework for density estimation on compact metric space using sieve priors. This is tailored to density bases such as the one considered herein and may also be used to exploit their particular shape-preserving properties. Furthermore, strong posterior consistency is shown to hold under notably weak regularity assumptions and adaptive convergence rates are obtained in terms of the approximation properties of positive linear operators generating our models. • We propose a density basis of the trigonometric polynomials with shape-preserving properties. • Nonparametric mixture priors are constructed using this basis for Bayesian inference. • We describe adaptive posterior convergence rates and consistency under weak assumptions. [ABSTRACT FROM AUTHOR]

In Siotani and Fujikoshi (1984), a precise local limit theorem for the multinomial distribution is derived by inverting the Fourier transform, where the error terms are explicit up to order N − 1. In this paper, we give an alternative (conceptually simpler) proof based on Stirling's formula and a careful handling of Taylor expansions, and we show how the result can be used to approximate multinomial probabilities on most subsets of R d. Furthermore, we discuss a recent application of the result to obtain asymptotic properties of Bernstein estimators on the simplex, we improve the main result in Carter (2002) on the Le Cam distance bound between multinomial and multivariate normal experiments while simultaneously simplifying the proof, and we mention another potential application related to finely tuned continuity corrections. • Local limit theorem for the multinomial distribution up to an N − 3 ∕ 2 error. • Simple proof using Stirling's formula and Taylor expansions. • Application to obtain asymptotic properties of Bernstein estimators. • Improves Le Cam distance between multinomial and multivariate normal experiments. • Potential applications to continuity corrections and power divergence statistics. [ABSTRACT FROM AUTHOR]

This paper is concerned with testing the second-order stationarity of a time series. By using a blockwise scheme, the test is transformed to compare local spectra of different segments of the blocked time series. Based on periodogram-ratios of each pair of segments at the same frequency points, an Anderson–Darling-like statistic is constructed to compare their spectra. By maximizing several Anderson–Darling-like statistics, a test statistic is proposed for testing second-order stationarity. Under the null, the probability distribution of the proposed statistic can be approximated by simulation. Extensive simulation examples show that the proposed test approach achieves good performance. • Spectral domain-based test for second-order stationarity. • The test is easy to program and quite computationally efficient. • The test is applicable to extensive types of time series. [ABSTRACT FROM AUTHOR]

Standard confidence intervals employed in applied statistical analysis are usually based on asymptotic approximations. Such approximations can be considerably inaccurate in small and moderate sized samples. We derive accurate confidence intervals based on higher-order approximate quantiles of the score function. The coverage approximation error is O (n − 3 ∕ 2) while the approximation error of confidence intervals based on the first-order asymptotic distribution of the Wald, score, and signed likelihood ratio statistic is O (n − 1 ∕ 2). Monte Carlo simulations confirm the theoretical findings. An implementation for regression models and real data applications is provided. • Accurate confidence intervals are presented. • Equivariant under interest-respecting reparameterizations. • Do not require computer-intensive resampling mechanisms. • Confidence limits are simply computed from modified score equations. • Software implementation provided for regression models. [ABSTRACT FROM AUTHOR]

In this paper, we consider the separable covariance model, which plays an important role in wireless communications and spatio-temporal statistics and describes a process where the time correlation does not depend on the spatial location and the spatial correlation does not depend on time. We established a central limit theorem for linear spectral statistics of general separable sample covariance matrices in the form of S n = 1 n T 1 n X n T 2 n X n ∗ T 1 n ∗ where X n = (x j k) is of m 1 × m 2 dimension, the entries { x j k , j = 1 , ... , m 1 , k = 1 , ... , m 2 } are independent and identically distributed complex variables with zero means and unit variances, T 1 n is a p × m 1 complex matrix and T 2 n is an m 2 × m 2 Hermitian matrix. We then apply this general central limit theorem to the problem of testing white noise in time series. • We established a central limit theorem for linear spectral statistics of a more general separable sample covariance matrix model. • We consider a case where the fourth moment of the underling distribution may not equal to 3. • We apply the general central limit theorem to the problem of testing white noise in time series. [ABSTRACT FROM AUTHOR]

