In August 2019, public health surveillance systems in Scotland and England identified seven, geographically dispersed cases infected with the same strain (defined as isolates that fell within the same five single nucleotide polymorphism single linage cluster) of Shiga toxin-producing Escherichia coli O157:H7. Epidemiological analysis of enhanced surveillance questionnaire data identified handling raw beef and shopping from the same national retailer (retailer A) as the common exposure. Concurrently, a microbiological survey of minced beef at retail identified the same strain in a sample of minced beef sold by retailer A, providing microbiological evidence of the link. Between September and November 2019, a further four primary and two secondary cases infected with the same strain were identified; two cases developed haemolytic uraemic syndrome. None of the four primary cases reported consumption of beef from retailer A and the transmission route of these subsequent cases was not identified, although all four primary cases visited the same petting farm. Generally, outbreaks of STEC O157:H7 in the UK appear to be distinct, short-lived events; however, on-going transmission linked to contaminated food, animals or environmental exposures and person-to-person contact do occur. Although outbreaks of STEC caused by contaminated fresh produce are increasingly common, undercooked meat products remain a risk of infection.

In the auto insurance industry, a Bonus-Malus System (BMS) is commonly used as a posteriori risk classification mechanism to set the premium for the next contract period based on a policyholder's claim history. Even though the recent literature reports evidence of a significant dependence between frequency and severity, the current BMS practice is to use a frequency-based transition rule while ignoring severity information. Although Oh et al. [(2020). Bonus-Malus premiums under the dependent frequency-severity modeling. Scandinavian Actuarial Journal 2020(3): 172–195] claimed that the frequency-driven BMS transition rule can accommodate the dependence between frequency and severity, their proposal is only a partial solution, as the transition rule still completely ignores the claim severity and is unable to penalize large claims. In this study, we propose to use the BMS with a transition rule based on both frequency and size of claim, based on the bivariate random effect model, which conveniently allows dependence between frequency and severity. We analytically derive the optimal relativities under the proposed BMS framework and show that the proposed BMS outperforms the existing frequency-driven BMS. Later, numerical experiments are also provided using both hypothetical and actual datasets in order to assess the effect of various dependencies on the BMS risk classification and confirm our theoretical findings.

Medium frequency radars with multiple receivers are able to track the movement of the interference pattern on the ground from echoes from irregularities in refractive index. In particular, refractive index in the mesosphere is determined by electron density – commonly known as the ionospheric D-region. Thus using this technique it is possible to determine winds in the height regime 70-90 km, depending on the degree of ionization throughout the year. In addition, by examining the fading times of the passage of these structures, it is possible to deduce metrics pertaining to neutral air turbulence. Here, we employ a well-established method to this effect. Thereafter, comparing the turbulent intensity to the kinematic viscosity of the neutral atmosphere, we determine the turbopause altitude. Above this height, atmospheric constituents behave independently, whereas below, all components are mixed. Contrary to earlier analyses, we present evidence the turbopause altitude has been constant since approximately 2004.

The literature on stochastic programming typically restricts attention to problems that fulfill constraint qualifications. The literature on estimation and inference under partial identification frequently restricts the geometry of identified sets with diverse high-level assumptions. These superficially appear to be different approaches to closely related problems. We extensively analyze their relation. Among other things, we show that for partial identification through pure moment inequalities, numerous assumptions from the literature essentially coincide with the Mangasarian–Fromowitz constraint qualification. This clarifies the relation between well-known contributions, including within econometrics, and elucidates stringency, as well as ease of verification, of some high-level assumptions in seminal papers.

For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional estimation techniques can be seen as variable selection that leads to a smaller set of variables (a “submodel”) where classical linear regression applies. We analyze linear regression estimators resulting from model selection by proving estimation error and linear representation bounds uniformly over sets of submodels. Based on deterministic inequalities, our results provide “good” rates when applied to both independent and dependent data. These results are useful in meaningfully interpreting the linear regression estimator obtained after exploring and reducing the variables and also in justifying post-model-selection inference. All results are derived under no model assumptions and are nonasymptotic in nature.

