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In the present investigation, a general set-up for inference from survey data that covers the estimation of variance of estimators of totals and distribution functions has been considered, using known first and second order moments of auxiliary information at the estimation stage. The traditional linear regression estimator of population total owed to Hansen et al. Sample survey methods and theory...
This paper considers a three-stage procedure which was proposed by Holm (1995) to yield a fixed-width confidence interval of the normal mean with a precise confidence level. The procedure is shown to be asymptotically second-order efficient. The procedure is also applied to such problems as bounded risk and hypothesis testing
M-estimators and M-kernel estimators with a redescending ψ-function are not in general consistent. This is often handled by means of coupling the estimator to a consistent one. Coupling the estimator to the (inconsistent) starting point improves the jump preserving properties. However, the consistency depends heavily on the shape of the density of the residuals. This paper shows inconsistency under...
We show that the recently developed non-parametric procedure for fitting the term structure of interest rates developed by Linton, Mammen, Nielsen, and Tanggaard (J Econ 105(1):185–223, 2001) overall performs notably better than the highly flexible McCulloch (J Finon 30:811–830, 1975) cubic spline and Fama and Bliss (Am Econ Rev 77:680–692, 1987) bootstrap methods. However, if interest is limited...
We consider the problem of estimating the scale parameter θ of the shifted exponential distribution with unknown shift based on a set of observed records drawn from a sequential sample of independent and identically distributed random variables. Under a large class of bowl-shaped loss functions, the best affine equivariant estimator (BAEE) of θ is shown to be inadmissible. Two dominating procedures...
A formula is presented for an unbiased estimator for the variance of an unbiased estimator of a survey population total as well as for an unbiased estimator of its variance based on sampling in two-stages following Rao et al. J Roy Stat Soc B 24: 482–491 (1962) scheme in both stages when the originally selected units in both stages cannot be fully covered in the survey but are to be randomly sub-sampled...
The paper deals with a method for the analysis of highly fractionated factorial designs proposed by Raghavarao and Altan in Metrika 58:185–191 (2003). We show that the method will find “active” factors with almost any set of random numbers. Once that an alias set is found active, Raghavarao and Altan claim that their method can resolve the alias structure of the design and identify which of several...
In the robustness framework, the parametric model underlying the data is usually embedded in a neighborhood of other plausible distributions. Accordingly, the asymptotic properties of robust estimates should be uniform over the whole set of possible models. In this paper, we study location M-estimates calculated with a previous generalized S-scale and show that, under some regularity conditions, they...
In this paper a sufficient condition for the identifiability of finite mixtures is given. This condition is less restrictive than Teicher’s condition Teicher H, Ann Math Stat 34:1265–1269 (1963) and therefore it can be applied to a wider range of families of mixtures. In particular, it applies to the classes of all finite mixtures of Log-gamma and of reversed Log-gamma distributions. These families...
Test procedures for detection of a change in the distribution of a sequence of independent observations based on empirical characteristic functions are developed and their limit properties are studied. Theoretical results are accompanied by a simulation study.
The present work develops a basic classification scheme for distortion in the framework of classical statistical inference. In particular, it emphasizes the still outstanding and consequent distinction between data contamination and model deviation. It is explored when different implications on the performance of statistical inference procedures under the two types of distortion are possible and how...
Generalized linear and nonlinear mixed-effects models are used extensively in biomedical, social, and agricultural sciences. The statistical analysis of these models is based on the asymptotic properties of the maximum likelihood estimator. However, it is usually assumed that the maximum likelihood estimator is consistent, without providing a proof. A rigorous proof of the consistency by verifying...
It is well known that in the case of independent random variables, the (reversed) hazard rate of the (maximum) minimum of two random variables is the sum of the individual (reversed) hazard rates and hence the onotonicity of the (reversed) hazard rate of the marginals is preserved by the monotonicity of the (reversed) hazard rate of the (maximum) minimum. However, for the bivariate distributions this...
The concept of desirability is a means for complexity reduction of multivariate quality optimization. This paper provides a theoretical breakthrough regarding desirability indices, which application fields were formerly limited primarily by the lack of its distribution. Focussed are the distributions of Harrington’s desirability functions and different types of the desirability index.
The role of uniformity measured by the centered L2-discrepancy (Hickernell 1998a) has been studied in fractional factorial designs. The issue of a lower bound for the centered L2-discrepancy is crucial in the construction of uniform designs. Fang and Mukerjee (2000) and Fang et al. (2002, 2003b) derived lower bounds for fractions of two- and three-level factorials. In this paper we report some new...
In this paper we investigate Hölder convergence of polygonal line process based on residuals of linear regression model. Bootstrap counterpart is also studied. Our results provide additional tools for testing epidemic type structural changes in regression models.
The discrepancy is an important optimality criterion for experimental designs. Sometimes for practical reasons one may choose a design on some finite subset of the original experimental domain. This article addresses the question of whether minimum discrepancy designs are the same for the discrepancy defined on the original experimental domain and the discrepancy defined on a subset. Under certain...
MM-estimators achieve simultaneous high efficiency and high breakdown point over contamination neighborhoods. Inference based on these estimators relies on their asymptotic properties, which have been studied for the case of random covariates. In this paper we show that, under relatively mild regularity conditions, MM-estimators for linear regression models are strongly consistent when the design...
Screening designs are useful for situations where a large number of factors are examined but only a few, k, of them are expected to be important. Traditionally orthogonal arrays such as Hadamard matrices and Plackett Burman designs have been studied for this purpose. It is therefore of practical interest for a given k to know all the classes of inequivalent projections of the design into the k dimensions...
In this paper we give a motivation for the shrinking rate $$1/ \sqrt{n}:$$ let p0 and qn be the outlier probability under the ideal model, and some member of a neighborhood about this ideal model of radius rn, respectively. Assuming n i.i.d. observations, the critical rate of rn may be defined such that the minimax test for outlier probability qn=p0 versus qn>p0 has asymptotic...
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