A vector multivariate hazard rate

A vector definition of multivariate hazard rate, and associated definitions of increasing and decreasing multivariate hazard rate distributions are presented. Consequences of these definitions are worked out in a number of special cases. Relationships between hazard rate and orthant dependence are established.     

On a new multivariate IFR ageing notion based on the standard construction

Many criteria of ageing for random variables or vectors have been proposed in the literature over many years. For instance, a random variable is increasing in failure rate (IFR) if, and only if, it can be ordered with an exponentially distributed random variable in the classical univariate convex transform order. A new multivariate generalization of the convex transform order has recently been proposed in the literature. In this work, we propose a new multivariate IFR notion for multivariate distributions based on comparisons in this new order with a properly defined exponentially distributed random vector. Properties, applications, and illustrations of this new notion are given as well. Copyright © 2016 John Wiley & Sons, Ltd.     

A new class of multivariate counting processes and its characterization

In this paper, we suggest a new class of multivariate counting processes which generalizes and extends the multivariate generalized Polya process recently studied in Cha and Giorgio [On a class of multivariate counting processes, Adv. Appl. Probab. 48 (2016), pp. 443–462]. Initially, we define this multivariate counting process by means of mixing. For further characterization of it, we suggest an alternative definition, which facilitates convenient characterization of the proposed process. We also discuss the dependence structure of the proposed multivariate counting process and other stochastic properties such as the joint distributions of the number of events in an arbitrary interval or disjoint intervals and the conditional joint distribution of the arrival times of different types of events given the number of events. The corresponding marginal processes are also characterized.     

On a measure of multivariate skewness and a test for multivariate normality

Summary We consider an extension of Pearson measure of skewness to a multivariate case and apply the proposed measure to a test of multivariate normality.     

On generating multivariate Poisson data in management science applications

Generating multivariate Poisson random variables is essential in many applications, such as multi echelon supply chain systems, multi‐item/multi‐period pricing models, accident monitoring systems, etc. Current simulation methods suffer from limitations ranging from computational complexity to restrictions on the structure of the correlation matrix, and therefore are rarely used in management science. Instead, multivariate Poisson data are commonly approximated by either univariate Poisson or multivariate Normal data. However, these approximations are often not adequate in practice. In this paper, we propose a conceptually appealing correction for NORTA (NORmal To Anything) for generating multivariate Poisson data with a flexible correlation structure and rates. NORTA is based on simulating data from a multivariate Normal distribution and converting it into an arbitrary continuous distribution with a specific correlation matrix. We show that our method is both highly accurate and computationally efficient. We also show the managerial advantages of generating multivariate Poisson data over univariate Poisson or multivariate Normal data. Copyright © 2011 John Wiley & Sons, Ltd.     

Monitoring the mean of multivariate financial time series

Timely detection of changes in the mean vector of multivariate financial time series is of great practical importance. In this paper, the covariance dynamics of the multivariate stochastic processes is assessed by either the RiskMetrics approach, the constant conditional correlation, or the dynamic conditional correlation models. For online monitoring of mean changes, we introduce several control schemes based on exponential smoothing and cumulative sums, which explicitly account for heteroscedasticity. The detecting ability of the introduced charts is compared for different processes in a Monte Carlo simulation study. The empirical study illustrates monitoring of changes in the mean vector of daily returns of exchange rates. Copyright © 2013 John Wiley & Sons, Ltd.     

Some Classes of Multivariate Life Distributions in Discrete Time

New classes of multivariate survival distribution functions based on monotonic behaviour of a multivariate failure rate are developed in the discrete set up. Relationship among the classes along with multivariate geometric distributions that act as boundaries of the various classes are identified.     

Some extension of Haldane's multivariate median and its application

Summary Some extension of Haldane's multivariate median is carried out by minimization principle of a specified distance function. Then, making use of the median, three types of measures of multivariate skewness are introduced and their asymptotic null distributions are obtained.     

On some multivariate gamma-distributions connected with spanning trees

Any correlation matrixR can be mapped to a graph with edges corresponding to the non-vanishing correlations. In particularR is said to be of a tree type if the corresponding graph is a spanning tree. The tridiagonal correlation matrices belong to this class. If the accompanying correlation matrixR or its inverse is of a tree type, then some representations of the multivariate gamma distribution are obtained with a much simpler structure than the integral or series representations for the general case.     

Multivariate Exponential Distributions with Constant Failure Rates

In this paper a multivariate failure rate representation based on Cox's conditional failure rate is introduced, characterizations of the Freund–Block and the Marshall–Olkin multivariate exponential distributions are obtained, and generalizations of the Block–Basu and the Friday–Patil bivariate exponential distributions are proposed.     

Uncertainty principles for the right-sided multivariate continuous quaternion wavelet transform

ABSTRACT

In this paper, we present some new elements of harmonic analysis related to the right-sided multivariate continuous quaternion wavelet transform. The main objective of this article is to introduce the concept of the right-sided multivariate continuous quaternion wavelet transform and investigate its different properties using the machinery of multivariate quaternion Fourier transform. Last, we have proven a number of uncertainty principles for the right-sided multivariate continuous quaternion wavelet transform.     