Modeling policyholders’ lapse behaviors is important to a life insurer, since lapses affect pricing, reserving, profitability, liquidity, risk management, and the solvency of the insurer. In this paper, we apply two machine learning methods to lapse modeling. Then, we evaluate the performance of these two methods along with two popular statistical methods by means of statistical accuracy and profitability measure. Moreover, we adopt an innovative point of view on the lapse prediction problem that comes from churn management. We transform the classification problem into a regression question and then perform optimization, which is new to lapse risk management. We apply the aforementioned four methods to a large real-world insurance dataset. The results show that Extreme Gradient Boosting (XGBoost) and support vector machine outperform logistic regression (LR) and classification and regression tree with respect to statistic accuracy, while LR performs as well as XGBoost in terms of retention gains. This highlights the importance of a proper validation metric when comparing different methods. The optimization after the transformation brings out significant and consistent increases in economic gains. Therefore, the insurer should conduct optimization on its economic objective to achieve optimal lapse management.

We develop the first nonparametric significance test for regression models with classical measurement error in the regressors. In particular, a Cramér-von Mises test and a Kolmogorov–Smirnov test for the null hypothesis $E\left [Y|X^{*},Z^{*}\right ]=E\left [Y|X^{*}\right ]$ are proposed when only noisy measurements of $X^{*}$ and $Z^{*}$ are available. The asymptotic null distributions of the test statistics are derived, and a bootstrap method is implemented to obtain the critical values. Despite the test statistics being constructed using deconvolution estimators, we show that the test can detect a sequence of local alternatives converging to the null at the $\sqrt {n}$-rate. We also highlight the finite sample performance of the test through a Monte Carlo study.

This study examines identification and estimation in a correlated random coefficients (CRC) model with an unknown transformation of the dependent variable, namely $\lambda \left (Y^{*}\right)=B_{0}+X^{\prime }B$, where the latent outcome $Y^{*}$ may be subject to a certain kind of censoring mechanism, $\lambda (\cdot)$ is an unknown, one-to-one monotone function, and the random coefficients $\left (B_{0},B\right)$ are allowed to be correlated with one or several components of X. Under a conditional median independence plus a conditional median zero restriction, the mean of B is shown to be identified up to scale. Moreover, we show the derivative of the median structural function (MSF) is point identified. This derivative of MSF resembles the marginal treatment effect introduced by Heckman and Vytlacil (2005, Econometrica 73, 669–738).

It generalizes the usual average treatment effect in a linear CRC model and coincides with $E(B)$ when $\lambda $ is equal to the identity function; it is invariant to both location and scale normalization on the coefficients. We develop estimators for the identified parameters and derive asymptotic properties for the derivative of MSF. An empirical example using the U.K. Family Expenditure Survey is provided.

For an $N \times T$ random matrix $X(\beta )$ with weakly dependent uniformly sub-Gaussian entries $x_{it}(\beta )$ that may depend on a possibly infinite-dimensional parameter $\beta \in \mathbf {B}$, we obtain a uniform bound on its operator norm of the form $\mathbb {E} \sup _{\beta \in \mathbf {B}} ||X(\beta )|| \leq CK \left (\sqrt {\max (N,T)} + \gamma _2(\mathbf {B},d_{\mathbf {B}})\right )$, where C is an absolute constant, K controls the tail behavior of (the increments of) $x_{it}(\cdot )$, and $\gamma _2(\mathbf {B},d_{\mathbf {B}})$ is Talagrand’s functional, a measure of multiscale complexity of the metric space $(\mathbf {B},d_{\mathbf {B}})$. We illustrate how this result may be used for estimation that seeks to minimize the operator norm of moment conditions as well as for estimation of the maximal number of factors with functional data.

