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1.
Two-period crossover design is one of the commonly used designs in clinical trials. But, the estimation of treatment effect is complicated by the possible presence of carryover effect. It is known that ignoring the carryover effect when it exists can lead to poor estimates of the treatment effect. The classical approach by Grizzle (1965) consists of two stages. First, a preliminary test is conducted on carryover effect. If the carryover effect is significant, analysis is based only on data from period one; otherwise, analysis is based on data from both periods. A Bayesian approach with improper priors was proposed by Grieve (1985) which uses a mixture of two models: a model with carryover effect and another without. The indeterminacy of the Bayes factor due to the arbitrary constant in the improper prior was addressed by assigning a minimally discriminatory value to the constant. In this article, we present an objective Bayesian estimation approach to the two-period crossover design which is also based on a mixture model, but using the commonly recommended Zellner–Siow g-prior. We provide simulation studies and a real data example and compare the numerical results with Grizzle (1965)’s and Grieve (1985)’s approaches. 相似文献
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This article proposes new symmetric and asymmetric distributions applying methods analogous as the ones in Kim (2005) and Arnold et al. (2009) to the exponentiated normal distribution studied in Durrans (1992), that we call the power-normal (PN) distribution. The proposed bimodal extension, the main focus of the paper, is called the bimodal power-normal model and is denoted by BPN(α) model, where α is the asymmetry parameter. The authors give some properties including moments and maximum likelihood estimation. Two important features of the model proposed is that its normalizing constant has closed and simple form and that the Fisher information matrix is nonsingular, guaranteeing large sample properties of the maximum likelihood estimators. Finally, simulation studies and real applications reveal that the proposed model can perform well in both situations. 相似文献
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Since the seminal paper of Ghirardato (1997), it is known that Fubini theorem for non additive measures can be available only for functions as “slice-comonotonic” in the framework of product algebra. Later, inspired by Ghirardato (1997), Chateauneuf and Lefort (2008) obtained some Fubini theorems for non additive measures in the framework of product σ-algebra. In this article, we study Fubini theorem for non additive measures in the framework of g-expectation. We give some different assumptions that provide Fubini theorem in the framework of g-expectation. 相似文献
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In analogy with the weighted Shannon entropy proposed by Belis and Guiasu (1968) and Guiasu (1986), we introduce a new information measure called weighted cumulative residual entropy (WCRE). This is based on the cumulative residual entropy (CRE), which is introduced by Rao et al. (2004). This new information measure is “length-biased” shift dependent that assigns larger weights to larger values of random variable. The properties of WCRE and a formula relating WCRE and weighted Shannon entropy are given. Related studies of reliability theory is covered. Our results include inequalities and various bounds to the WCRE. Conditional WCRE and some of its properties are discussed. The empirical WCRE is proposed to estimate this new information measure. Finally, strong consistency and central limit theorem are provided. 相似文献
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This paper treats the problem of stochastic comparisons for the extreme order statistics arising from heterogeneous beta distributions. Some sufficient conditions involved in majorization-type partial orders are provided for comparing the extreme order statistics in the sense of various magnitude orderings including the likelihood ratio order, the reversed hazard rate order, the usual stochastic order, and the usual multivariate stochastic order. The results established here strengthen and extend those including Kochar and Xu (2007), Mao and Hu (2010), Balakrishnan et al. (2014), and Torrado (2015). A real application in system assembly and some numerical examples are also presented to illustrate the theoretical results. 相似文献
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Housila P. Singh 《统计学通讯:理论与方法》2017,46(2):521-531
