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This paper obtains some specific density functions for aggregated discounted claims where the claim amounts are dependent, or the inter-claim times are dependent, or the claim amounts and the claim arrival process are both dependent. The dependence is structured through mixing, and the claim arrival process studied is either an ordinary Poisson process or a mixed Poisson process. Closed form densities are obtained for gamma, generalized exponential, generalized Pareto and beta mixing, and an important use of them is illustrated.

This paper is concerned with inference of panel data varying-coefficient partially linear models with a one-way error structure. The model is a natural extension of the well-known panel data linear model (due to Baltagi 1995) to the setting of semiparametric regressions. The authors propose a weighted profile least squares estimator (WPLSE) and a weighted local polynomial estimator (WLPE) for the parametric and nonparametric components, respectively. It is shown that the WPLSE is asymptotically more efficient than the usual profile least squares estimator (PLSE), and that the WLPE is also asymptotically more efficient than the usual local polynomial estimator (LPE). The latter is an interesting result. According to Ruckstuhl, Welsh and Carroll (2000) and Lin and Carroll (2000), ignoring the correlation structure entirely and "pretending" that the data are really independent will result in more efficient estimators when estimating nonparametric regression with longitudinal or panel data. The result in this paper shows that this is not true when the design points of the nonparametric component have a closeness property within groups. The asymptotic properties of the proposed weighted estimators are derived. In addition, a block bootstrap test is proposed for the goodness of fit of models, which can accommodate the correlations within groups. Some simulation studies are conducted to illustrate the finite sample performances of the proposed procedures. [ABSTRACT FROM AUTHOR]

Abstract Consider a repeated measurement partially linear regression model with an unknown vector parameter ß1, an unknown function g(·), and unknown heteroscedastic error variances. In order to improve the semiparametric generalized least squares estimator (SGLSE) of ß, we propose an iterative weighted semiparametric least squares estimator (IWSLSE) and show that it improves upon the SGLSE in terms of asymptotic covariance matrix. An adaptive procedure is given to determine the number of iterations. We also show that when the number of replicates is less than or equal to two, the IWSLSE can not improve upon the SGLSE. These results are generalizations of those in [2] to the case of semiparametric regressions. [ABSTRACT FROM AUTHOR]

Consider a partially linear regression model with an unknown vector parameter Β, an unknown function g(·), and unknown heteroscedastic error variances. In this paper we develop an asymptotic semiparametric generalized least squares estimation theory under some weak moment conditions. These moment conditions are satisfied by many of the error distributions encountered in practice, and our theory does not require the number of replications to go to infinity. [ABSTRACT FROM AUTHOR]

Insight into the causes and consequences of changes in aquatic biodiversity requires an improved understanding of the nature of the relationships between species richness and ecosystem function over a much longer temporal perspective than we currently possess. We used high-resolution paleoecological records from two prairie lakes to show that diatom species richness (as fossil frustules) was negatively correlated (r² = 0.09-0.24, p < 0.001) with diatom production (as fossil pigments) during the past 2,000 yr. By comparing analyses from intervals of fresh and saline waters, we demonstrate that these significant richness-production relationships arose during freshwater periods (r² = 0.13-0.45, p < 0.001) and could be eliminated (r² < 0.02, p > 0.1) by abiotic disturbances such as droughts. Procrustes analyses of the concordance of species change within freshwater communities and the change in richness--production relationships through time revealed that shifts in diatom community composition could have a large influence in determining the negative relationship between richness and production. Finally, significant correlations (r² = 0.09-0.24, p < 0.0001) between past diatom species richness and ratios of stable isotopes (primarily δ15N) suggested that C and N biogeochemical cycles are also linked to changes in algal biodiversity. Taken together, these analyses suggest that the ongoing disruption of climate and biogeochemical systems by humans may obscure the relationship between aquatic biodiversity and ecosystem function in the future. [ABSTRACT FROM AUTHOR]

A lower-sided and an upper-sided exponentially weighted moving average (EWMA) chart for detecting mean changes (decreases and increases) in processes characterized by Weibull distributions are developed in this paper when censoring occurs at a fixed level. We show that the lower-sided EWMA chart performs better than its counterpart, the Shewhart-type; that a Shewhart-type chart is not appropriate to detect mean increases when the censoring rate is high; and that the upper-sided EWMA chart works well in detecting mean increases. [ABSTRACT FROM AUTHOR]

Consider a partially linear regression model with an unknown vector parameter ß, an unknown function g(·), and unknown heteroscedastic error variances. Chen, You [23] proposed a semiparametric generalized least squares estimator (SGLSE) for ß, which takes the heteroscedasticity into account to increase efficiency. For inference based on this SGLSE, it is necessary to construct a consistent estimator for its asymptotic covariance matrix. However, when there exists within-group correlation, the traditional delta method and the delete-1 jackknife estimation fail to offer such a consistent estimator. In this paper, by deleting grouped partial residuals a delete-group jackknife method is examined. It is shown that the delete-group jackknife method indeed can provide a consistent estimator for the asymptotic covariance matrix in the presence of within-group correlations. This result is an extension of that in [21]. [ABSTRACT FROM AUTHOR]