The weighted average quantile derivative (AQD) is the expected value of the partial derivative of the conditional quantile function (CQF) weighted by a function of the covariates. We consider two weighting functions: a known function chosen by researchers and the density function of the covariates that is parallel to the average mean derivative in Powell, Stock, and Stoker (1989, Econometrica 57, 1403–1430). The AQD summarizes the marginal response of the covariates on the CQF and defines a nonparametric quantile regression coefficient. In semiparametric single-index and partially linear models, the AQD identifies the coefficients up to scale. In nonparametric nonseparable structural models, the AQD conveys an average structural effect under certain independence assumptions. Including a stochastic trimming function, the proposed two-step estimator is root-n-consistent for the AQD defined by the entire support of the covariates. To facilitate tractable asymptotic analysis, a key preliminary result is a new Bahadur-type linear representation of the generalized inverse kernel-based CQF estimator uniformly over the covariates in an expanding compact set and over the quantile levels. The weak convergence to Gaussian processes applies to the differentiable nonlinear functionals of the quantile processes.

Antibiotic resistance (ABR) threatens the effectiveness of infectious disease treatments and contributes to increasing global morbidity and mortality. In this study, we systematically reviewed the identified risk factors for ABR among people in the healthcare system of mainland China. Five databases were systematically searched to identify relevant articles published in either English and Chinese between 1 January 2003 and 30 June 2019. A total of 176 facility-based references were reviewed for this study, ranging across 31 provinces in mainland China and reporting information from over 50 000 patients. Four major ABR risk factor domains were identified: (1) sociodemographic factors (includes migrant status, low income and urban residence), (2) patient clinical information (includes disease status and certain laboratory results), (3) admission to healthcare settings (includes length of hospitalisation and performance of invasive procedures) and (4) drug exposure (includes current or prior antibiotic therapy). ABR constitutes an ongoing major public health challenge in China. The healthcare sector-associated risk factors was the most important aspect identified in this review and need to be addressed. Primary health care system and ABR surveillance networks need to be further strengthened to prevent and control the communicable diseases, over-prescription and overuse of antibiotics.

This paper considers risk-sensitive average optimization for denumerable continuous-time Markov decision processes (CTMDPs), in which the transition and cost rates are allowed to be unbounded, and the policies can be randomized history dependent. We first derive the multiplicative dynamic programming principle and some new facts for risk-sensitive finite-horizon CTMDPs. Then, we establish the existence and uniqueness of a solution to the risk-sensitive average optimality equation (RS-AOE) through the results for risk-sensitive finite-horizon CTMDPs developed here, and also prove the existence of an optimal stationary policy via the RS-AOE. Furthermore, for the case of finite actions available at each state, we construct a sequence of models of finite-state CTMDPs with optimal stationary policies which can be obtained by a policy iteration algorithm in a finite number of iterations, and prove that an average optimal policy for the case of infinitely countable states can be approximated by those of the finite-state models. Finally, we illustrate the conditions and the iteration algorithm with an example.

In this paper we study a large system of N servers, each with capacity to process at most C simultaneous jobs; an incoming job is routed to a server if it has the lowest occupancy amongst d (out of N) randomly selected servers. A job that is routed to a server with no vacancy is assumed to be blocked and lost. Such randomized policies are referred to JSQ(d) (Join the Shortest Queue out of d) policies. Under the assumption that jobs arrive according to a Poisson process with rate $N\lambda^{(N)}$ where $\lambda^{(N)}=\sigma-\frac{\beta}{\sqrt{N}\,}$, $\sigma\in\mathbb{R}_+$ and $\beta\in\mathbb{R}$, we establish functional central limit theorems for the fluctuation process in both the transient and stationary regimes when service time distributions are exponential. In particular, we show that the limit is an Ornstein–Uhlenbeck process whose mean and variance depend on the mean field of the considered model. Using this, we obtain approximations to the blocking probabilities for large N, where we can precisely estimate the accuracy of first-order approximations.