The goal of this study was to test the equality of two covariance matrices by using modified Pillai's trace statistics under a high-dimensional framework, i.e., the dimension and sample sizes go to infinity proportionally. In this paper, we introduce two modified Pillai's trace statistics and obtain their asymptotic distributions under the null hypothesis. The benefits of the proposed statistics include the following: (1) the sample size can be smaller than the dimensions; (2) the limiting distributions of the proposed statistics are universal; and (3) we do not restrict the structure of the population covariance matrices. The theoretical results are established under mild and practical assumptions, and their properties are demonstrated numerically by simulations and a real data analysis. • Two modified Pillai's trace statistics are proposed. • The tests are invariant to the null hypothesis. • The tests allow the sample size to be smaller than the dimensions. • The tests do not restrict the structure of the population covariance matrix. [ABSTRACT FROM AUTHOR]

Item non-response in surveys is usually handled by single imputation, whose main objective is to reduce the non-response bias. Imputation methods need to be adapted to the study variable. For instance, in business surveys, the interest variables often contain a large number of zeros. Motivated by a mixture regression model, we propose two imputation procedures for such data and study their statistical properties. We show that these procedures preserve the distribution function if the imputation model is well specified. The results of a simulation study illustrate the good performance of the proposed methods in terms of bias and mean square error. • Imputation needs to be adapted for zero-inflated data. • A proposed method leads to consistent estimators and preserves distribution. • We propose a balanced imputation method which is fully efficient. [ABSTRACT FROM AUTHOR]

We discuss an approach for deriving robust posterior distributions from M -estimating functions using Approximate Bayesian Computation (ABC) methods. In particular, we use M -estimating functions to construct suitable summary statistics in ABC algorithms. The theoretical properties of the robust posterior distributions are discussed. Special attention is given to the application of the method to linear mixed models. Simulation results and an application to a clinical study demonstrate the usefulness of the method. An R implementation is also provided in the robustBLME package. [ABSTRACT FROM AUTHOR]

We consider the class of completely monotone probability mass functions (pmf) from a statistical perspective. An element in this class is known to be a mixture of geometric pmfs, a consequence of the celebrated Hausdorff Theorem. We show that the complete monotone least squares estimator exists, is strongly consistent and converges weakly to the truth at the n -rate. Furthermore, we fully describe its limit distribution as the unique solution of a well-posed minimization problem. Through a simulation study we assess the performance of the method under different scenarios. • Completely monotone class from a statistical perspective. • Thorough study of the complete monotone LSE. • Derivation of the limit theory of the LSE. • Potential in species richness applications. [ABSTRACT FROM AUTHOR]

We propose a new Kalman filter algorithm to provide a formal statistical analysis of space–time data with an autoregressive structure. The Kalman filter technique allows to capture the temporal dependence as well as the spatial correlation structure through state-space equations, and it is aimed to perform statistical inference in terms of both parameter estimation and prediction at unobserved locations. We put in relevance the nugget effect at the observation equation. We test our procedure and compare it with classical kriging prediction via an intensive simulation study. We show that the Kalman filter is superior in both the estimation, without using a plug-in approach, and prediction for spatio-temporal data, providing a suitable formal procedure for the statistical analysis of space–time data. Finally, an application to the prediction of daily air temperature data in some regions of southern Chile is presented. • A space–time autoregressive model is formulated. • Place in relevance the nugget effect at the observation equation does not cause difficulties in the estimation. • The predictions obtained are compared with those of simple kriging. • The use of the proposed model is better than that for the simple kriging, in terms of a prediction gain criterion. [ABSTRACT FROM AUTHOR]

Abstract A Gaussian graphical model is a graphical representation of the dependence structure for a Gaussian random vector. Gaussian graphical model selection is a statistical problem that identifies the Gaussian graphical model from observations. There are several statistical approaches for Gaussian graphical model identification. Their properties, such as unbiasedeness and optimality, are not established. In this paper we study these properties. We consider the graphical model selection problem in the framework of multiple decision theory and suggest assessing these procedures using an additive loss function. Associated risk function in this case is a linear combination of the expected numbers of the two types of error (False Positive and False Negative). We combine the tests of a Neyman structure for individual hypotheses with simultaneous inference and prove that the obtained multiple decision procedure is optimal in the class of unbiased multiple decision procedures. Highlights • General approach to measure uncertainty of Gaussian graphical model selection procedures. • Proof of the optimality of the procedure of simultaneous inference for Gaussian graphical model selection. • Discussion of the unbiasedness in multiple testing. [ABSTRACT FROM AUTHOR]

