Lack-of-fit testing of a regression model with response missing at random

This paper proposes a class of lack-of-fit tests for fitting a linear regression model when some response variables are missing at random. These tests are based on a class of minimum integrated square distances between a kernel type estimator of a regression function and the parametric regression function being fitted. These tests are shown to be consistent against a large class of fixed alternatives. The corresponding test statistics are shown to have asymptotic normal distributions under null hypothesis and a class of nonparametric local alternatives. Some simulation results are also presented.     

A class of distributions with the linear mean residual quantile function and it’s generalizations

In the present paper, we introduce and study a class of distributions that has the linear mean residual quantile function. Various distributional properties and reliability characteristics of the class are studied. Some characterizations of the class of distributions are presented. We then present generalizations of this class of distributions using the relationship between various quantile based reliability measures. The method of L-moments is employed to estimate parameters of the class of distributions. Finally, we apply the proposed class of distributions to a real data set.     

A Class of Distributions with Linear Hazard Quantile Function

In this article, we introduce and study a class of distributions that has linear hazard quantile function. Various distributional properties and reliability characteristics of the class are studied. Some characterizations of the class of distributions are presented. The method of L-moments is employed to estimate parameters of the class of distributions. Finally, we apply the proposed class to a real data set.     

A software reliability model using mean residual quantile function

In this paper, we propose a class of distributions with the inverse linear mean residual quantile function. The distributional properties of the family of distributions are studied. We then discuss the reliability characteristics of the family of distributions. Some characterizations of the class of distributions are also discussed. The parameters of the class of distributions are estimated using the method of L-moments. The proposed class of distributions is applied to a real data set.     

Stochastic ordering and a class of multivariate new better than used distributions

A new characterization for the univariate class of new better than used ‘NBU’ distributions in terms of stochastic ordering is introduced. A multivariate version of this characterization is then used to define a multivariate class of NBU distributions. Basic properties of this class are derived. Comparisons and relationships of this new class with earlier classes are developed. Two multivariate new worse than used (NWU) classes of life distributions are defined and compared and their basic properties are studied.     

U-Statistics and Their Asymptotic Results for Some Inequality and Poverty Measures

U-statistics form a general class of statistics that have certain important features in common. This class arises as a generalization of the sample mean and the sample variance, and typically members of the class are asymptotically normal with good consistency properties. The class encompasses some widely used income inequality and poverty measures, in particular the variance, the Gini index, the poverty rate, the average poverty gap ratios, the Foster-Greer-Thorbecke index, and the Sen index and its modified form. This paper illustrates how these measures come together within the class of U-statistics, and thereby why U-statistics are useful in econometrics.     

Finite Population Variance Estimation in Presence of Measurement Errors

In this article, we propose a class of estimators for the population variance of a quantity of interest. The estimators in the class use auxiliary information to improve efficiency, and we suppose that measurement errors are present both in the study and auxiliary variate. We take into account such problem using a regression approach. We show that the class proposed is quite flexible and general, allowing to consider many kinds of information as auxiliary one. Comparisons within estimators in the class are studied theoretically and through simulations.     

Semi-Parametric Density Estimation for Time-Series with Multiplicative Adjustment

In this article, we extend a class of semi-parametric density estimators to time-series context. The asymptotic theory and simulation study are discussed. Theoretical results and numerical comparison show that in the time-series case, the estimators in this class are better than, or at least competitive with, the traditional kernel density estimator in a broad class of densities.     

On the Ratio of Two Folded Normal Distributions

A class of distributions associated with the ratio of two folded normal random variables is introduced which strictly includes the half standard Cauchy distribution. The properties of this class of distributions are studied, along with a graph of the possible shapes of its density functions. The salient features of this class are mathematical tractability and statistical applicability. Utility of the class of distributions is demonstrated by presenting four applications.     

A class of modified stein estimators with easily computable risk functions

Consider the problem of estimating the mean of a p (≥3)-variate multi-normal distribution with identity variance-covariance matrix and with unweighted sum of squared error loss. A class of minimax, noncomparable (i.e. no estimate in the class dominates any other estimate in the class) estimates is proposed; the class contains rules dominating the simple James-Stein estimates. The estimates are essentially smoothed versions of the scaled, truncated James-Stein estimates studied by Efron and Morris. Explicit and analytically tractable expressions for their risks are obtained and are used to give guidelines for selecting estimates within the class.     

The compound class of linear failure rate-power series distributions: Model,properties, and applications

In this article, a new class of distributions is introduced, which generalizes the linear failure rate distribution and is obtained by compounding this distribution and power series class of distributions. This new class of distributions is called the linear failure rate-power series distributions and contains some new distributions such as linear failure rate-geometric, linear failure rate-Poisson, linear failure rate-logarithmic, linear failure rate-binomial distributions, and Rayleigh-power series class of distributions. Some former works such as exponential-power series class of distributions, exponential-geometric, exponential-Poisson, and exponential-logarithmic distributions are special cases of the new proposed model. The ability of the linear failure rate-power series class of distributions is in covering five possible hazard rate function, that is, increasing, decreasing, upside-down bathtub (unimodal), bathtub and increasing-decreasing-increasing shaped. Several properties of this class of distributions such as moments, maximum likelihood estimation procedure via an EM-algorithm and inference for a large sample, are discussed in this article. In order to show the flexibility and potentiality, the fitted results of the new class of distributions and some of its submodels are compared using two real datasets.     

