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In this paper estimation of the shape parameter of a Pareto distribution is considered under the a priori assumption that it is bounded below by a known constant. The loss function is scale invariant squared error. A class of minimax estimators is presented when the scale parameter of the distribution is known. In consequence, it has been shown that the generalized Bayes estimator with respect to...
In this paper, we study a general additive frailty model along with some special cases and examples. The monotonicity of the population hazard is investigated in comparison to the baseline hazard rate. Examples are provided where the unconditional failure rate turns out to be increasing or bathtub shaped even when the baseline hazard is increasing. Association measure, for the additive case, of the...
In this paper, we present several useful mixture representations for the reliability function of the inactivity time of systems with heterogeneous components based on order statistics, signatures and mean reliability functions. Some stochastic comparisons of inactivity times between two systems are discussed. These results form nice extensions of some existing results for the case when the components...
The varying coefficient models are very important tools to explore the hidden structure between the response variable and its predictors. However, variable selection and identification of varying coefficients of the models are poorly understood. In this paper, we develop a novel method to overcome these difficulties using local polynomial smoothing and the SCAD penalty. Under some regularity conditions,...
Though several interesting models for contingency tables are defined by a system of inequality constraints on a suitable set of marginal log-linear parameters, the specific features of the corresponding testing problems and the related procedures are not widely well known. After reviewing the most common difficulties which are intrinsic to inequality restricted testing problems, the paper concentrates...
Peer reviewing is the key ingredient of evaluating the quality of scientific work. Based on the review scores assigned by individual reviewers to papers, program committees of conferences and journal editors decide which papers to accept for publication and which to reject. A similar procedure is part of the selection process of grant applications and, among other fields, in sports. It is well known...
The objective of this paper is to study the issue of the generalized projection discrepancy along the line of Qin et al. (J Stat Plan Inference 142:1170–1177, 2012) based on generalized discrete discrepancy measure proposed by Chatterjee and Qin (J Stat Plan Inference 141:951–960, 2011). We shall study the projection properties for general asymmetric factorials and provide some analytic connections...
The concept of $$m$$ m -extended negatively dependent ( $$m$$ m -END, in short) random variables is introduced and the Kolmogorov exponential inequality for $$m$$ m -END random variables is established. As applications of the Kolmogorov exponential inequality, we further investigate the complete convergence for arrays of rowwise $$m$$ m -END random variables and the...
This paper addresses the problem of fitting a known distribution function to the marginal distribution of a stationary long memory moving average random field observed on increasing $$\nu $$ ν -dimensional “cubic” domains when its mean $$\mu $$ μ and scale $$\sigma $$ σ are known or unknown. Using two suitable estimators of $$\mu $$ μ and a classical estimate of...
We introduce a special correlation structure in the growth curve model, which can be viewed as a transition between the serial and the uniform correlation structure. Estimators of unknown variance parameters are derived.
In the present paper we derive lower asymptotic information bounds of Cramér-Rao type for estimators of nonparametric statistical functionals. The results are based on dense differentiability and dense regularity concepts which lead to weak assumptions. As explicit examples L-estimators are treated. In addition a new rapid method for the treatment of survival functionals under randomly right censored...
Two new tests for exponentiality, of integral- and Kolmogorov-type, are proposed. They are based on a recent characterization and formed using appropriate V-statistics. Their asymptotic properties are examined and their local Bahadur efficiencies against some common alternatives are found. A class of locally optimal alternatives for each test is obtained. The powers of these tests, for some small...
Let $$\left\{ X_{t},t\ge 1\right\} $$ X t , t ≥ 1 be a sequence of random variables with two possible values as either “1” (success) or “0” (failure). Define an independent sequence of random variables $$\left\{ D_{i},i\ge 1\right\} $$ D i , i ≥ 1 . The random variable $$D_{i}$$ D i is associated with the success when it occupies the ith place in a run of successes...
To overcome the drawbacks of Shannon’s entropy, the concept of cumulative residual and past entropy has been proposed in the information theoretic literature. Furthermore, the Shannon entropy has been generalized in a number of different ways by many researchers. One important extension is Kerridge inaccuracy measure. In the present communication we study the cumulative residual and past inaccuracy...
The problem of distribution function (df) estimation arises naturally in many contexts. The empirical and the kernel df estimators are well known. There is another df estimator based on a Bernstein polynomial of degree m. For a Bernstein df estimator, plays the same role as the bandwidth in a kernel estimator. The asymptotic properties of the Bernstein estimator has been studied so far assuming...
We improve a known result on the strong consistency of M-estimates of the regression parameters in a linear model for independent and identically distributed random errors under some mild conditions.
A broad class of local divergences between two probability measures or between the respective probability distributions is proposed in this paper. The introduced local divergences are based on the classic Csiszár $$\phi $$ ϕ -divergence and they provide with a pseudo-distance between two distributions on a specific area of their common domain. The range of values of the introduced class of...
In this paper EWMA control charts are introduced for detecting changes in the mean of a long-memory process. Besides the modified EWMA scheme the EWMA residual chart is also considered. The control design of the charts is calculated for an ARFIMA(p,d,q) process. In order to assess the introduced charts, the average run length is used as a performance criterion. Using an extensive simulation study,...
The small sample distribution of the trimmed mean is usually approximated by a Student’s t distribution. But this approximation is valid only when the observations come from a standard normal model and the sample size is not very small. Moreover, until now, there is only empirical justification for this approximation but no formal proof. Although there are some accurate saddlepoint approximations...
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