This paper aimed at providing an efficient new unbiased estimator for estimating the proportion of a potentially sensitive attribute in survey sampling. The suggested randomization device makes use of the means, variances of scrambling variables, and the two scalars lie between “zero” and “one.” Thus, the same amount of information has been used at the estimation stage. The variance formula of the suggested estimator has been obtained. We have compared the proposed unbiased estimator with that of Kuk (1990) and Franklin (1989), and Singh and Chen (2009) estimators. Relevant conditions are obtained in which the proposed estimator is more efficient than Kuk (1990) and Franklin (1989) and Singh and Chen (2009) estimators. The optimum estimator (OE) in the proposed class of estimators has been identified which finally depends on moments ratios of the scrambling variables. The variance of the optimum estimator has been obtained and compared with that of the Kuk (1990) and Franklin (1989) estimator and Singh and Chen (2009) estimator. It is interesting to mention that the “optimum estimator” of the class of estimators due to Singh and Chen (2009) depends on the parameter π under investigation which limits the use of Singh and Chen (2009) OE in practice while the proposed OE in this paper is free from such a constraint. The proposed OE depends only on the moments ratios of scrambling variables. This is an advantage over the Singh and Chen (2009) estimator. Numerical illustrations are given in the support of the present study when the scrambling variables follow normal distribution. Theoretical and empirical results are very sound and quite illuminating in the favor of the present study. 相似文献
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This article recasts the optimal allocations of coverage limits for two independent random losses. Under some regularity conditions on the two concerned probability density functions, we build the sufficient and necessary condition for the existence of the optimal allocation of coverage limits, and derive the optimal allocation whenever they do exist. The results supplement Lu and Meng (2011, Proposition 5.2) and Hu and Wang (2014, Theorem 5.1). 相似文献
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T. Imada 《统计学通讯:理论与方法》2017,46(7):3186-3199
In this study we discuss multiple comparison procedures for checking differences among a sequence of normal means with ordered restriction. Lee and Spurrier (1995) proposed a multiple comparison procedure which tests the difference between two adjacent means using the difference of sample means. In this study we propose a multiple comparison procedure modifying Lee and Spurrier's (1995) procedure using isotonic regression estimators instead of sample means. We determine the critical value for pairwise comparisons for a specified significance level. Furthermore, we formulate the power of the test. Finally, we give some numerical examples regarding critical values and power of the test intended to compare our procedure with Lee and Spurrier's (1995) procedure. 相似文献
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Sanaullah et al. (2014) have suggested generalized exponential chain ratio estimators under stratified two-phase sampling scheme for estimating the finite population mean. However, the bias and mean square error (MSE) expressions presented in that work need some corrections, and consequently the study based on efficiency comparison also requires corrections. In this article, we revisit Sanaullah et al. (2014) estimator and provide the correct bias and MSE expressions of their estimator. We also propose an estimator which is more efficient than several competing estimators including the classes of estimators in Sanaullah et al. (2014). Three real datasets are used for efficiency comparisons. 相似文献
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In this paper, we establish a complete convergence result and a complete moment convergence result for i.i.d. random variables under moment condition which is slightly weaker than the existence of the moment generating function. The main results extend and improve the related known results of Lanzinger (1998) and Gut and Stadtmüller (2011). 相似文献
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Amir T. Payandeh Najafabadi Fatemeh Atatalab Maryam Omidi Najafabadi 《统计学通讯:理论与方法》2017,46(1):415-426
Credibility formula has been developed in many fields of actuarial sciences. Based upon Payandeh (2010), this article extends concept of credibility formula to relatively premium of a given rate-making system. More precisely, it calculates Payandeh’s (2010) credibility factor for zero-inflated Poisson gamma distributions with respect to several loss functions. A comparison study has been given. 相似文献
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In this article, we establish the complete moment convergence of a moving-average process generated by a class of random variables satisfying the Rosenthal-type maximal inequality and the week mean dominating condition. On the one hand, we give the correct proof for the case p = 1 in Ko (2015); on the other hand, we also consider the case αp = 1 which was not considered in Ko (2015). The results obtained in this article generalize some corresponding ones for some dependent sequences. 相似文献
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To deal with multicollinearity problem, the biased estimators with two biasing parameters have recently attracted much research interest. The aim of this article is to compare one of the last proposals given by Yang and Chang (2010) with Liu-type estimator (Liu 2003) and k ? d class estimator (Sakallioglu and Kaciranlar 2008) under the matrix mean squared error criterion. As well as giving these comparisons theoretically, we support the results with the extended simulation studies and real data example, which show the advantages of the proposal given by Yang and Chang (2010) over the other proposals with increasing multicollinearity level. 相似文献
15.
