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In this paper, we investigate tests of linear hypotheses in heteroscedastic one-way MANOVA via proposing a modified Bartlett (MB) test. The MB test is easy to conduct via using the usual χ2-table. It is shown to be invariant under affine transformations, different choices of the contrast matrix used to define the same hypothesis and different labeling schemes of the mean vectors. Simulation studies...
In this paper, we propose a nonparametric method to estimate the spatial density of a functional stationary random field. This latter is with values in some infinite dimensional normed space and admitted a density with respect to some reference measure. We study both the weak and strong consistencies of the considered estimator and also give some rates of convergence. Special attention is paid to...
One of the central considerations in the theory of Markov chains is their convergence to an equilibrium. Coefficients of ergodicity provide an efficient method for such an analysis. Besides giving sufficient and sometimes necessary conditions for convergence, they additionally measure its rate. In this paper we explore coefficients of ergodicity for the case of imprecise Markov chains. The latter...
In this paper, we investigate checking the adequacy of varying coefficient models with response missing at random. In doing so, we first construct two completed data sets based on imputation and marginal inverse probability weighted methods, respectively. The empirical process-based tests by using these two completed data sets are suggested and the asymptotic properties of the test statistics under...
A supersaturated design is a factorial design in which the number of effects to be estimated is greater than the number of runs. It is used in many experiments, for screening purpose, i.e., for studying a large number of factors and identifying the active ones. In this paper, we propose a method for screening out the important factors from a large set of potentially active variables through the symmetrical...
We consider the mixed AR(1) time series model $$X_t=\left\{\begin{array}{ll}\alpha X_{t-1}+ \xi_t \quad {\rm w.p.} \qquad \frac{\alpha^p}{\alpha^p-\beta ^p},\\ \beta X_{t-1} + \xi_{t} \quad {\rm w.p.} \quad -\frac{\beta^p}{\alpha^p-\beta ^p} \end{array}\right.$$ for −1 < βp ≤ 0 ≤ αp < 1 and αp − βp > 0 when Xt has the two-parameter beta distribution B2(p, q) with parameters...
Block bootstrap has been introduced in the literature for resampling dependent data, i.e. stationary processes. One of the main assumptions in block bootstrapping is that the blocks of observations are exchangeable, i.e. their joint distribution is immune to permutations. In this paper we propose a new Bayesian approach to block bootstrapping, starting from the construction of exchangeable blocks...
The problem of the optimal duration of a burn-in experiment is considered in the case of simultaneous testing n components with the conditionally independent time-transformed exponential life-times, given an unknown parameter. The explicit solution is derived by reformulation of the problem considered to an optimal stopping problem for a suitable defined three-dimensional Markov process and reduction...
The least absolute deviations (LAD) variable selection for linear models with randomly censored data is studied through the Lasso. The proposed procedure can select significant variables in the parameters. With appropriate selection of the tuning parameters, we establish the consistency of this procedure and the oracle property of the resulting estimators. Simulation studies are conducted to compare...
We consider the problem of comparing two diagnostic tests based on a sample of paired test results without true state determinations, in cases where the second test can reasonably be assumed to be at least as specific as the first. For such cases, we provide two informative confidence bounds: A lower one for the prevalence times the sensitivity gain of the second test with respect to the first, and...
The behaviour of the goodness-of-fit procedure for normality based on weighted integrals of the empirical characteristic function, discussed in the case of i.i.d. data, for instance, in Epps and Pulley (Biometrika 70:723–726, 1983), is considered here in the context of ranked set sampling (RSS) data. In the RSS context, we obtain the limiting distribution of the empirical characteristic process and...
Variable selection plays an important role in the high dimensionality data analysis, the Dantzig selector performs variable selection and model fitting for linear and generalized linear models. In this paper we focus on variable selection and parametric estimation for partially linear models via the Dantzig selector. Large sample asymptotic properties of the Dantzig selector estimator are studied...
This paper addresses the problem of fitting a known density to the marginal error density of a stationary long memory moving average process when its mean is known and unknown. In the case of unknown mean, when mean is estimated by the sample mean, the first order difference between the residual empirical and null distribution functions is known to be asymptotically degenerate at zero, and hence can...
The Weibull distribution was discovered by Rosin, Rammler, Sperling and Bennett between 1932 and 1936 in the context of particle measurement. Weibull found the same distribution a little later while investigating the strength of materials. More than 10 years after, in 1951, he finally showed that this distribution has the potential for wide applications in statistics. However, does this justify that...
We present a unification of the Archimedean and the Lévy-frailty copula model for portfolio default models. The new default model exhibits a copula known as scale mixture of Marshall-Olkin copulas and an investigation of the dependence structure reveals that desirable properties of both original models are combined. This allows for a wider range of dependence patterns, while the analytical tractability...
Considering the presence of first order residual effects of treatments, a family of variance balanced changeover designs has been presented and universal optimality of the designs is established. The designs use only v experimental units and (v − 1)/2 periods for v = 4t + 3 prime or prime power number of treatments; t being a positive integer. A special feature of the proposed designs is that ‘in...
In this paper, we discuss interval estimation for the common mean of several heterogeneous log-normal (LN) populations. The proposed procedure is based on a higher order likelihood method. The merits of our proposed method are numerically compared with other three methods with respect to their expected lengths and coverage probabilities. Numerical studies have shown that the coverage probabilities...
In this work the ranked set sampling technique has been applied to estimate the scale parameter $$\alpha $$ of a log-logistic distribution under a situation where the units in a sample can be ordered by judgement method without any error. We have evaluated the Fisher information contained in the order statistics arising from this distribution and observed that median of a random sample contains...
For longitudinal data, the within-subject covariance matrix plays an important role in statistical inference and it is of great interest to investigate this. In the paper, two kinds of estimators are investigated for the random effect covariance matrix D1 and the error variance σ2 in linear mixed models. One is to estimate D1 first and then to estimate σ2; the other kind is to estimate σ2 first...
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