Related papers: On Sequential Estimation and Prediction for Discre…
Non-uniform sampling arises when an experimenter does not have full control over the sampling characteristics of the process under investigation. Moreover, it is introduced intentionally in algorithms such as Bayesian optimization and…
We address the problem of nonparametric estimation of characteristics for stationary and ergodic time series. We consider finite-alphabet time series and real-valued ones and the following four problems: i) estimation of the (limiting)…
Evaluating predictive models is a crucial task in predictive analytics. This process is especially challenging with time series data where the observations show temporal dependencies. Several studies have analysed how different performance…
We consider the problem of inference for non-stationary time series with heavy-tailed error distribution. Under a time-varying linear process framework we show that there exists a suitable local approximation by a stationary process with…
Variance estimation is important for statistical inference. It becomes non-trivial when observations are masked by serial dependence structures and time-varying mean structures. Existing methods either ignore or sub-optimally handle these…
Forecasting the evolution of complex systems is one of the grand challenges of modern data science. The fundamental difficulty lies in understanding the structure of the observed stochastic process. In this paper, we show that every…
Debiased estimation has long been an area of research in the group testing literature. This has led to the development of several estimators with the goal of bias minimization and, recently, an unbiased estimator based on sequential…
The forward estimation problem for stationary and ergodic time series $\{X_n\}_{n=0}^{\infty}$ taking values from a finite alphabet ${\cal X}$ is to estimate the probability that $X_{n+1}=x$ based on the observations $X_i$, $0\le i\le n$…
Methods of estimation and forecasting for stationary models are well known in classical time series analysis. However, stationarity is an idealization which, in practice, can at best hold as an approximation, but for many time series may be…
We introduce a new concept of approximation applicable to decision problems and functions, inspired by Bayesian probability. From the perspective of a Bayesian reasoner with limited computational resources, the answer to a problem that…
Estimation using pooled sampling has long been an area of interest in the group testing literature. Such research has focused primarily on the assumed use of fixed sampling plans (i), although some recent papers have suggested alternative…
Let $(B(t))_{t\in \Theta}$ with $\Theta={\mathbb Z}$ or $\Theta={\mathbb R}$ be a wide sense stationary process with discrete or continuous time. The classical linear prediction problem consists of finding an element in…
Statistical inference for time series such as curve estimation for time-varying models or testing for existence of change-point have garnered significant attention. However, these works are generally restricted to the assumption of…
Performance estimation aims at estimating the loss that a predictive model will incur on unseen data. These procedures are part of the pipeline in every machine learning project and are used for assessing the overall generalisation ability…
Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…
This paper studies hypothesis testing and parameter estimation in the context of the divide and conquer algorithm. In a unified likelihood based framework, we propose new test statistics and point estimators obtained by aggregating various…
Assuming that a reflected Ornstein-Uhlenbeck state process is observed at discrete time instants, we propose generalized moment estimators to estimate all drift and diffusion parameters via the celebrated ergodic theorem. With the sampling…
A large class of problems in sciences and engineering can be formulated as the general problem of constructing random intervals with pre-specified coverage probabilities for the mean. Wee propose a general approach for statistical inference…
Forecasts of various processes have always been a sophisticated problem for statistics and data science. Over the past decades the solution procedures were updated by deep learning and kernel methods. According to many specialists, these…
A sequence $x_1,\dots,x_n,\dots$ of discrete-valued observations is generated according to some unknown probabilistic law (measure) $\mu$. After observing each outcome, one is required to give conditional probabilities of the next…