U-Statistics and Their Asymptotic Results for Some Inequality and Poverty Measures

U-statistics form a general class of statistics that have certain important features in common. This class arises as a generalization of the sample mean and the sample variance, and typically members of the class are asymptotically normal with good consistency properties. The class encompasses some widely used income inequality and poverty measures, in particular the variance, the Gini index, the poverty rate, the average poverty gap ratios, the Foster-Greer-Thorbecke index, and the Sen index and its modified form. This paper illustrates how these measures come together within the class of U-statistics, and thereby why U-statistics are useful in econometrics.     

A General Class of Distributions: Properties and Applications

ABSTRACT

In this article, we derive a general class of distributions and establish its relationship to χ² distribution. The proposed class includes normal, inverse Gaussian, lognormal, gamma, Rayleigh, and Maxwell distributions. Various statistical properties of the class are discussed. Some applications of the class are given.     

Optimal goodness-of-fit tests for recurrent event data

A class of tests for the hypothesis that the baseline intensity belongs to a parametric class of intensities is given in the recurrent event setting. Asymptotic properties of a weighted general class of processes that compare the non-parametric versus parametric estimators for the cumulative intensity are presented. These results are given for a sequence of Pitman alternatives. Test statistics are proposed and methods of obtaining critical values are examined. Optimal choices for the weight function are given for a class of chi-squared tests. Based on Khmaladze’s transformation we propose distributional free tests. These include the types of Kolmogorov–Smirnov and Cramér–von Mises. The tests are used to analyze two different data sets.     

EWMA charts: ARL considerations in case of changes in location and scale

Widely spread tools within the area of Statistical Process Control are control charts of various designs. Control chart applications are used to keep process parameters (e.g., mean \(\mu \) , standard deviation \(\sigma \) or percent defective \(p\) ) under surveillance so that a certain level of process quality can be assured. Well-established schemes such as exponentially weighted moving average charts (EWMA), cumulative sum charts or the classical Shewhart charts are frequently treated in theory and practice. Since Shewhart introduced a \(p\) chart (for attribute data), the question of controlling the percent defective was rarely a subject of an analysis, while several extensions were made using more advanced schemes (e.g., EWMA) to monitor effects on parameter deteriorations. Here, performance comparisons between a newly designed EWMA \(p\) control chart for application to continuous types of data, \(p=f(\mu ,\sigma )\) , and popular EWMA designs ( \(\bar{X}\) , \(\bar{X}\) - \(S^2\) ) are presented. Thus, isolines of the average run length are introduced for each scheme taking both changes in mean and standard deviation into account. Adequate extensions of the classical EWMA designs are used to make these specific comparisons feasible. The results presented are computed by using numerical methods.     

New class of location-parameter discrete probability distributions and their characterizations

A new class of location-parameter discrete probability distributions (LDPD) has been defined where the population mean is the location parameter. It has been shown that some single parameter discrete distributions do not belong to this class and all discrete probability distributions belonging to this class can be characterized by their variances only. Expressions are given for the first four central moments and a recurrence formula for higher central moments has been obtained. Eight theorems are given to characterize the various distributions in the LDPD class.     

The Ornstein-Uhlenbeck Dirichlet process and other time-varying processes for Bayesian nonparametric inference

This paper introduces a new class of time-varying, measure-valued stochastic processes for Bayesian nonparametric inference. The class of priors is constructed by normalising a stochastic process derived from non-Gaussian Ornstein-Uhlenbeck processes and generalises the class of normalised random measures with independent increments from static problems. Some properties of the normalised measure are investigated. A particle filter and MCMC schemes are described for inference. The methods are applied to an example in the modelling of financial data.     

The estimation for Lévy processes in high frequency data

In this article, a generalized Lévy model is proposed and its parameters are estimated in high-frequency data settings. An infinitesimal generator of Lévy processes is used to study the asymptotic properties of the drift and volatility estimators. They are consistent asymptotically and are independent of other parameters making them better than those in Chen et al. (2010 Chen, S. X., Delaigle, A., Hall, P. (2010). Nonparametric estimation for a class of Lévy processes. Journal of Econometrics 157:257–271.[Crossref], [Web of Science ®] , [Google Scholar]). The estimators proposed here also have fast convergence rates and are simple to implement.     

A class of weighted multivariate elliptical models useful for robust analysis of nonnormal and bimodal data

A class of weighted elliptical models useful for analyzing nonnormal and bimodal multivariate data is introduced. It is obtained from the marginal distribution of a centrally truncated multivariate elliptical distribution. As a special case, a finite mixture of weighted multinormal distribution is examined in detail, establishing connections with the multinormal and the finite mixture of multinormal. The special class of distributions is studied from several aspects such as weighting of probability density functions, association with centrally truncated distributions, and a finite scale mixture scheme. The relationships among these aspects are given, and various properties of the class are also discussed. For the inference of the class, an MCMC procedure and its numerical example are provided.     

Complex elliptically symmetric distributions

In this paper, the authors introduce a class of distributions known as complex elliptically symmetric distributions. The complex multivariate normal and complex multivariate t distributions are members of this class. Various properties of the complex elliptically symmetric distributions are studied. Finally, the robustness of certain test procedures are discussed when the assumption of complex multivariate normality is violated but the underlying distribution still belongs to the class of elliptically symmetric distributions.