Abstract In this paper, the k sample Behrens–Fisher problem is investigated in high dimensional setting. We propose new test statistics and demonstrate that the proposed test statistics are expected to have higher power than some existing tests especially when sample sizes are unbalanced. We provide theoretical investigation as well as numerical studies on both size and power of the proposed tests and existing tests. Highlights • We propose a test for k sample high dimensional mean vectors. • We provide theoretical and numerical studies. • The proposed test is efficient for unbalanced sample sizes. [ABSTRACT FROM AUTHOR]

Abstract Lack-of-fit checking for parametric models is essential in reducing misspecification. However, for massive data sets which are increasingly prevalent, classical tests become prohibitively costly in computation and their feasibility is questionable even with modern parallel computing platforms. Building on the divide and conquer strategy, we propose a new nonparametric testing method, that is fast to compute and easy to implement with only one tuning parameter determined by a given time budget. Under mild conditions, we show that the proposed test statistic is asymptotically equivalent to that based on the whole data. Benefiting from using the sample-splitting idea for choosing the smoothing parameter, the proposed test is able to retain the type-I error rate pretty well with asymptotic distributions and achieves adaptive rate-optimal detection properties. Its advantage relative to existing methods is also demonstrated in numerical simulations and a data illustration. [ABSTRACT FROM AUTHOR]

We show that the locally most powerful tests of uniformity on the circle given by Beran have optimality properties not just against the parametric alternatives described by Beran but also against many non-parametric alternatives. We compare these local results to asymptotic versions of this optimality. [ABSTRACT FROM AUTHOR]

Abstract: This paper reviews the formulation of the K-aberration criterion for baseline two-level designs and the efficient complete search algorithm developed by Mukerjee and Tang (2012). An efficient incomplete search algorithm is proposed that can be used to find near optimal baseline designs in situations where the complete search algorithm is not feasible. Lower bounds for values of K 2 and K 3 are established. A catalogue of optimal (or near optimal) 20-run baseline designs is provided. [Copyright &y& Elsevier]

Abstract: Computer experiments are becoming increasingly popular in studying complex real world systems. A special class of sliced Latin hypercube design is proposed in this paper. Such designs are particularly suitable for computer experiments with both qualitative and quantitative factors, multi-fidelity computer experiments, cross-validation and data pooling. The resulting sliced Latin hypercube designs possess a desirable sliced structure and have an attractive low-dimensional uniformity. Meanwhile within each slice, it is also a Latin hypercube design with the same low-dimensional uniformity. The new sliced Latin hypercube designs can be constructed via both symmetric and asymmetric orthogonal arrays. The same desirable properties are possessed, although the uniformity may be differed. The construction methods are easy to implement, and unlike the existing methods, the resulting designs are very flexible in run sizes and numbers of factors. A detailed comparison with existing designs is made. [Copyright &y& Elsevier]

Abstract: The goal of this work is to describe some connections between cryptology and statistics. Starting from basic frequency analysis, throughout history, statistical ideas have been employed to attack cryptographic systems and continue to be important in modern day cryptanalysis. Brief descriptions of hypothesis testing based distinguishing attacks, differential cryptanalysis and statistical ideas used in side channel attacks are provided. From the designer's point of view, we consider three connections. A brief description is provided of the cryptographic ideas that have been suggested to strengthen the technique of randomised response. In recent times, a new notion of privacy of statistical databases has arisen and has been called differential privacy. We provide a brief description of this idea and mention some of its applications. Lastly, we consider the problem of defining and proving security of public key encryption schemes and provide a simple example of this method. It is hoped that the topics outlined here will motivate researchers to further investigate the connection between these two subjects. [Copyright &y& Elsevier]

