This paper addresses the following classical question: giving a sequence of identically distributed random variables in the domain of attraction of a normal law, does the associated linear process ...satisfy the central limit theorem? We study the question for several classes of dependent random variables. For independent and identically distributed random variables we show that the central limit theorem for the linear process is equivalent to the fact that the variables are in the domain of attraction of a normal law, answering in this way an open problem in the literature. The study is also motivated by models arising in economic applications where often the innovations have infinite variance, coefficients are not absolutely summable, and the innovations are dependent.
It is shown that the variable bandwidth density estimator proposed by McKay (1993a and b) following earlier findings by Abramson (1982) approximates density functions in \(C^4(\mathbb R^d)\) at the ...minimax rate in the supremum norm over bounded sets where the preliminary density estimates on which they are based are bounded away from zero. A somewhat more complicated estimator proposed by Jones McKay and Hu (1994) to approximate densities in \(C^6(\mathbb R)\) is also shown to attain minimax rates in sup norm over the same kind of sets. These estimators are strict probability densities.
It is shown that the Hall, Hu and Marron Hall, P., Hu, T., and Marron J.S. (1995), Improved Variable Window Kernel Estimates of Probability Densities, {\it Annals of Statistics}, 23, 1--10 ...modification of Abramson's Abramson, I. (1982), On Bandwidth Variation in Kernel Estimates - A Square-root Law, {\it Annals of Statistics}, 10, 1217--1223 variable bandwidth kernel density estimator satisfies the optimal asymptotic properties for estimating densities with four uniformly continuous derivatives, uniformly on bounded sets where the preliminary estimator of the density is bounded away from zero.
Renz (Ann. Probab. 1996) has established a rate of convergence \(1/\sqrt{n}\) in the central limit theorem for martingales with some restrictive conditions. In the present paper a modification of the ...methods, developed by Bolthausen (Ann. Probab. 1982) and Grama and Haeusler (Stochastic Process. Appl. 2000), is applied for obtaining the same convergence rate for a class of more general martingales. An application to linear processes is discussed.
We study a rank based univariate two-sample distribution-free test. The test statistic is the difference between the average of between-group rank distances and the average of within-group rank ...distances. This test statistic is closely related to the two-sample Cramér-von Mises criterion. They are different empirical versions of a same quantity for testing the equality of two population distributions. Although they may be different for finite samples, they share the same expected value, variance and asymptotic properties. The advantage of the new rank based test over the classical one is its ease to generalize to the multivariate case. Rather than using the empirical process approach, we provide a different easier proof, bringing in a different perspective and insight. In particular, we apply the Hájek projection and orthogonal decomposition technique in deriving the asymptotics of the proposed rank based statistic. A numerical study compares power performance of the rank formulation test with other commonly-used nonparametric tests and recommendations on those tests are provided. Lastly, we propose a multivariate extension of the test based on the spatial rank.
The United States Department of Agriculture's National Agricultural Statistics Service (NASS) conducts the June Agricultural Survey (JAS) annually. Substantial misclassification occurs during the ...pre-screening process and from field-estimating farm status for non-response and inaccessible records, resulting in a biased estimate of the number of US farms from the JAS. Here the Annual Land Utilization Survey (ALUS) is proposed as a follow-on survey to the JAS to adjust the estimates of the number of US farms and other important variables. A three-phase survey design-based estimator is developed for the JAS-ALUS with non-response adjustment for the second phase (ALUS). A design-unbiased estimator of the variance is provided in explicit form.
Large and moderate deviation probabilities play an important role in many applied areas, such as insurance and risk analysis. This paper studies the exact moderate and large deviation asymptotics in ...non-logarithmic form for linear processes with independent innovations. The linear processes we analyze are general and therefore they include the long memory case. We give an asymptotic representation for probability of the tail of the normalized sums and specify the zones in which it can be approximated either by a standard normal distribution or by the marginal distribution of the innovation process. The results are then applied to regression estimates, moving averages, fractionally integrated processes, linear processes with regularly varying exponents and functions of linear processes. We also consider the computation of value at risk and expected shortfall, fundamental quantities in risk theory and finance.