Consider the partly linear regression model % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D % aebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq % Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq % Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaca % WG5bWaaSbaaSqaaiaadMgaaeqaaOGaeyypa0JabmiEayaafaWaaSba % aSqaaiaadMgaaeqaaOGaeqOSdiMaey4kaSIaam4zamaabmaabaGaam % iDamaaBaaaleaacaWGPbaabeaaaOGaayjkaiaawMcaaiabgUcaRiab % ew7aLnaaBaaaleaacaWGPbaabeaakiaacYcacaaMe8UaaGjbVlaayI % W7caaIXaGaeyizImQaamyAaiabgsMiJkaad6gaaaa!53DA! $$ y_{i} = {x}''_{i} \beta + g{\left( {t_{i} } \right)} + \varepsilon _{i} ,\;\;{\kern 1pt} 1 \leqslant i \leqslant n $$ , where y i?s are responses, % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D % aebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq % Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq % Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaca % WG4bWaaSbaaSqaaiaadMgaaeqaaOGaeyypa0ZaaeWaaeaacaWG4bWa % aSbaaSqaaiaadMgacaaIXaaabeaakiaacYcacaWG4bWaaSbaaSqaai % aadMgacaaIYaaabeaakiaacYcacqWIVlctcaGGSaGaamiEamaaBaaa % leaacaWGPbGaamiCaaqabaaakiaawIcacaGLPaaadaahaaWcbeqaaO % Gamai4gkdiIcaacaaMe8UaaGjbVlaaysW7caqGHbGaaeOBaiaabsga % caaMe8UaaGjbVlaaysW7caWG0bWaaSbaaSqaaiaadMgaaeqaaOGaey % icI4Saamivaaaa!5D82! $$ x_{i} = {\left( {x_{{i1}} ,x_{{i2}} , \cdots ,x_{{ip}} } \right)}^{\prime } \;\;\;{\text{and}}\;\;\;t_{i} \in {\cal T} $$ are known and nonrandom design points, % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D % aebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq % Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq % Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaca % WGubaaaa!393B! $$ {\cal T} $$ is a compact set in the real line % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D % aebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq % Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq % Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaca % WGsbaaaa!3939! $$ {\cal R} $$ , ß = ( ß 1, ··· , ß p)? is an unknown parameter vector, g(·) is an unknown function and { e i} is a linear process, i.e., % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D % aebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq % Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq % Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacq % aH1oqzdaWgaaWcbaGaamyAaaqabaGccaaMi8Uaeyypa0JaaGjcVpaa % qahabaGaeqiYdK3aaSbaaSqaaiaadQgaaeqaaOGaamyzamaaBaaale % aacaWGPbGaeyOeI0IaamOAaaqabaGccaGGSaGaaGjcVlaaysW7cqaH % ipqEdaWgaaWcbaGaaGimaaqabaGccaaMi8Uaeyypa0JaaGjcVlaaig % dacaGGSaGaaGjbVlaayIW7daaeWbqaamaaemaabaGaeqiYdK3aaSba % aSqaaiaadQgaaeqaaaGccaGLhWUaayjcSdGaeyipaWJaeyOhIukale % aacaWGQbGaeyypa0JaaGimaaqaaiabg6HiLcqdcqGHris5aaWcbaGa % amOAaiabg2da9iaaicdaaeaacqGHEisPa0GaeyyeIuoaaaa!6ABD! $$ \varepsilon _{i} {\kern 1pt} = {\kern 1pt} {\sum\limits_{j = 0}^\infty {\psi _{j} e_{{i - j}} ,{\kern 1pt} \;\psi _{0} {\kern 1pt} = {\kern 1pt} 1,\;{\kern 1pt} {\sum\limits_{j = 0}^\infty {{\left| {\psi _{j} } \right|} < \infty } }} } $$ , where e j are i.i.d. random variables with zero mean and variance % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D % aebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq % Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq % Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacq % aHdpWCdaqhaaWcbaGaamyzaaqaaiaaikdaaaaaaa!3BF8! $$ \sigma ^{2}_{e} $$ . Drawing upon B-spline estimation of g(·) and least squares estimation of ß, we construct estimators of the autocovariances of { e i}. The uniform strong convergence rate of these estimators to their true values is then established. These results not only are a compensation for those of [23], but also have some application in modeling error structure. When the errors { e i} are an ARMA process, our result can be used to develop a consistent procedure for determining the order of the ARMA process and identifying the non-zero coeffcients of the process. Moreover, our result can be used to construct the asymptotically effcient estimators for parameters in the ARMA error process. [ABSTRACT FROM AUTHOR]

Proposes a chart for an improved monitoring of the p fraction. Two alternatives to the p chart; Guidelines for choosing an appropriate chart; Advantages of simple adjustments; Explanation of T.P. Ryan's rule of thumb.