Abstract: The theory and practice of statistical methods in situations where the available data are functions (instead of real numbers or vectors) is often referred to as Functional Data Analysis (FDA). This subject has become increasingly popular from the end of the 1990s and is now a major research field in statistics. The aim of this expository paper is to offer a short tutorial as well as a partial survey of the state of the art in FDA theory. Both the selection of topics and the references list are far from exhaustive. Many interesting ideas and references have been left out for the sake of brevity and readability. In summary, this paper provides: [(a)] A discussion on the nature and treatment of the functional data. [(b)] A review of some probabilistic tools especially suited for FDA. [(c)] A discussion about how the usual centrality parameters, mean, median and mode, can be defined and estimated in the functional setting. [(d)] Short accounts of the main ideas and current literature on regression, classification, dimension reduction and bootstrap methods in FDA. [(e)] Some final comments regarding software for FDA. [Copyright &y& Elsevier]

Abstract: This paper demonstrates that flexible and statistically tractable multi-modal diffusion models can be attained by transformation of simple well-known diffusion models such as the Ornstein–Uhlenbeck model, or more generally a Pearson diffusion. The transformed diffusion inherits many properties of the underlying simple diffusion including its mixing rates and distributions of first passage times. Likelihood inference and martingale estimating functions are considered in the case of a discretely observed bimodal diffusion. It is further demonstrated that model parameters can be identified and estimated when the diffusion is observed with additional measurement error. The new approach is applied to molecular dynamics data in the form of a reaction coordinate of the small Trp-zipper protein, from which the folding and unfolding rates of the protein are estimated. Because the diffusion coefficient is state-dependent, the new models provide a better fit to this type of protein folding data than the previous models with a constant diffusion coefficient, particularly when the effect of errors with a short time-scale is taken into account. [Copyright &y& Elsevier]

In this article we consider Lévy driven continuous time moving average processes observed on a lattice, which are stationary time series. We show asymptotic normality of the sample mean, the sample autocovariances and the sample autocorrelations. A comparison with the classical setting of discrete moving average time series shows that in the last case a correction term should be added to the classical Bartlett formula that yields the asymptotic variance. An application to the asymptotic normality of the estimator of the Hurst exponent of fractional Lévy processes is also deduced from these results. [ABSTRACT FROM AUTHOR]

Abstract: The use of covariates in block designs is necessary when the experimental errors cannot be controlled using only the qualitative factors. The choice of values of the covariates for a given set-up attaining minimum variance for estimation of the regression parameters has attracted attention in recent times. In this paper, optimum covariate designs (OCD) have been considered for the set-up of the balanced treatment incomplete block (BTIB) designs, which form an important class of test-control designs. It is seen that the OCDs depend much on the methods of construction of the basic BTIB designs. The series of BTIB designs considered in this paper are mainly those as described by Bechhofer and Tamhane (1981) and Das et al. (2005). Different combinatorial arrangements and tools such as Hadamard matrices and different kinds of products of matrices viz Khatri-Rao product and Kronecker product have been conveniently used to construct OCDs with as many covariates as possible. [Copyright &y& Elsevier]

Abstract: The main object of this paper is to propose a multivariate extension to the alpha-power model which is an alternative to the multivariate skew-normal model (Arellano-Valle and Azzalini, 2008). It also extends the power-normal model discussed in Gupta and Gupta (2008) by making it more flexible. Inference is dealt with by using the likelihood approach and a pseudo-likelihood approach based on conditional distributions which, although slightly less efficient, is simpler to implement. An application to a real data set is used to demonstrate the usefulness of the extension. [Copyright &y& Elsevier]

Abstract: Consider the D-optimal designs for a combined polynomial and trigonometric regression on a partial circle. It is shown that the optimal design is equally supported and the structure of the optimal design depends only on the length of the design interval and the support points are analytic functions of this parameter. Moreover, the Taylor expansion of the optimal support points can be determined efficiently by a recursive procedure. Examples are presented to illustrate the procedures for computing the optimal designs. [Copyright &y& Elsevier]

Abstract: Here we consider wavelet-based identification and estimation of a censored nonparametric regression model via block thresholding methods and investigate their asymptotic convergence rates. We show that these estimators, based on block thresholding of empirical wavelet coefficients, achieve optimal convergence rates over a large range of Besov function classes, and in particular enjoy those rates without the extraneous logarithmic penalties that are usually suffered by term-by-term thresholding methods. This work is extension of results in Li et al. (2008). The performance of proposed estimator is investigated by a numerical study. [Copyright &y& Elsevier]

