Multivariate Positive Dependence on the Simplex

The Liouville and Generalized Liouville families have been proposed as parametric models for data constrained to the simplex. These families have generated practical interest owing primarily to inadequacies, such as a completely negative covariance structure, that are inherent in the better-known Dirichlet class. Although there is some numerical evidence suggesting that the Liouville and Generalized Liouville families can produce completely positive and mixed covariance structures, no general paradigms have been developed. Research toward this end might naturally be focused on the many classical "positive dependence" concepts available in the literature, all of which imply a nonnegative covariance structure. However, in this article it is shown that no strictly positive distribution on the simplex can possess any of these classical dependence properties. The same result holds for Liouville and generalized Liouville distributions even if the condition of strict positivity is relaxed.     

Goodness of fit tests for Nakagami distribution based on smooth tests

ABSTRACT

Nakagami distribution is one of the most common distributions used to model positive valued and right skewed data. In this study, we interest goodness of fit problem for Nakagami distribution. Thus, we propose smooth tests for Nakagami distribution based on orthonormal functions. We also compare these tests with some classical goodness of fit tests such as Cramer–von Mises, Anderson–Darling, and Kolmogorov–Smirnov tests in respect to type-I error rates and powers of tests. Simulation study indicates that smooth tests give better results than these classical tests give in respect to almost all cases considered.     

Conditional Generalized Liouville Distributions on the Simplex

Liouville and generalized Liouville distributions on the simplex have been proposed for modeling compositional data and have been shown to be free from the extreme independence structure that characterizes the Dirichlet class. In this article, generalized Liouville distributions are shown to be rich enough to distinguish some lesser modes of independence as well. Unfortunately, it is noted that the applicability of the Liouville family will be limited, owing to the lack of invariance with respect to the chosen fill-up value. As an alternative, a new family of simplex distributions is proposed, one that admits invariance with respect to choice of fill-up value, as well as the ability to differentiate among many forms of independence.     

Bayes two-decision procedures for two-sample problems and rank-order data

A two-sample problem for rank-order data is formulated as a two-decision problem. Using the general Bayes solution, Bayes procedures are derived for several configurations of the set of states of nature including some for which the problem is distribution-free. It is shown that for certain prior distributions these procedures reduce to classical LMP rank tests. Some devices for selection of prior distributions are suggested. It is shown that the Bayes risk of these procedures tends to zero as sample sizes increase.     

The Generalized Birnbaum–Saunders Distribution and Its Theory,Methodology, and Application

In this paper, we discuss the class of generalized Birnbaum–Saunders distributions, which is a very flexible family suitable for modeling lifetime data as it allows for different degrees of kurtosis and asymmetry and unimodality as well as bimodality. We describe the theoretical developments on this model including properties, transformations and related distributions, lifetime analysis, and shape analysis. We also discuss methods of inference based on uncensored and censored data, diagnostics methods, goodness-of-fit tests, and random number generation algorithms for the generalized Birnbaum–Saunders model. Finally, we present some illustrative examples and show that this distribution fits the data better than the classical Birnbaum–Saunders model.     

Some count-based nonparametric tests for circular symmetry of a bivariate distribution

In this paper, we revisit the problem of testing of the hypothesis of circular symmetry of a bivariate distribution. We propose some nonparametric tests based on sector counts. These include tests based on chi-square goodness-of-fit test, the classical likelihood ratio, mean deviation, and the range. The proposed tests are easy to implement and the exact null distributions for small sample sizes of the test statistics are obtained. Two examples with small and large data sets are given to illustrate the application of the tests proposed. For small and moderate sample sizes, the performances of the proposed tests are evaluated using empirical powers (empirical sizes are also reported). Also, we evaluate the performance of these count-based tests with adaptations of several well-known tests such as the Kolmogorov–Smirnov-type tests, tests based on kernel density estimator, and the Wilcoxon-type tests. It is observed that among the count-based tests the likelihood ratio test performs better.     

