General results of complete convergence and complete moment convergence for weighted sums of some class of random variables

ABSTRACT

In the article, the complete convergence and complete moment convergence for weighted sums of sequences of random variables satisfying a maximal Rosenthal type inequality are studied. As an application, the Marcinkiewicz–Zygmund type strong law of large numbers is obtained. Our partial results generalize and improve the corresponding ones of Shen (2013 Shen, A.T. (2013). On strong convergence for weighted sums of a class of random variables. Abstr. Appl. Anal.2013, Article ID 216236: 1–7. [Google Scholar]).     

A note on the estimation of pr{y<x} for truncation parameter distributions

In this note a relationship in the treatment of the lower and upper truncations considered in Beg (1980) is pointed out and the minimum variance unbiased estimator of P = Pr{Y<X) for the (upper) truncated exponential distribution is obtained.     

Estimation of pr{y<x) for truncation parameter distributions

Blackwell-Rao-Lehmann-Scheffe theory is used to derive the minimum variance ur biased estimator of P=Pr{Y<X} when the independent random variables X and Y follow thf truncation parameter distributions The two-parameter exponential, Pareto, power function and uniform distributions are considered in examples.     

A test of simultaneous homogeneity against ordered alternatives in multifactorial design

A test of simultaneous homogeneity of main effects of several factors against an alternative hypothesis with simple order restrictions in main effects of more than one factor in a multifactorial design is considered. This can be regarded as an extension of Shorack's (1967) work where the alternative hypo t hqaLs involves simple order restriction in main effects of one faetor. We derive the likelihood ratio test statistic, E^-2 , and its null hypothesis distribution which involves the convolutions of PIrobabilities P(l,k) used in the statistical inference under order restriction , The powers of the E^-2 test and the usual F test are compar-ed by simulation.     

Distribution of sample mean when observations are correlated

It i s well known that even if the sample observations are correlated and not normal, the sample mean is normal in 1arge samples. But how large is large? This question i s investigated in this paper. In particular , the relation between the rate of convergence and the correlation property of the observations i s explored. It i s observed that the correlation, in general, retards the rate of convergence.     

Estimation of the number of jumps of the jump regression functions

This paper suggests an estimator of the number of jumps of the jump regression functions. The estimator is based on the difference between right and left onesided kernel smoothers. It is proved to be a.s. consistent. Some results about its rate of convergence are also provided.     

Convergence rates for empirical bayes estimators of parameters in multi-parameter exponential families

This paper obtains the convergence rates of the empirical Bayes estimators of parameters in the multi-parameter exponential families. The rates can approximate to 0(n=¹) arbitrarily. The paper presents the multivariate orthogonal polynomials which are continuous on the total space R^p.     

Darling–Erdős limit results for change-point detection in panel data

We wish to test the null hypothesis if the means of N panels remain the same during the observation period of length T. A quasi-likelihood argument leads to self-normalized statistics whose limit distribution under the null hypothesis is double exponential. The main results are derived assuming that the each panel is based on independent observations and then extended to linear processes. The proofs are based on an approximation of the sum of squared CUSUM processes using the Skorokhod embedding scheme. A simulation study illustrates that our results can be used in case of small and moderate N and T. We apply our results to detect change in the “corruption index”.     

Forecasting With Bayesian Vector Autoregressions—Five Years of Experience

The results obtained in five years of forecasting with Bayesian vector autoregressions (BVAR's) demonstrate that this inexpensive, reproducible statistical technique is as accurate, on average, as those used by the best known commercial forecasting services. This article considers the problem of economic forecasting, the justification for the Bayesian approach, its implementation, and the performance of one small BVAR model over the past five years.     

Testing for a Unit Root in a Time Series With a Changing Mean

This study considers testing for a unit root in a time series characterized by a structural change in its mean level. My approach follows the “intervention analysis” of Box and Tiao (1975) in the sense that I consider the change as being exogenous and as occurring at a known date. Standard unit-root tests are shown to be biased toward nonrejection of the hypothesis of a unit root when the full sample is used. Since tests using split sample regressions usually have low power, I design test statistics that allow the presence of a change in the mean of the series under both the null and alternative hypotheses. The limiting distribution of the statistics is derived and tabulated under the null hypothesis of a unit root. My analysis is illustrated by considering the behavior of various univariate time series for which the unit-root hypothesis has been advanced in the literature. This study complements that of Perron (1989), which considered time series with trends.