Abstract: An improved likelihood-based method is proposed to test for the significance of the first-order moving average model. Compared with commonly used tests which depend on the asymptotic properties of the maximum likelihood estimate and the likelihood ratio statistic, the proposed method has remarkable accuracy. Application of the method to a data set on book sales is presented to demonstrate the implementation of the method. Simulation studies are subsequently performed to illustrate the accuracy of the method compared to the traditional methods. Additionally, a simple and effective correction is used to deal with the boundary problem. [Copyright &y& Elsevier]

Abstract: We propose a new method to test the order between two high-dimensional mean curves. The new statistic extends the approach of to high-dimensional data by adapting the strategy of . The proposed procedure is an alternative to the non-negative basis matrix factorization (NBMF) based test of for the same hypothesis, but it is much easier to implement. We derive the asymptotic mean and variance of the proposed test statistic under the null hypothesis of equal mean curves. Based on theoretical results, we put forward a permutation procedure to approximate the null distribution of the new test statistic. We compare the power of the proposed test with that of the NBMF-based test via simulations. We illustrate the approach by an application to tidal volume traces. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to introduce new statistical criteria for estimation, suitable for inference in models with common continuous support. This proposal is in the direct line of a renewed interest for divergence based inference tools imbedding the most classical ones, such as maximum likelihood, Chi-square or Kullback–Leibler. General pseudodistances with decomposable structure are considered, they allowing defining minimum pseudodistance estimators, without using nonparametric density estimators. A special class of pseudodistances indexed by , leading for to the Kullback–Leibler divergence, is presented in detail. Corresponding estimation criteria are developed and asymptotic properties are studied. The estimation method is then extended to regression models. Finally, some examples based on Monte Carlo simulations are discussed. [Copyright &y& Elsevier]

Abstract: In this paper it is shown that data depth does not only provide consistent and robust estimators but also consistent and robust tests. Thereby, consistency of a test means that the Type I () error and the Type II () error converge to zero with growing sample size in the interior of the nullhypothesis and the alternative, respectively. Robustness is measured by the breakdown point which depends here on a so-called concentration parameter. The consistency and robustness properties are shown for cases where the parameter of maximum depth is a biased estimator and has to be corrected. This bias is a disadvantage for estimation but an advantage for testing. It causes that the corresponding simplicial depth is not a degenerated U-statistic so that tests can be derived easily. However, the straightforward tests have a very poor power although they are asymptotic tests. To improve the power, a new method is presented to modify these tests so that even consistency of the modified tests is achieved. Examples of two-dimensional copulas and the Weibull distribution show the applicability of the new method. [Copyright &y& Elsevier]

Abstract: A new statistic, SΓ(p), is developed for variable selection in a system-of-equations model. The standardized total mean square error in the SΓ(p)statistic is weighted by the covariance matrix of dependent variables instead of the error covariance matrix of the true model as in the original definition. The new statistic can be also used for model selection in the non-nested models. The estimate of SΓ(p), SC(p), is derived and shown to become SC ε (p) in the similar form of C p in a single-equation model when the covariance matrix of sampled dependent variables is replaced by the error covariance matrix under the full model. [Copyright &y& Elsevier]

Abstract: Many recent multiple testing papers have provided more efficient and/or robust methodology for control of a particular error rate. However, different multiple testing scenarios call for the control of different error rates. Hence, the procedure possessing the desired optimality and/or robustness properties may not be applicable to the problem at hand. This paper provides a general method for extending any multiple testing procedure to control any error rate, thereby allowing for the procedure possessing the desired properties to be used to control the most relevant error rate. As an example, two popular procedures that were originally designed to control the marginal and positive False Discovery Rate are extended to control the False Discovery Rate and Family-wise Error Rate. It is shown that optimality and/or robustness properties of the original procedure are retained when it is modified using the proposed method. [Copyright &y& Elsevier]