Consider an urn containing balls labeled with integer values. Define a discrete-time random process by drawing two balls, one at a time and with replacement, and noting the labels. Add a new ball labeled with the sum of the two drawn labels. This model was introduced by Siegmund and Yakir (2005) Ann. Prob. 33, 2036 for labels taking values in a finite group, in which case the distribution defined by the urn converges to the uniform distribution on the group. For the urn of integers, the main result of this paper is an exponential limit law. The mean of the exponential is a random variable with distribution depending on the starting configuration. This is a novel urn model which combines multi-drawing and an infinite type of balls. The proof of convergence uses the contraction method for recursive distributional equations.

We consider a gradual-impulse control problem of continuous-time Markov decision processes, where the system performance is measured by the expectation of the exponential utility of the total cost. We show, under natural conditions on the system primitives, the existence of a deterministic stationary optimal policy out of a more general class of policies that allow multiple simultaneous impulses, randomized selection of impulses with random effects, and accumulation of jumps. After characterizing the value function using the optimality equation, we reduce the gradual-impulse control problem to an equivalent simple discrete-time Markov decision process, whose action space is the union of the sets of gradual and impulsive actions.

The performance and effectiveness of an age replacement policy can be assessed by its mean time to failure (MTTF) function. We develop shock model theory in different scenarios for classes of life distributions based on the MTTF function where the probabilities $\bar{P}_k$ of surviving the first k shocks are assumed to have discrete DMTTF, IMTTF and IDMTTF properties. The cumulative damage model of A-Hameed and Proschan [1] is studied in this context and analogous results are established. Weak convergence and moment convergence issues within the IDMTTF class of life distributions are explored. The preservation of the IDMTTF property under some basic reliability operations is also investigated. Finally we show that the intersection of IDMRL and IDMTTF classes contains the BFR family and establish results outlining the positions of various non-monotonic ageing classes in the hierarchy.

Pitman (2003), and subsequently Gnedin and Pitman (2006), showed that a large class of random partitions of the integers derived from a stable subordinator of index $\alpha\in(0,1)$ have infinite Gibbs (product) structure as a characterizing feature. The most notable case are random partitions derived from the two-parameter Poisson–Dirichlet distribution, $\textrm{PD}(\alpha,\theta)$, whose corresponding $\alpha$-diversity/local time have generalized Mittag–Leffler distributions, denoted by $\textrm{ML}(\alpha,\theta)$. Our aim in this work is to provide indications on the utility of the wider class of Gibbs partitions as it relates to a study of Riemann–Liouville fractional integrals and size-biased sampling, and in decompositions of special functions, and its potential use in the understanding of various constructions of more exotic processes. We provide characterizations of general laws associated with nested families of $\textrm{PD}(\alpha,\theta)$ mass partitions that are constructed from fragmentation operations described in Dong et al. (2014). These operations are known to be related in distribution to various constructions of discrete random trees/graphs in [n], and their scaling limits. A centerpiece of our work is results related to Mittag–Leffler functions, which play a key role in fractional calculus and are otherwise Laplace transforms of the $\textrm{ML}(\alpha,\theta)$ variables. Notably, this leads to an interpretation within the context of $\textrm{PD}(\alpha,\theta)$ laws conditioned on Poisson point process counts over intervals of scaled lengths of the $\alpha$-diversity.

In open Kelly and Jackson networks, servers are assigned to individual stations, serving customers only where they are assigned. We investigate the performance of modified networks where servers cooperate. A server who would be idle at the assigned station will serve customers at another station, speeding up service there. We assume interchangeable servers: the service rate of a server at a station depends only on the station, not the server. This gives work conservation, which is used in various ways. We investigate three levels of server cooperation, from full cooperation, where all servers are busy when there is work to do anywhere in the network, to one-way cooperation, where a server assigned to one station may assist a server at another, but not the converse. We obtain the same stability conditions for each level and, in a series of examples, obtain substantial performance improvement with server cooperation, even when stations before modification are moderately loaded.