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To draw scientifically meaningful conclusions and build reliable models of quantitative phenomena, cause and effect must be taken into consideration (either implicitly or explicitly). This is particularly challenging when the measurements…
An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…
Training a neural network (NN) typically relies on some type of curve-following method, such as gradient descent (GD) (and stochastic gradient descent (SGD)), ADADELTA, ADAM or limited memory algorithms. Convergence for these algorithms…
In this paper, we explore provable acceleration of diffusion models without any additional retraining. Focusing on the task of approximating a target data distribution in $\mathbb{R}^d$ to within $\varepsilon$ total-variation distance, we…
Despite their deterministic nature, dynamical systems often exhibit seemingly random behaviour. Consequently, a dynamical system is usually represented by a probabilistic model of which the unknown parameters must be estimated using…
Standard gradient descent methods yield point estimates with no measure of confidence. This limitation is acute in overparameterized and low-data regimes, where models have many parameters relative to available data and can easily overfit.…
The second-order dependence structure of purely nondeterministic stationary process is described by the coefficients of the famous Wold representation. These coefficients can be obtained by factorizing the spectral density of the process.…
This paper is mainly concerned with asymptotic studies of weighted bootstrap for u- and v-statistics. We derive the consistency of the weighted bootstrap u- and v-statistics, based on i.i.d. and non i.i.d. observations, from some more…
In this paper we consider a location model of the form $Y = m(X) + \varepsilon$, where $m(\cdot)$ is the unknown regression function, the error $\varepsilon$ is independent of the $p$-dimensional covariate $X$ and $E(\varepsilon)=0$. Given…
In modern experimental science, there is a common problem of estimating the coefficients of a linear regression in a context where the variables of interest cannot be observed simultaneously. When there is a categorical variable that is…
In this paper, we propose a new statistical inference method for massive data sets, which is very simple and efficient by combining divide-and-conquer method and empirical likelihood. Compared with two popular methods (the bag of little…
A bootstrap procedure for constructing prediction bands for a stationary functional time series is proposed. The procedure exploits a general vector autoregressive representation of the time-reversed series of Fourier coefficients appearing…
The validity of various bootstrapping methods has been proved for the sample mean of strongly mixing data. But in many applications, there appear nonlinear statistics of processes that are not strongly mixing. We investigate the…
Distribution forecast can quantify forecast uncertainty and provide various forecast scenarios with their corresponding estimated probabilities. Accurate distribution forecast is crucial for planning - for example when making production…
Standard confidence intervals employed in applied statistical analysis are usually based on asymptotic approximations. Such approximations can be considerably inaccurate in small and moderate sized samples. We derive accurate confidence…
The partially linear binary choice model can be used for estimating structural equations where nonlinearity may appear due to diminishing marginal returns, different life cycle regimes, or hectic physical phenomena. The inference procedure…
This paper focuses on the bootstrap for network dependent processes under the conditional $\psi$-weak dependence. Such processes are distinct from other forms of random fields studied in the statistics and econometrics literature so that…
This paper investigates the accuracy of bootstrap-based bias correction of persistence measures for long memory fractionally integrated processes. The bootstrap method is based on the semi-parametric sieve approach, with the dynamics in the…
We propose a Bayesian elastic net that uses empirical likelihood and develop an efficient tuning of Hamiltonian Monte Carlo for posterior sampling. The proposed model relaxes the assumptions on the identity of the error distribution,…
We introduce and evaluate a new class of hypothesis testing procedures for moment structures. The methods are valid under weak assumptions and includes the well-known Satorra-Bentler adjustment as a special case. The proposed procedures…