Asymptotics for non-parametric likelihood estimation with doubly censored multivariate failure times

This paper considers non-parametric estimation of a multivariate failure time distribution function when only doubly censored data are available, which occurs in many situations such as epidemiological studies. In these situations, each of multivariate failure times of interest is defined as the elapsed time between an initial event and a subsequent event and the observations on both events can suffer censoring. As a consequence, the estimation of multivariate distribution is much more complicated than that for multivariate right- or interval-censored failure time data both theoretically and practically. For the problem, although several procedures have been proposed, they are only ad-hoc approaches as the asymptotic properties of the resulting estimates are basically unknown. We investigate both the consistency and the convergence rate of a commonly used non-parametric estimate and show that as the dimension of multivariate failure time increases or the number of censoring intervals of multivariate failure time decreases, the convergence rate for non-parametric estimate decreases, and is slower than that with multivariate singly right-censored or interval-censored data.     

Characterizations of multivariate life distributions

Characterizations of multivariate distributions has been a topic of great interest in applied statistics literature for the last three decades. In this paper, we develop characterizations of multivariate lifetime distributions by relationship between multivariate failure rates (reversed failure rates) and the left (right) truncated expectations of functions of random variables. We, then, discuss the application of the results to derive a multivariate Stein type identity.     

Decomposition and approximation of multivariate functions on the cube

In this paper, we present a decomposition method of multivariate functions. This method shows that any multivariate function f on [0, 1]d is a finite sum of the form ∑jφjψj , where each φj can be extended to a smooth periodic function, each ψj is an algebraic polynomial, and each φjψj is a product of separated variable type and its smoothness is same as f . Since any smooth periodic function can be approximated well by trigonometric polynomials, using our decomposition method, we find that any smooth multivariate function on [0, 1]d can be approximated well by a combination of algebraic polynomials and trigonometric polynomials. Meanwhile, we give a precise estimate of the approximation error.     

Forecasting mortality rate by multivariate singular spectrum analysis

In this paper, we investigate the possibility of using multivariate singular spectrum analysis (SSA), a nonparametric technique in the field of time series analysis, for mortality forecasting. We consider a real data application with 9 European countries: Belgium, Denmark, Finland, France, Italy, Netherlands, Norway, Sweden, and Switzerland, over a period 1900 to 2009, and a simulation study based on the data set. The results show the superiority of multivariate SSA in comparison with the univariate SSA, in terms of forecasting accuracy.     

A class of multivariate skew-normal models

The existing model for multivariate skew normal data does not cohere with the joint distribution of a random sample from a univariate skew normal distribution. This incoherence causes awkward interpretation for data analysis in practice, especially in the development of the sampling distribution theory. In this paper, we propose a refined model that is coherent with the joint distribution of the univariate skew normal random sample, for multivariate skew normal data. The proposed model extends and strengthens the multivariate skew model described in Azzalini (1985,Scandinavian Journal of Statistics,12, 171–178). We present a stochastic representation for the newly proposed model, and discuss a bivariate setting, which confirms that the newly proposed model is more plausible than the one given by Azzalini and Dalla Valle (1996,Biometrika,83, 715–726).     

A simple construction of optimal estimation in multivariate marginal Cox regression

The multivariate extension of the Cox model proposed by Wei,Lin and Weissfeld in 1989 has been widely used for analyzing multivariate survival data.Under the model assumption,failure times from an individual are assumed to marginally follow their respective proportional hazards regression relation,leaving the joint distribution completely unspecified.This paper presents a simple approach to efficiency improvement through segmentation of stochastic integrals in the marginal estimating equations and incorporation of the limiting covariance structure.It is shown that when partition of the time interval is done at a suitable rate,the resulting estimator is consistent and asymptotically normal.Through the reproducing kernel Hilbert space arising from the covariance function of the limiting Gaussian process,it is also shown that the proposed estimator is asymptotically optimal within a reasonable class of estimators under marginal specification.Simulations are conducted to assess the finite-sample performance of the proposed method.     

Detection of multiple change-points in multivariate time series

We consider the multiple change-point problem for multivariate time series, including strongly dependent processes, with an unknown number of change-points. We assume that the covariance structure of the series changes abruptly at some unknown common change-point times. The proposed adaptive method is able to detect changes in multivariate i.i.d., weakly and strongly dependent series. This adaptive method outperforms the Schwarz criteria, mainly for the case of weakly dependent data. We consider applications to multivariate series of daily stock indices returns and series generated by an artificial financial market. __________ Translated from Lietuvos Matematikos Rinkinys, Vol. 46, No. 3, pp. 351–376, July–September, 2006.     

A condition of Schoenberg-Whitney type for multivariate spline interpolation

Lagrange interpolation by finite-dimensional spaces of multivariate spline functions defined on a polyhedral regionK in ^k is studied. A condition of Schoenberg-Whitney type is introduced. The main result of this paper shows that this condition characterizes all configurationsT inK such that in every neighborhood ofT inK there must exist a configuration which admits unique Lagrange interpolation.     

Asymptotic optimality of multivariate linear hypothesis tests

The optimal exponential rate at which the Type II error probability of a multivariate linear hypothesis test can tend to zero while the Type I error probability is held fixed is given. The likelihood ratio test, the test of Hotelling and Lawley, the test of Bartlett, Nanda, and Pillai, and the test of Roy are shown to be asymptotically optimal in the sense that for each of these tests the exponential rate of convergence of the type II error probability attains the optimal value. Some other tests for the multivariate linear hypothesis are shown not to be asymptotically optimal.