Recent and classical tests for normality - a comparative study

We give a critical synopsis of classical and recent tests for univariate normality, our emphasis being on procedures which are consistent against all alternatives. The power performance of some selected tests (Anderson-Darling, Shapiro-Wilk, Shapiro-Francia, Epps-Pulley) is assessed in a simulation study. Numerical results are illuminated by plots of isodynes, i.e., lines of constant estimated power, for the Johnson-system of distributions.     

Survival and lifetime data analysis with a flexible class of distributions

We introduce a general class of continuous univariate distributions with positive support obtained by transforming the class of two-piece distributions. We show that this class of distributions is very flexible, easy to implement, and contains members that can capture different tail behaviours and shapes, producing also a variety of hazard functions. The proposed distributions represent a flexible alternative to the classical choices such as the log-normal, Gamma, and Weibull distributions. We investigate empirically the inferential properties of the proposed models through an extensive simulation study. We present some applications using real data in the contexts of time-to-event and accelerated failure time models. In the second kind of applications, we explore the use of these models in the estimation of the distribution of the individual remaining life.     

Oracle GMM estimation for misspecified models via thresholding

We propose a thresholding generalized method of moments (GMM) estimator for misspecified time series moment condition models. This estimator has the following oracle property: its asymptotic behavior is the same as of any efficient GMM estimator obtained under the a priori information that the true model were known. We propose data adaptive selection methods for thresholding parameter using multiple testing procedures. We determine the limiting null distributions of classical parameter tests and show the consistency of the corresponding block-bootstrap tests used in conjunction with thresholding GMM inference. We present the results of a simulation study for a misspecified instrumental variable regression model and for a vector autoregressive model with measurement error. We illustrate an application of the proposed methodology to data analysis of a real-world dataset.     

Union-intersection rank tests for ordered alternatives in some simple linear models

The theory of locally most powerful rank tests and the union intersection principle are incorporated in the formulation of some distribution-free rank tests for ordered alternatives in some simple linear models (including the classical one-way layout as a special case). Some approximations for the null-hypothesis distributions of the test statistics ( for finite sample sizes) are considered, and the theory is supplemented by some numerical and simulation results.     

Tests of fit for normal inverse Gaussian distributions

Goodness-of-fit tests for the family of symmetric normal inverse Gaussian distributions are constructed. The tests are based on a weighted integral incorporating the empirical characteristic function of suitably standardized data. An EM-type algorithm is employed for the estimation of the parameters involved in the test statistic. Monte Carlo results show that the new procedure is competitive with classical goodness-of-fit methods. An application with financial data is also included.     

Parameter change test for zero-inflated generalized Poisson autoregressive models

In this paper, we consider the problem of testing for parameter change in zero-inflated generalized Poisson (ZIGP) autoregressive models. We verify that the ZIGP process is stationary and ergodic and that the conditional maximum likelihood estimator (CMLE) is strongly consistent and asymptotically normal. Based on these results, we construct CMLE- and residual-based cumulative sum tests and show that their limiting null distributions are a function of independent Brownian bridges. The simulation results are provided for illustration. A real data analysis is performed on some crime data of Australia.     

Tests for homogeneity of extreme value scale parameters

It is often assumed in situations in which life data from Weibull or extreme-value distributions are involved that data in different samples come from extreme-value distributions with the same scale parameter (equivalently, Weibull distributions with the same shape parameter). This paper proposes a number of tests for homogeneity for extreme-value scale parameters, based on a number of commonly used estimators for these scale parameters. Previous theoretical work and some simulation results provided here indicate that the null distributions of the test statistics proposed are well approximated by the x2 distribution under a wide range of conditions     