Abstract: This paper deals with the allocation of active redundancies to a k-out-of-n system with independent and identically distributed (i.i.d.) components in the sense of the hazard rate order. It is shown that the system''s hazard rate may be decreased by balancing the allocation of active redundancies. This generalizes the main result of and improves the corresponding one of as well. As an application, we build the reversed hazard rate order on order statistics from sample having proportional hazard rates, which strengthens the usual stochastic order in Theorem 2.1 of to the reversed hazard order in the situation that all components are of (rational) proportional hazard rates. [Copyright &y& Elsevier]

Abstract: We develop a simple approach to finding the Fisher information matrix (FIM) for a single pair of order statistic and its concomitant, and Type II right, left, and doubly censored samples from an arbitrary bivariate distribution. We use it to determine explicit expressions for the FIM for the three parameters of Downton''s bivariate exponential distribution for single pairs and Type II censored samples. We evaluate the FIM in censored samples for finite sample sizes and determine its limiting form as the sample size increases. We discuss implications of our findings to inference and experimental design using small and large censored samples and for ranked-set samples from this distribution. [Copyright &y& Elsevier]

Abstract: considered order preserving property of maximum likelihood estimators. In this paper there are given conditions under which the moment estimators have the property of preserving stochastic orders. The preserving property for the usual stochastic order as well as for likelihood ratio one is considered. Sufficient conditions are established for some parametric families of distributions. [Copyright &y& Elsevier]

Abstract: In this paper, we derive the asymptotic distribution of innovational outlier unit root test for trending series with a break. The results of are applied to provide the limiting results of these new test statistics. We tabulate their asymptotic and finite sample critical values, and illustrate the use of the new statistics with an application to the unemployment rate series for 23 OECD countries. [Copyright &y& Elsevier]

Abstract: In this paper we derive some new tests for goodness-of-fit based on Rubin''s empirical distribution function (EDF). Substituting Rubin''s EDF for the classical EDF in the Kolmogorov–Smirnov, Cramér–von Mises, Anderson–Darling statistics, since Rubin''s EDF for a given sample is a randomized distribution function, randomized statistics are derived, of which the qth quantile and the expectation are chosen as test statistics. We show that the new tests are consistent under simple hypothesis. Several power comparisons are also performed to show that the new tests are generally more powerful than the classical ones. [Copyright &y& Elsevier]

Abstract: In this paper, we consider to apply the empirical likelihood method to a probability density function under an associated sample. It is shown that the empirical likelihood ratio statistic is asymptotically distributed under some mild conditions. The result is used to construct empirical likelihood-based confidence intervals on the probability density function. [Copyright &y& Elsevier]

Abstract: We give a new characterization of method for computing c-optimal designs in k dimensions which gives explicit formulae for the k unknown optimal weights and k unknown signs in Elfving''s characterization. This eliminates the need to search over these parameters to compute c-optimal designs, and thus reduces the computational burden from solving a family of optimization problems to solving a single optimization problem for the optimal finite support set. We give two illustrative examples: a high dimensional polynomial regression model and a logistic regression model, the latter showing that the method can be used for locally optimal designs in nonlinear models as well. [Copyright &y& Elsevier]

Abstract: We investigate the optimal configurations of points on the unit sphere for a class of potential functions. In particular, we characterize these optimal configurations in terms of their approximation properties within frame theory. Furthermore, we consider similar optimal configurations in terms of random distributions of points on the sphere. In this probabilistic setting, we characterize these optimal distributions by means of special classes of probabilistic frames. Our work also indicates some connections between statistical shape analysis and frame theory. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the asymptotic theory for U-statistics based on sample spacings, i.e. the gaps between successive observations. The usual asymptotic theory for U-statistics does not apply here because spacings are dependent variables. However, under the null hypothesis, the uniform spacings can be expressed as conditionally independent Exponential random variables. We exploit this idea to derive the relevant asymptotic theory both under the null hypothesis and under a sequence of close alternatives. The generalized Gini mean difference of the sample spacings is a prime example of a U-statistic of this type. We show that such a Gini spacings test is analogous to Rao''s spacings test. We find the asymptotically locally most powerful test in this class, and it has the same efficacy as the Greenwood statistic. [Copyright &y& Elsevier]

