相关论文: Exact and asymptotic properties of $\delta$-record…
We consider records and sequences of records drawn from discrete time series of the form $X_{n}=Y_{n}+cn$, where the $Y_{n}$ are independent and identically distributed random variables and $c$ is a constant drift. For very small and very…
This paper focuses on nonparametric statistical inference of the hazard rate function of discrete distributions based on $\delta$-record data. We derive the explicit expression of the maximum likelihood estimator and determine its exact…
Let $\{X_n,n\ge1\}$ be a sequence of independent and identically distributed random variables, taking non-negative integer values, and call $X_n$ a $\delta$-record if $X_n>\max\{X_1,...,X_{n-1}\}+\delta$, where $\delta$ is an integer…
The statistics of records in sequences of independent, identically distributed random variables is a classic subject of study. One of the earliest results concerns the stochastic independence of record events. Recently, records statistics…
We study the statistics of records of a one-dimensional random walk of n steps, starting from the origin, and in presence of a constant bias c. At each time-step the walker makes a random jump of length \eta drawn from a continuous…
For a partial structural change in a linear regression model with a single break, we develop a continuous record asymptotic framework to build inference methods for the break date. We have T observations with a sampling frequency h over a…
Record-breaking temperature events are now very frequently in the news, viewed as evidence of climate change. With this as motivation, we undertake the first substantial spatial modeling investigation of temperature record-breaking across…
The Latent Block Model (LBM) is a model-based method to cluster simultaneously the $d$ columns and $n$ rows of a data matrix. Parameter estimation in LBM is a difficult and multifaceted problem. Although various estimation strategies have…
The deviation principles of record numbers in random walk models have not been completely investigated, especially for the non-nearest neighbor cases. In this paper, we derive the asymptotic probabilities of large and moderate deviations…
In the context of this paper, a record is an entry in a sequence of random variables (RV's) that is larger or smaller than all previous entries. After a brief review of the classic theory of records, which is largely restricted to sequences…
Data-driven methods for modeling dynamic systems have received considerable attention as they provide a mechanism for control synthesis directly from the observed time-series data. In the absence of prior assumptions on how the time-series…
Here in this paper, it is tried to obtain and compare the ML estimations based on upper record values and a random sample. In continue, some theorems have been proven about the behavior of these estimations asymptotically.
A trained ML model is deployed on another `test' dataset where target feature values (labels) are unknown. Drift is distribution change between the training and deployment data, which is concerning if model performance changes. For a…
We study statistical models for one-dimensional diffusions which are recurrent null. A first parameter in the drift is the principal one, and determines regular varying rates of convergence for the score and the information process. A…
Asymptotic laws of records values have usually been investigated as limits in type. In this paper, we use functional representations of the tail of cumulative distribution functions in the extreme value domain of attraction to directly…
We characterise probability distributions via a martingale property associated with a natural generalisation of record values, known as $\delta$-records. For an independent and identically distributed sequence $(X_n)$ with running maximum…
The analysis of record-breaking events is of interest in fields such as climatology, hydrology or anthropology. In connection with the record occurrence, we propose three distribution-free statistics for the changepoint detection problem.…
Record-breaking temperature events are now frequently in the news, proffered as evidence of climate change, and often bring significant economic and human impacts. Our previous work undertook the first substantial spatial modelling…
We provide a complete asymptotic distribution theory for clustered data with a large number of independent groups, generalizing the classic laws of large numbers, uniform laws, central limit theory, and clustered covariance matrix…
We consider the occurrence of record-breaking events in random walks with asymmetric jump distributions. The statistics of records in symmetric random walks was previously analyzed by Majumdar and Ziff and is well understood. Unlike the…