Each year, the National Agricultural Statistics Service (NASS) publishes an estimate of the number of farms in the United States based on the June Area Survey (JAS). Independent studies showed that ...the JAS number of farm indications have significant undercount due to misclassification. To adjust for this undercount, a follow-on survey to the JAS called the Annual Land Utilization Survey (ALUS) has been proposed. ALUS is designed and developed based on the Farm Numbers Research Project (FNRP). NASS conducted the FNRP in the fall of 2009 (Abreu, McCarthy and Colburn, 2010). ALUS samples from all JAS segments containing any estimated or non-agricultural JAS tracts. For a selected segment, all estimated and non-agricultural JAS tracts will be re-evaluated. The collection of eligible segments in a particular year will be called the ALUS population. The sample allocation of ALUS segments to each state-stratum combination considers two factors: the proportion of the ALUS population in the stratum and the proportion of the FNRP adjustment from non-agricultural tracts in the stratum. ALUS can be treated as a second phase to the JAS. The two-phase stratified design, JAS-ALUS, can be applied to any estimate produced by the JAS. However, ALUS has non-response. In this paper, methodology for a three-phase sampling design is developed by extending the two-phase sampling design methodology proposed by Sarndal and Swensson (1987). A general sampling design is allowed in each phase; that is, the inclusion probabilities in each phase are arbitrary. The estimator is unbiased, and an unbiased estimator for the variance is provided. Here, this method is applied to the two-phase JAS-ALUS with the third phase being response/non-response.
During the past three years, the National Agricultural Statistics Service (NASS) has made an effort to address, quantify, and adjust for an undercount in the number of farms indication from its ...annual June Area Survey (JAS), which is based on an area frame. This undercount is a direct result of the misclassification of agricultural tracts as non-agricultural. The 2007 Census of Agriculture mailing list (CML) was evaluated as a potential source to assess misclassification on the 2007 JAS. The CML was found to be a rich source from which to quantify the undercount of farms on the JAS. However, the CML is only available every five years, and misclassification on the JAS should be assessed each year. Independently of the area frame, NASS maintains a list of agricultural operators, referred to as the list frame. Yearly list-based samples are selected from the list frame. In addition, the list frame serves as the foundation for building the CML. The list frame is updated on an on-going basis and operators are categorized as either active or inactive. Although the CML includes all active records, some of these do not qualify as farming operations. This research report explores the potential of using the list frame on a yearly basis to assess the misclassification of farms on the JAS.
•4-PBA protects LPS-induced acute lung injury and inflammation in mouse model.•4-PBA decreases the levels of ER stress and autophagy induced by LPS in vivo and in vitro.•Inhibition of autophagy by ...3-MA aggravates cell injury induced by LPS, ER stress-associated autophagy may play a protective effect in LPS-induced lung injury.
Acute lung injury (ALI) is a common clinical disorder that causes substantial health problems worldwide. An excessive inflammatory response is the central feature of ALI, but the mechanism is still unclear, especially the role of endoplasmic-reticulum (ER) stress and autophagy. To identify the cellular mechanism of lung inflammation during lipopolysaccharide (LPS)-induced mouse model of ALI, we investigated the influence of classic ER stress inhibitor 4-phenyl butyric acid (4-PBA) on ER stress and autophagy, which partially affect the activation of inflammation, both in LPS-induced ALI mouse model and human alveolar epithelial cell model. We demonstrated that 4-PBA, which further prevented the activation of the NF-κB pathway, decreased the release of the pro-inflammatory mediators IL-1β, TNF-α and IL-6, significantly inhibited LPS-activated ER stress. Moreover, it was found that autophagy was also decreased by the treatment of 4-PBA, which may play a protective role in ALI models through the classical AKT/mTOR signaling pathway. Inhibition of autophagy by 3-MA exacerbates cytotoxicity induced by LPS in A549 alveolar epithelial cells. Taken together, our study indicated that ER stress is a key promoter in the induction of inflammation by LPS, the protective effect of 4-PBA is related to the inhibition of ER stress and autophagy in LPS-induced ALI models. Furthermore, the role of autophagy that contributes to cell survival may depend on the activation of ER stress.