Abstract: A q-Pólya urn model is introduced by assuming that the probability of drawing a white ball at a drawing varies geometrically, with rate q, both with the number of drawings and the number of white balls drawn in the previous drawings. Then, the probability mass functions and moments of (a) the number of white balls drawn in a specific number of drawings and (b) the number of black balls drawn until a specific number of white balls are drawn are derived. These two distributions turned out to be q-analogs of the Pólya and the inverse Pólya distributions, respectively. Also, the limiting distributions of the q-Pólya and the inverse q-Pólya distributions, as the number of balls in the urn tends to infinity, are shown to be a q-binomial and a negative q-binomial distribution, respectively. In addition, the positive or negative q-hypergeometric distribution is obtained as conditional distribution of a positive or negative q-binomial distribution, given its sum with another positive or negative q-binomial distribution, independent of it. [Copyright &y& Elsevier]

Abstract: Neighbor designs have their own importance in the experiments to remove the neighbor effects where the performance of a treatment is affected by the treatments applied to its adjacent plots. If each pair of distinct treatments appears exactly once as neighbors, neighbor designs are called minimal. Most of the neighbor designs require a large number of blocks of equal sizes. In this situation minimal neighbor designs in unequal block sizes are preferred to reduce the experimental material. In this article some series are presented to construct minimal neighbor designs in circular blocks of unequal sizes. [Copyright &y& Elsevier]

Abstract: Locating the optimal operating conditions of the process parameters is critical in a lifetime improvement experiment. For log-normal lifetime distribution with compound error structure (i.e., symmetry, inter-class and intra-class correlation error structures), we have developed methods for construction of D-optimal robust first order designs. It is shown that D-optimal robust first order designs are always robust first order rotatable but the converse is not always true. [Copyright &y& Elsevier]

Abstract: This note constitutes a corrigendum to the article of Azomahou [2009, Memory properties and aggregation of spatial autoregressive models. J. Statist. Plann. Inference, 139, 2581–2597]. The aggregation of isotropic four nearest neighbors autoregressive models on the lattice , with random coefficient, is investigated. The spectral density of the resulting random field is studied in details for a large class of law of the AR coefficient. Depending on this law, the aggregated field may exhibit short memory or isotropic long memory. [Copyright &y& Elsevier]

Abstract: Neighbor balanced designs are used to remove the neighbor effects but most of these designs require a large number of blocks. To neutralize the neighbor effects in such situations, GN2-designs are most desirable. This article deals with the (i) refinement of some series of GN2-designs constructed by and (ii) construction of some new series of GN2-designs in circular blocks of equal size. [Copyright &y& Elsevier]

Abstract: The Weibull intensity is often used in survival analysis of technical products, it is an extremely important intensity to characterize the probabilistic behavior of a large number of real phenomena. This intensity is especially useful as a failure model analyzing the reliability of different types of systems. In this paper we develop statistical methods for an alternating repair model using Weibull intensity. The maximum likelihood estimator is considered for determining the estimations of the model parameters. The distribution of the life times after perfect repairs and imperfect repairs are obtained. The estimation of the Fisher information matrix is given. Simultaneous confidence regions based on the likelihood ratio statistics are developed for the estimators of the shape and scale parameter of the Weibull intensity. Finally simulation study will be given. [Copyright &y& Elsevier]

Abstract: A new test statistic based on runs of weighted deviations is introduced. Its use for observations sampled from independent normal distributions is worked out in detail. It supplements the classic test which ignores the ordering of observations and provides additional sensitivity to local deviations from expectations. The exact distribution of the statistic in the non-parametric case is derived and an algorithm to compute p-values is presented. The computational complexity of the algorithm is derived employing a novel identity for integer partitions. [Copyright &y& Elsevier]

Abstract: A generalization of the Probit model is presented, with the extended skew-normal cumulative distribution as a link function, which can be used for modelling a binary response variable in the presence of selectivity bias. The estimate of the parameters via ML is addressed, and inference on the parameters expressing the degree of selection is discussed. The assumption underlying the model is that the selection mechanism influences the unmeasured factors and does not affect the explanatory variables. When this assumption is violated, but other conditional independencies hold, then the model proposed here is derived. In particular, the instrumental variable formula still applies and the model results at the second stage of the estimating procedure. [Copyright &y& Elsevier]