Sample size estimation for comparing the rates of change in two-arm repeated measurements has been investigated by many investigators. In contrast, the literature has paid relatively less attention to sample size estimation for studies with multi-arm repeated measurements where the design and data analysis can be more complex than two-arm trials. For continuous outcomes, Jung and Ahn (2004) and Zhang and Ahn (2013) have presented sample size formulas to compare the rates of change and time-averaged responses in multi-arm trials, using the generalized estimating equation (GEE) approach. To our knowledge, there has been no corresponding development for multi-arm trials with count outcomes. We present a sample size formula for comparing the rates of change in multi-arm repeated count outcomes using the GEE approach that accommodates various correlation structures, missing data patterns, and unbalanced designs. We conduct simulation studies to assess the performance of the proposed sample size formula under a wide range of designing configurations. Simulation results suggest that empirical type I error and power are maintained close to their nominal levels. The proposed method is illustrated using an epileptic clinical trial example. 相似文献
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Pao-Sheng Shen 《统计学通讯:理论与方法》2017,46(4):1916-1926
The complication in analyzing tumor data is that the tumors detected in a screening program tend to be slowly progressive tumors, which is the so-called left-truncated sampling that is inherent in screening studies. Under the assumption that all subjects have the same tumor growth function, Ghosh (2008) developed estimation procedures for the Cox proportional hazards model. Shen (2011a) demonstrated that Ghosh (2008)'s approach can be extended to the case when each subject has a specific growth function. In this article, under linear transformation model, we present a general framework to the analysis of data from cancer screening studies. We developed estimation procedures under linear transformation model, which includes Cox's model as a special case. A simulation study is conducted to demonstrate the potential usefulness of the proposed estimators. 相似文献
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We investigate a self-normalized central limit theorem for a ρ-mixing stationary sequence {Xi, i ? 1} of random variables such that L(x) ? E(X21I{|X1| ? x}) is a slowly varying function as x → ∞. The results obtained generalize the results of Gine, Gotze, and Mason (1997) and Mason (2005) to ρ-mixing sequences. 相似文献
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We discuss a one-sample location test that can be used when the dimension and the sample size are large. It is well-known that the power of Hotelling’s test decreases when the dimension is close to the sample size. To address this loss of power, some non exact approaches were proposed, e.g., Dempster (1958, 1960), Bai and Saranadasa (1996), and Srivastava and Du (2008). In this article, we focus on Hotelling’s test and Dempster’s test. The comparative merits and demerits of these two tests vary according to the local parameters. In particular, we consider the situation where it is difficult to determine which test should be used, that is, where the two tests are asymptotically equivalent in terms of local power. We propose a new statistic based on the weighted averaging of Hotelling’s T2-statistic and Dempster’s statistic that can be applied in such a situation. Our weight is determined on the basis of the maximum local asymptotic power on a restricted parameter space that induces local asymptotic equivalence between Hotelling’s test and Dempster’s test. Numerical results show that our test is more stable than Hotelling’s T2-statistic and Dempster’s statistic in most parameter settings. 相似文献
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Marek Dvořák 《统计学通讯:理论与方法》2017,46(1):465-484
The aim of this article is the construction of the test statistic for the detection of changes in vector autoregressive (AR) models where both AR parameters and the variance matrix of the error term are the subjects of a change. The approximating distribution of the proposed statistic is the Gumbel distribution. The proof stands on the approximation of weakly dependent random vectors by independent ones and by application of Horváth’s extension of Darling-Erdös extremal result for random vectors, see Darling and Erdös (1956) and Horváth (1993). The test statistic is a modification of the likelihood ratio. 相似文献
20.
Techniques used in variability assessment are subsequently used to draw conclusions regarding the “spread”/uniformity of data curves. Due to the limitations of these techniques, they are not adequate for circumstances where data manifest with multiple peaks. Examples of these manifestations (in three-dimensional space) include under-foot pressure distributions recorded for different types of footwear (Becerro-de-Bengoa-Vallejo et al., 2014; Cibulka et al., 1994; Davies et al., 2003), surface textures and interfaces designed to impact friction, and and and molecular surface structures such as viral epitopes (Torras and Garcia-Valls, 2004; Pacejka, 1997; Fustaffson, 1997). This article proposes a technique for generating a single variable – Λ that will quantify the uniformity of such surfaces. We define and validate this technique using several mathematical and graphical models. 相似文献