Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userDetection and Estimation of Local Signals
131
0
0.0
(
0
)
Added by
Xiao Fang
Publication date
2020
fields
Mathematical Statistics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
We study the maximum score statistic to detect and estimate local signals in the form of change-points in the level, slope, or other property of a sequence of observations, and to segment the sequence when there appear to be multiple changes. We find that when observations are serially dependent, the change-points can lead to upwardly biased estimates of autocorrelations, resulting in a sometimes serious loss of power. Examples involving temperature variations, the level of atmospheric greenhouse gases, suicide rates and daily incidence of COVID-19 illustrate the general theory.
rate research
Read More
A novel sequential change detection problem is proposed, in which the change should be not only detected but also accelerated. Specifically, it is assumed that the sequentially collected observations are responses to treatments selected in real time. The assigned treatments not only determine the pre-change and post-change distributions of the responses, but also influence when the change happens. The problem is to find a treatment assignment rule and a stopping rule that minimize the expected total number of observations subject to a user-specified bound on the false alarm probability. The optimal solution to this problem is obtained under a general Markovian change-point model. Moreover, an alternative procedure is proposed, whose applicability is not restricted to Markovian change-point models and whose design requires minimal computation. For a large class of change-point models, the proposed procedure is shown to achieve the optimal performance in an asymptotic sense. Finally, its performance is found in two simulation studies to be close to the optimal, uniformly with respect to the error probability.
In this paper, we study limiting laws and consistent estimation criteria for the extreme eigenvalues in a spiked covariance model of dimension $p$. Firstly, for fixed $p$, we propose a generalized estimation criterion that can consistently estimate, $k$, the number of spiked eigenvalues. Compared with the existing literature, we show that consistency can be achieved under weaker conditions on the penalty term. Next, allowing both $p$ and $k$ to diverge, we derive limiting distributions of the spiked sample eigenvalues using random matrix theory techniques. Notably, our results do not require the spiked eigenvalues to be uniformly bounded from above or tending to infinity, as have been assumed in the existing literature. Based on the above derived results, we formulate a generalized estimation criterion and show that it can consistently estimate $k$, while $k$ can be fixed or grow at an order of $k=o(n^{1/3})$. We further show that the results in our work continue to hold under a general population distribution without assuming normality. The efficacy of the proposed estimation criteria is illustrated through comparative simulation studies.
Additive models, as a natural generalization of linear regression, have played an important role in studying nonlinear relationships. Despite of a rich literature and many recent advances on the topic, the statistical inference problem in additive models is still relatively poorly understood. Motivated by the inference for the exposure effect and other applications, we tackle in this paper the statistical inference problem for $f_1(x_0)$ in additive models, where $f_1$ denotes the univariate function of interest and $f_1(x_0)$ denotes its first order derivative evaluated at a specific point $x_0$. The main challenge for this local inference problem is the understanding and control of the additional uncertainty due to the need of estimating other components in the additive model as nuisance functions. To address this, we propose a decorrelated local linear estimator, which is particularly useful in reducing the effect of the nuisance function estimation error on the estimation accuracy of $f_1(x_0)$. We establish the asymptotic limiting distribution for the proposed estimator and then construct confidence interval and hypothesis testing procedures for $f_1(x_0)$. The variance level of the proposed estimator is of the same order as that of the local least squares in nonparametric regression, or equivalently the additive model with one component, while the bias of the proposed estimator is jointly determined by the statistical accuracies in estimating the nuisance functions and the relationship between the variable of interest and the nuisance variables. The method is developed for general additive models and is demonstrated in the high-dimensional sparse setting.
Assuming that data are collected sequentially from independent streams, we consider the simultaneous testing of multiple binary hypotheses under two general setups; when the number of signals (correct alternatives) is known in advance, and when we only have a lower and an upper bound for it. In each of these setups, we propose feasible procedures that control, without any distributional assumptions, the familywise error probabilities of both type I and type II below given, user-specified levels. Then, in the case of i.i.d. observations in each stream, we show that the proposed procedures achieve the optimal expected sample size, under every possible signal configuration, asymptotically as the two error probabilities vanish at arbitrary rates. A simulation study is presented in a completely symmetric case and supports insights obtained from our asymptotic results, such as the fact that knowledge of the exact number of signals roughly halves the expected number of observations compared to the case of no prior information.
We study nonparametric maximum likelihood estimation of a log-concave probability density and its distribution and hazard function. Some general properties of these estimators are derived from two characterizations. It is shown that the rate of convergence with respect to supremum norm on a compact interval for the density and hazard rate estimator is at least $(log(n)/n)^{1/3}$ and typically $(log(n)/n)^{2/5}$, whereas the difference between the empirical and estimated distribution function vanishes with rate $o_{mathrm{p}}(n^{-1/2})$ under certain regularity assumptions.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
