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The estimation of variance function plays an extremely important role in statistical inference of the regression models. In this paper we propose a variance modelling method for constructing the variance structure via combining the exponential polynomial modelling method and the kernel smoothing technique. A simple estimation method for the parameters in heteroscedastic linear regression models is developed when the covariance matrix is unknown diagonal and the variance function is a positive function of the mean. The consistency and asymptotic normality of the resulting estimators are established under some mild assumptions. In particular, a simple version of bootstrap test is adapted to test misspecification of the variance function. Some Monte Carlo simulation studies are carried out to examine the finite sample performance of the proposed methods. Finally, the methodologies are illustrated by the ozone concentration dataset. [ABSTRACT FROM AUTHOR]

The generalized case-cohort design is widely used in large cohort studies to reduce the cost and improve the efficiency. Taking prior information of parameters into consideration in modeling process can further raise the inference efficiency. In this paper, we consider fitting proportional hazards model with constraints for generalized case-cohort studies. We establish a working likelihood function for the estimation of model parameters. The asymptotic properties of the proposed estimator are derived via the Karush-Kuhn-Tucker conditions, and their finite properties are assessed by simulation studies. A modified minorization-maximization algorithm is developed for the numerical calculation of the constrained estimator. An application to a Wilms tumor study demonstrates the utility of the proposed method in practice. [ABSTRACT FROM AUTHOR]

Much research has been conducted over the last half century in developing stochastic processes, and their dynamical nature. Typically, for time indexed processes, the temporal distribution is restricted to those having marginal distributions of a specified and familiar lifetime family. Extensions of temporal models to the spatio-temporal setting can be challenging. We generalize the results from a spatial statistic that captures local correlation, Moran's index, to the spatio-temporal frame and describe a model that can be applied to temporal dynamical phenomena. The proposed approach leads to novel statistical inference results. Ensuring a foundational Moran measure is critical in describing event occurrence and progression over time of the process from observed initial conditions. In this paper, we provide a descriptive form of discrete spatio-temporal Moran's index statistics based on processes motivated by the spread of an infectious plant disease in an agricultural setting. This family possesses an underlying Poisson point process in space and time. Estimators are developed and applied to simulated data and the output are analyzed. Our results adds substantially to known results in the literature and elude to the description of the time dependent Moran's values. [ABSTRACT FROM AUTHOR]

There are several failure modes may cause system failed in reliability and survival analysis. It is usually assumed that the causes of failure modes are independent each other, though this assumption does not always hold. Dependent competing risks modes from Marshall-Olkin bivariate Weibull distribution under Type-I progressive interval censoring scheme are considered in this paper. We derive the maximum likelihood function, the maximum likelihood estimates, the 95% Bootstrap confidence intervals and the 95% coverage percentages of the parameters when shape parameter is known, and EM algorithm is applied when shape parameter is unknown. The Monte-Carlo simulation is given to illustrate the theoretical analysis and the effects of parameters estimates under different sample sizes. Finally, a data set has been analyzed for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this paper, a one-stage multiple comparison procedures with the average for exponential location parameters based on the doubly censored sample under heteroscedasticity is proposed. These intervals can be used to identify a subset which includes all no-worse-than-the-average treatments in an experimental design and to identify better-than-the-average, worse-than-the-average and not-much-different-from-the-average products in agriculture, emerging market, pharmaceutical industries. The critical values are tabulated in a table for practical use. A simulation study on the confidence length and coverage probabilities is done. At last, an example of comparing four drugs in the treatment of leukemia is given to demonstrate the proposed procedures. [ABSTRACT FROM AUTHOR]

Unlike traditional Type I and II censoring, progressive censoring allows for removal of surviving units throughout the life test. This feature has several benefits and in the literature, much work has been done on inference based on progressively censored samples and identifying optimal progressive censoring schemes. In this paper, we introduce restricted progressive censoring and within this class, the problem of identifying optimal schemes under different minimum variance criteria. We explore these plans geometrically as well as provide some useful properties. In particular, we look at the vertices of the set of admissible plans and their role in approximating optimal plans. We also provide computational results for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this paper, we expand a first-order nonlinear autoregressive (AR) model with skew normal innovations. A semiparametric method is proposed to estimate a nonlinear part of model by using the conditional least squares method for parametric estimation and the nonparametric kernel approach for the AR adjustment estimation. Then computational techniques for parameter estimation are carried out by the maximum likelihood (ML) approach using Expectation-Maximization (EM) type optimization and the explicit iterative form for the ML estimators are obtained. Furthermore, in a simulation study and a real application, the accuracy of the proposed methods is verified. [ABSTRACT FROM AUTHOR]

