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离散结果 Copula 回归模型的非参数估计AI 解读

Multivariate discrete outcomes are common in a wide range of areas including insurance, finance, and biology. When the interplay between outcomes is significant, quantifying dependencies among interrelated variables is of great importance. Due to their ability to accommodate dependence flexibly, copulas are being applied increasingly. Yet, the application of copulas on discrete data is still in its infancy; one of the biggest barriers is the nonuniqueness of copulas, calling…

用基尼指数概括保险评分AI 解读

Individuals, corporations and government entities regularly exchange financial risks y at prices Π. Comparing distributions of risks and prices can be difficult, particularly when the financial risk distribution is complex. For example, with insurance, it is not uncommon for a risk distribution to be a mixture of 0’s (corresponding to no claims) and a right-skewed distribution with thick tails (the claims distribution). However, analysts do not work in a vacuum, and in the…

线性纵向模型的影响诊断AI 解读

Influence diagnostics are important for analyzing cross-sectional regression studies, because they allow the analyst to understand the impact of individual observations on the estimated regression model. In this article we consider the role of influence diagnostics in subject-specific longitudinal models. Diagnostics are proposed under both fixed and random subject effects. Our approach is based on subject deletion, which in this setting involves deleting a group of…

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观测值函数的密度估计AI 解读

Density estimates, such as histograms and more sophisticated versions, are important in applied and theoretical statistics. In applied statistics, a density estimate gives the data analyst a graphical overview of the shape of the distribution. This overview allows the data analyst to arrive immediately at a qualitative impression of the location, scale, and various aspects of the extremes of the distribution. In theoretical statistics, the shape of the density allows the…

序贯设计实验后的估计AI 解读

We investigate the design of experiments for the nonparametric estimation of the root of an unknown regression function. Approaches to this problem include the Robbins-Monro (1951), Venter (1967), and Lai-Robbins (1979, 1981) stochastic approximation procedures and Wu's (1985, 1986) sequential maximum likelihood estimators. Because the regression function is not assumed to belong to a parametric family, only experimentation near to the root is informative and the sequential…

序贯设计实验后的估计AI 解读

We investigate the design of experiments for the nonparametric estimation of the root of an unknown regression function. Approaches to this problem include the Robbins-Monro (1951), Venter (1967), and Lai-Robbins (1979, 1981) stochastic approximation procedures and Wu's (1985, 1986) sequential maximum likelihood estimators. Because the regression function is not assumed to belong to a parametric family, only experimentation near to the root is informative and the sequential…

ABSTRACT This paper introduces an estimator of stock price volatility that eliminates, at least asymptotically, the biases that are caused by the discreteness of observed stock prices. Assuming that the observed stock prices are continuously monitored, an estimator is constructed using the notion of how quickly the price changes rather than how much the price changes. It is shown that this estimator has desirable asymptotic properties, including consistency and asymptotic…

The cost of certain types of warranties is closely related to functions that arise in renewal theory. The problem of estimating the warranty cost for a random sample of size n can be reduced to estimating these functions. In an earlier paper, I gave several methods of estimating the expected number of renewals, called the renewal function. This answered an important accounting question of how to arrive at a good approximation of the expected warranty cost. In this article,…

发现新物种概率的非参数估计AI 解读

A random sample is taken from a population consisting of an unknown number of distinct species. A quantity of interest is the probability of discovering a new species when an additional draw from the population is made. An estimator of this quantity was introduced by Starr (1979). We prove a conjecture of Starr's that the estimator is uniformly minimum variance unbiased and give various asymptotic properties of the estimator. A nonparametric maximum likelihood estimator that…

更新函数的非参数估计AI 解读

The renewal function is a basic tool used in many probabilistic models and sequential analysis. Based on a random sample of size $n$, a nonparametric estimator of the renewal function is introduced. Asymptotic properties of the estimator such as consistency and asymptotic normality are developed. A discussion of an application to warranty analysis is also provided.

序贯非参数年龄更换策略AI 解读

Under an age replacement policy, a stochastically failing unit is replaced at failure or after being in service for $t$ units of time, whichever comes first. An important problem is the estimation of $\phi^\ast,$ the optimal replacement time when the form of the failure distribution is unknown. Here, $\phi^\ast$ is optimal in the sense that it is the replacement time that achieves the smallest long-run expected cost. It is shown that substantial cost savings can be effected…