The impact of fat-tailed distributions on some leading unit roots tests

There is substantial evidence that many time series associated with financial and insurance claim data are fat-tailed, with a (much) higher probability of " outliers' compared with the normal distribution. However, standard tests, or variants of them, for the presence of unit roots assume a normal distribution for the innovations driving the series. Application of the former to the latter therefore involves an inconsistency. We assess the impact of this inconsistency and provide information on its impact on inference when innovations are drawn from the Cauchy and sequence of t(v) distributions. A simple prediction that fat tails will uniformly lead to over-sizing of standard tests (because the fatness in the tail translates to the test distribution) turns out to be incorrect: we find that some tests are over-sized but some are under-sized. We also consider size retention and the power of the Dickey-Fuller pivotal and normalized bias test statistics and weighted symmetric versions of these tests. To make the unit root testing procedure feasible, we develop an entropy-based test for some fat-tailed distributions and apply it to share prices from the FTSE100.     

An adaptive two-sample location-scale test of lepage type for symmetric distributions

For the two-sample location and scale problem we propose an adaptive test which is based on so called Lepage type tests. The well known test of Lepage (1971) is a combination of the Wilcoxon test for location alternatives and the Ansari-Bradley test for scale alternatives and it behaves well for symmetric and medium-tailed distributions. For the cae of short-, medium- and long-tailed distributions we replace the Wilcoxon test and the .Ansari-Bradley test by suitable other two-sample tests for location and scale, respectively, in oder to get higher power than the classical Lepage test for such distribotions. These tests here are called Lepage type tests. in practice, however, we generally have no clear idea about the distribution having generated our data. Thus, an adaptive test should be applied which takes the the given data set inio consideration. The proposed adaptive test is based on the concept of Hogg (1974), i.e., first, to classify the unknown symmetric distribution function with respect to a measure for tailweight and second, to apply an appropriate Lepage type test for this classified type of distribution. We compare the adaptive test with the three Lepage type tests in the adaptive scheme and with the classical Lepage test as well as with other parametric and nonparametric tests. The power comparison is carried out via Monte Carlo simulation. It is shown that the adaptive test is the best one for the broad class of distributions considered.     

The present status of confidence interval estimation on variance components in balanced and unbalanced random models

Much research has been conducted to develop confidence Intervals on linear combinations and ratios of variance components in balanced and unbalanced random models.This paper first presents confidence intervals on functions of variance components in balanced designs.These results assume that classical analysis of variance sums of squares are independent and have exact scaled chi-squared distributions.In unbalanced designs, either one or both of these assumptions are violated, and modifications to the balanced model intervals are required.We report results of some recent work that examines various modifications for some particular unbalanced designs.     

Tests for the total time on test transform order

In this paper we consider two test statistics for testing the strict TTT transform order between two life distributions of interest. We give their asymptotic distributions and compare our tests with some other related tests in terms of Pitman's asymptotic efficiency. Also we present some results to show the performance and the asymptotic normality of our tests.     

Inference in flexible families of distributions with normal kernel

This paper addresses the inference problem for a flexible class of distributions with normal kernel known as skew-bimodal-normal family of distributions. We obtain posterior and predictive distributions assuming different prior specifications. We provide conditions for the existence of the maximum-likelihood estimators (MLE). An EM-type algorithm is built to compute them. As a by product, we obtain important results related to classical and Bayesian inferences for two special subclasses called bimodal-normal and skew-normal (SN) distribution families. We perform a Monte Carlo simulation study to analyse behaviour of the MLE and some Bayesian ones. Considering the frontier data previously studied in the literature, we use the skew-bimodal-normal (SBN) distribution for density estimation. For that data set, we conclude that the SBN model provides as good a fit as the one obtained using the location-scale SN model. Since the former is a more parsimonious model, such a result is shown to be more attractive.     

Approximate asymptotic Bahadur efficiency of independence tests with random sample size

We compare various kind of independence tests based on samples with random size, in order to provide practitioners with some guidance for their choice based on approximate Bahadur efficiency. Such results are obtained for a wide class of distributions of the random index; the efficiency slopes of the statistics we consider are then expressed in terms of the parameters of these same distributions.