In this paper, a probability plots class of tests for multivariate normality is introduced. Based on independent standardized principal components of a d-variate normal data set, we obtained the sum of squared differences between corresponding observations of an ordered set of each principal component observations and the set of the population pth quantiles of the standard normal distribution. We proposed the sum of these d-sums of squared differences as an appropriate statistic for testing multivariate normality. We evaluated empirical critical values of the statistic and compared its power with those of some highly regarded techniques with a wonderful result. [ABSTRACT FROM AUTHOR]

Degradation analysis is a useful technique when life tests result in few or even no failures. The degradation measurements are recorded over time and the estimation of time-to-failure distribution plays a vital role in degradation analysis. The parametric method to estimate the time-to-failure distribution assumed a specific parametric model with known shape for the random effects parameter. To avoid any assumption about the model shape, a nonparametric method can be used. In this paper, we suggest to use the nonparametric fourth-order kernel method to estimate the time-to-failure distribution and its percentiles for the simple linear degradation model. The performances of the proposed method are investigated and compared with the classical kernel; maximum likelihood and ordinary least squares methods via simulation technique. The numerical results show the good performance of the fourth-order kernel method and demonstrate its superiority over the parametric method when there is no information about the shape of the random effect parameter distribution. [ABSTRACT FROM AUTHOR]

Feature extraction from observed noisy samples is a common important problem in statistics and engineering. This paper presents a novel general statistical approach to the region detection problem in long data sequences. The proposed technique is a multiscale kernel regression in conjunction with statistical multiple testing for region detection while controlling the false discovery rate (FDR) and maximizing the signal-to-noise ratio via matched filtering. This is achieved by considering a one-dimensional region detection problem as its equivalent zero-dimensional peak detection problem. The detection method does not require a priori knowledge of the shape of the nonzero regions. However, if the shape of the nonzero regions is known a priori, e.g., rectangular pulse, the signal regions can also be reconstructed from the detected peaks, seen as their topological point representatives. Simulations show that the method can effectively perform signal detection and reconstruction in the simulated data under high noise conditions, while controlling the FDR of detected regions and their reconstructed length. [ABSTRACT FROM AUTHOR]

Asymmetric models have been extensively studied in recent years, in situations where the normality assumption is not satisfied due to lack of symmetry of the data. Techniques for assessing the quality of fit and diagnostic analysis are important for model validation. This paper presents a study of the mean-shift method for detecting outliers in asymmetric normal regression models. Analytical solutions for the estimators of the parameters are obtained using the algorithm. Simulation studies and application to real data are presented, showing the efficiency of the method in detecting outliers. [ABSTRACT FROM AUTHOR]

Efron and Petrosian (1999) formulated the problem of double truncation and proposed nonparametric methods on testing and estimation. An alternative estimation method was proposed by Shen (2010a), utilizing the inverse-probability-weighting technique. One aim of this paper was to assess the computational complexity of the existing estimation methods. Through a simulation study, we found that these two estimation methods have the same level of computational efficiency. The other aim was to study the noniterative IPW estimator under the condition that truncation variables are independent. The IPW estimator and the interval estimation was proved satisfactory in the simulation study. [ABSTRACT FROM AUTHOR]

Spatio-temporal surveillance methods for detecting outbreaks of disease are fairly common in the literature with the scan statistic setting the benchmark. If the shape and size of the outbreaks are known in advance, then the scan approach can be designed to efficiently detect these, however, this is seldom true. Therefore we want to devise plans that are efficient at detecting a number of outbreaks that vary in size and shape. This paper examines plans which use the exponential weighted moving average statistic to build temporal memory into plans and tries to develop robust plans for detecting outbreaks of unknown shapes and sizes. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the inference for the component and system lifetime distribution of ak-unit parallel system with independent components based on system data. The components are assumed to have identical Weibull distribution. We obtain the maximum likelihood estimates of the unknown parameters based on system data. The Fisher information matrix has been derived. We propose β-expectation tolerance interval and β-content γ-level tolerance interval for the life distribution of the system. Performance of the estimators and tolerance intervals is investigated via simulation study. A simulated dataset is analyzed for illustration. [ABSTRACT FROM AUTHOR]

