Statistical Methodology最新文献

The odd Weibull distribution is a three-parameter generalization of the Weibull and the inverse Weibull distributions having rich density and hazard shapes for modeling lifetime data. This paper explored the odd Weibull parameter regions having finite moments and examined the relation to some well-known distributions based on skewness and kurtosis functions. The existence of maximum likelihood estimators have shown with complete data for any sample size. The proof for the uniqueness of these estimators is given only when the absolute value of the second shape parameter is between zero and one. Furthermore, elements of the Fisher information matrix are obtained based on complete data using a single integral representation which have shown to exist for any parameter values. The performance of the odd Weibull distribution over various density and hazard shapes is compared with generalized gamma distribution using two different test statistics. Finally, analysis of two data sets has been performed for illustrative purposes.

This paper is concerned with the estimation and inference for a threshold VECM with more than one cointegrating relation thus extending the literature in this context which has mostly considered only one cointegrating relationship so far. We then go on to develop an appropriate test for the number of cointegrating relationships in a threshold VECM. Asymptotic distributions of our test statistics are derived and tabulated. Finite sample performance of the proposed testing procedure is investigated.

A moment-based density approximation technique whereby the derivative of the logarithm of a density approximant is expressed as a rational function is introduced in this paper. Guidelines for the selection of the polynomial orders of the numerator and denominator are proposed. The coefficients are then determined by solving a system of linear equations. The resulting density approximation, referred to as a differentiated logdensity approximant or $\mathrm{DLA}$, satisfies a differential equation whose explicit solution is provided. It is shown that a unique solution exists when a polynomial is utilized in lieu of a rational function. The proposed methodology is successfully applied to two test statistics and several distributions. It is also explained that the same moment-matching technique can yield density estimates on the basis of sample moments. An example involving a widely analyzed data set illustrates this approach.

Nonconvex penalties (such as the smoothly clipped absolute deviation penalty and the minimax concave penalty) have some attractive properties including the unbiasedness, continuity and sparsity, and the ridge regression can deal with the collinearity problem. Combining the strengths of nonconvex penalties and ridge regression (abbreviated as NPR), we study the oracle selection property of the NPR estimator for high-dimensional partially linear additive models with highly correlated predictors, where the dimensionality of covariates $p_n$ is allowed to increase exponentially with the sample size $n$. Simulation studies and a real data analysis are carried out to show the performance of the NPR method.

We propose a new discrete distribution with finite support, which generalizes truncated Pareto and beta distributions as well as uniform and Benford’s laws. Although our focus is on basic properties and stochastic representations, we also consider parameter estimation and include an illustration from ecology showing potential applications of this new stochastic model.

Count data is abundant in entomology, more broadly, in statistical ecology. In 1949, Frank Anscombe pioneered the role of negative binomial (NB) modeling while working with insect count data. Since then, the spectrum of available research methods has grown immensely in more than past sixty years in involving count data modeled by a NB distribution. NB distribution also finds extensive use in agriculture, insect infestation, soil and weed science, etc. In this paper we have used a real dataset on potato beetle infestation (Beall, 1939) to illustrate smooth data collection under various sequential inferential procedures to draw important and practical conclusions.

We begin by selectively reviewing a majority of influential research methods for a number of formulations and their executions in the context of fixed-sample-size inferential procedures (Section  2). Subsequently, we elaborate on purely sequential and two-stage sampling methodologies for data collection (Sections  3 Sequential inferential problems: tests of hypotheses, 4 Sequential inferential problems: estimation). In Section  5, we summarize some major results with their interpretations including large-sample first- and second-order properties as appropriate. The illustrations of all the sequential inferential procedures on the real dataset gives interesting insights (Section  6). We also propose a number of selected directions for future research of substantial nature (Section  7). Finally, our own R codes are provided in the Appendix.

Tolerance intervals are enclosure intervals which will cover a fixed portion of the population distribution with a specified confidence. These intervals are widely used in clinical, environmental, biological and industrial applications, including quality control and environmental monitoring, to help determine limits for detection or assessment monitoring. In many of these applications the measurement of the variable of interest is costly and/or destructive but a small number of sampling units can be ranked easily by using expert-opinion knowledge or inexpensive and easily obtained measurements from these units. In this paper, we construct tolerance intervals based on the expensive measurements that are obtained using randomized nomination sampling (RNS) with the help of inexpensive auxiliary information. We study the performance of our proposed RNS-based tolerance intervals based on the corresponding coverage probabilities and the necessary sample size for their existence with those based on simple random sampling (SRS). The efficiency of the constructed RNS-based tolerance intervals compared to their SRS counterparts is discussed. We investigate the performance of RNS-based tolerance intervals for different values of the design parameters and various population shapes. We find the values of the design parameters which improve RNS over SRS. The RNS design in presence of ranking error is discussed and a new method for estimating ranking error probabilities is proposed. Theoretical results are augmented with numerical evaluations and a case study based on a fish mercury level dataset.

Motivated by seasonality and regime-switching features of some insurance claim counting processes, we study the statistical analysis of a Markov-modulated Poisson process featuring seasonality. We prove the strong consistency and the asymptotic normality of a maximum split-time likelihood estimator of the parameters of this model, and present an algorithm to compute it in practice. The method is illustrated on a small simulation study and a real data analysis.

We introduce a class of processes termed as filtered fractional Poisson processes (FFPP) and study their properties and give some applications of these to stochastic models. In addition, we study filtered fractional Levy processes (FFLP) as a generalization of these models.

In this paper, we consider concomitants of order statistics arising from the extended Farlie–Gumbel–Morgenstern bivariate logistic distribution and develop its distribution theory. Using ranked set sample obtained from the above distribution, unbiased estimators of the parameters associated with the study variate involved in it are generated. The best linear unbiased estimators (BLUEs) based on observations in the ranked set sample of those parameters as well have been derived. The efficiencies of the BLUEs relative to the respective unbiased estimators generated also have been evaluated.