Poisson point processes play important role in various domains of Probability Theory and Mathematical Statistics. In this article, we investigate only two applications of Poisson point processes: a generated white noise problem and parameters estimation problem. This work continues the investigations started in paper Egorov and Kondybaev (2009). [ABSTRACT FROM AUTHOR]

The X¯ and S (or R) control charts are most commonly used in practice for monitoring the process mean and variance, respectively. A method for detecting changes in the process mean or variance is to obtain a stopping time at which the control charts issue a signal. The potential delay in generating a signal from the control charts calls for the change point estimation combined with control charts. In this paper, when X¯ and S control charts issue a signal, a maximum likelihood joint estimator of the change point is suggested considering simultaneous change in the process mean and variance. The use of the proposed estimator is illustrated with an example. [ABSTRACT FROM AUTHOR]

In this paper we study the predictor behaviour of the additive model. The prediction equation is introduced as well as the computational considerations to select the smoothing parameters through cross-validation. The additive predictor is compared with a partially linear predictor in a broad simulation study and an application to a real case, prediction of the atmospheric concentration of SO2 in sample stations. [ABSTRACT FROM AUTHOR]

In this paper, we examine the problem of testing equality and inequality constraints on the regression coefficients in linear models with multivariate t-distribution for the within-subject errors. Iterative processes for evaluating the parameters under equality and inequality constraints are presented for fixed degrees of freedom. Under certain regularity assumptions the likelihood ratio, score (Rao) and Wald tests are asymptotically distributed as a mixture of chi-squared distributions, where the weights do not depend on the null parameters, but may depend on the correlations. Thus, one has to search through the set of correlation coefficients for least favorable points. Some particular cases are discussed and the empirical performances of the statistical tests for small and moderate sample sizes are compared via Monte Carlo studies. Comparisons between the theoretical and empirical distributions of the statistical one-sided tests are also made. The quality of the approximation seems to be good even for small (about n = 20) sample sizes. We present an illustrative example with real data in which statistical tests based on normal and t models are compared, confirming the robustness of the t models against outliers. This robustness is reflected directly on the decision from the one-sided tests. [ABSTRACT FROM AUTHOR]

The poly-Weibull model is a general family which arise on competing risk scenarios when there is no direct information about which risk was responsible for the failure. Its advantage over the single-Weibull model is to allow not only constant, increasing or decreasing hazard curves with zero or non zero asymptotes, but also nonmonotones ones, including bathtub-shaped. In this paper we consider the non-identifiability problem, which arises when the shape parameters of a poly-Weibull model are close. Theoretical calculation of the information and correlation matrixes are used to assess when a poly-Weibull model is likely to be feasible. From the practical point of view, a graphical method, based on the total-time-on-test plot and its simulated envelop, is considered for detecting when a poly-Weibull model is likely to be identifiable. We also provide a general framework for constructing hypothesis tests for non-identifiability by using parametric bootstrap-based methods. We set up a simulation study and show that the bootstrap tests have desirable properties with respect to size and power. In some situations only a single Weibull model is enough for fitting the data. We determine the cost of estimating the parameters of a single-Weibull model if a bi-Weibull model is considered instead. [ABSTRACT FROM AUTHOR]

In this paper, a class of nonparametric tests for independence between two continuous random variables is proposed. The members of the class are characterized by the size of the partitions of the sample space on which the test statistics are based. The test statistic that corresponds to the smallest partition size may be seen as an extension of Hoeffding's statistic with an Anderson–Darling-type weight function. In this simplest case, we have proven its asymptotic null distribution as well as its omnibus consistency. In a simulation study, the powers of the new tests are compared to those of some other tests for independence. It is concluded that overall high powers are obtained with these new tests. [ABSTRACT FROM AUTHOR]

Constrained M (CM) estimates of multivariate location and scatter [Kent, J. T., Tyler, D. E. (1996). Constrained M-estimation for multivariate location and scatter. Ann. Statist. 24:1346–1370] are defined as the global minimum of an objective function subject to a constraint. These estimates combine the good global robustness properties of the S estimates and the good local robustness properties of the redescending M estimates. The CM estimates are not explicitly defined. Numerical methods have to be used to compute the CM estimates. In this paper, we give an algorithm to compute the CM estimates. Using the algorithm, we give a small simulation study to demonstrate the capability of the algorithm finding the CM estimates, and also to explore the finite sample behavior of the CM estimates. We also use the CM estimators to estimate the location and scatter parameters of some multivariate data sets to see the performance of the CM estimates dealing with the real data sets that may contain outliers. [ABSTRACT FROM AUTHOR]

It is well known that prior application of GLS detrending, as advocated by Elliot et al. [Elliot, G., Rothenberg, T., Stock, J. (1996). Efficient tests for an autoregressive unit root. Econometrica 64:813–836], can produce a significant increase in power to reject the unit root null over that obtained from a conventional OLS-based Dickey and Fuller [Dickey, D., Fuller, W. (1979). Distribution of the estimators for autoregressive time series with a unit root. J. Am. Statist. Assoc. 74:427–431] testing equation. However, this paper employs Monte Carlo simulation to demonstrate that this increase in power is not necessarily obtained when breaks occur in either level or trend. It is found that neither OLS nor GLS-based tests are robust to level or trend breaks, their size and power properties both deteriorating as the break size increases. [ABSTRACT FROM AUTHOR]

In this paper, we discuss goodness-of-fit tests of the exponential distribution based on Kullback-Leibler information. To construct test statistics, Van Es' and Correa's entropy estimator are used as an estimator of Shannon's entropy. Critical values for various sample sizes determined by means of Monte Carlo simulations are presented for each of test statistics. Also, formulas for calculating approximate critical values for given sample sizes are provided for the respective test statistics. A Monte Carlo power analysis is performed for various alternatives and sample sizes in order to compare the proposed tests with several existing goodness-of-fit tests based on the empirical distribution function (EDF). Simulation results show that Kullback-Leibler information tests have higher powers than the EDF tests. [ABSTRACT FROM AUTHOR]

For non-negative integer-valued random variables, the concept of "damaged" observations was introduced, for the first time, by Rao and Rubin [Rao, C. R., Rubin, H. (1964). On a characterization of the Poisson distribution. Sankhya 26:295-298] in 1964 on a paper concerning the characterization of Poisson distribution. In 1965, Rao [Rao, C. R. (1965). On discrete distribution arising out of methods of ascertainment. Sankhya Ser. A. 27:311-324] discusses some results related with inferences for parameters of a Poisson Model when it has occurred partial destruction of observations. A random variable is said to be damaged if it is unobservable, due to a damage mechanism which randomly reduces its magnitude. In subsequent years, considerable attention has been given to characterizations of distributions of such random variables that satisfy the "Rao-Rubin" condition. This article presents some inference aspects of a damaged Poisson distribution, under reasonable assumption that, when an observation on the random variable is made, it is also possible to determine whether or not some damage has occurred. In other words, we do not know how many items are damaged, but we can identify the existence of damage. Particularly it is illustrated the situation in which it is possible to identify the occurrence of some damage although it is not possible to determine the amount of items damaged. Maximum likelihood estimators of the underlying parameters and their asymptotic covariance matrix are obtained. Convergence of the estimates of parameters to the asymptotic values are studied through Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

The present paper is motivated by the work of Kozachenko and Leonenko (Kozachenko, L. F., Leonenko, N. N. (1987). On statistical estimation of entropy of random vector. Problems Infor. Transmiss. 23:9-16) where a new estimator of entropy is proposed. Here we reformulate it in terms of spacings of order m and we compare the mean square error (MSE) of the reformulated estimator with those of three alternative competitors, introduced in literature by Vasicek (Vasicek, O. (1976). A test of normality based on sample entropy. J. Roy. Stat. Soc., Ser. B 38:254-256), and more recently by van Es (van Es, B. (1992). Estimating functionals related to a density by class of statistics based on spacing. Scand. J. Statist. 19:61-72) and Correa (Correa, J. C. (1995). A new estimator of entropy. Commun. Statist.--Theory Meth. 24:2439-2449), respectively. [ABSTRACT FROM AUTHOR]

This paper presents general one-stage and two-stage sampling procedures for testing the hypotheses of the equality of means when the variances are unknown and unequal. The methods use a new range test and an ANOVA test based on independent t variables for an one-way layout. The one-stage procedure is an exact statistical procedure which provides a feasible solution to the two-stage procedure when the required two-stage sample sizes are not met due to time limitation, budget shortage, or other factors that result in early termination of the experiment. An extension to the two-way layout is also considered and the percentage points of the range test for testing the associated hypotheses are tabulated. [ABSTRACT FROM AUTHOR]