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Recently, Tibshirani et al. (2016) proposed a method for making inferences about parameters defined by model selection, in a typical regression setting with normally distributed errors. Here, we study the large sample properties of this…
We propose a hypothesis test that allows for many tested restrictions in a heteroskedastic linear regression model. The test compares the conventional F statistic to a critical value that corrects for many restrictions and conditional…
A standard model of (conditional) heteroscedasticity, i.e., the phenomenon that the variance of a process changes over time, is the Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) model, which is especially important for…
In this paper we propose a new test of heteroscedasticity for parametric regression models and partial linear regression models in high dimensional settings. When the dimension of covariates is large, existing tests of heteroscedasticity…
In this paper, we study the problem of testing the equality of two multivariate distributions. One class of tests used for this purpose utilizes geometric graphs constructed using inter-point distances. So far, the asymptotic theory of…
In many applications, hypothesis testing is based on an asymptotic distribution of statistics. The aim of this paper is to clarify and extend multiple correction procedures when the statistics are asymptotically Gaussian. We propose a…
We propose new tests to detect a change in the mean of a time series. Like many existing tests, the new ones are based on the CUSUM process. Existing CUSUM tests require an estimator of a scale parameter to make them asymptotically…
Two non-integer parameters are defined for MAX statistics, which are maxima of $d$ simpler test statistics. The first parameter, $d_{MAX}$, is the fractional number of tests, representing the equivalent numbers of independent tests in MAX.…
Gaussian process models typically contain finite dimensional parameters in the covariance function that need to be estimated from the data. We study the Bayesian fixed-domain asymptotics for the covariance parameters in a universal kriging…
This paper studies distributed binary test of statistical independence under communication (information bits) constraints. While testing independence is very relevant in various applications, distributed independence test is particularly…
Recently, designs of pseudorandom number generators (PRNGs) using integer-valued variants of logistic maps and their applications to some cryptographic schemes have been studied, due mostly to their ease of implementation and performance.…
We consider the classical sequential binary hypothesis testing problem in which there are two hypotheses governed respectively by distributions $P_0$ and $P_1$ and we would like to decide which hypothesis is true using a sequential test. It…
We consider the sparse estimation for stochastic processes with possibly infinite-dimensional nuisance parameters, by using the Dantzig selector which is a sparse estimation method similar to $Z$-estimation. When a consistent estimator for…
We consider semiparametric transformation models, where after pre-estimation of a parametric transformation of the response the data are modeled by means of nonparametric regression. We suggest subsequent procedures for testing lack-of-fit…
There are a large number of methods for solving under-determined linear inverse problem. Many of them have very high time complexity for large datasets. We propose a new method called Two-Stage Sparse Representation (TSSR) to tackle this…
Stochastic gradient descent procedures have gained popularity for parameter estimation from large data sets. However, their statistical properties are not well understood, in theory. And in practice, avoiding numerical instability requires…
Fan et al. (2015) recently introduced a remarkable method for increasing asymptotic power of tests in high-dimensional testing problems. If applicable to a given test, their power enhancement principle leads to an improved test that has the…
We consider parametric estimation and tests for multi-dimensional diffusion processes with a small dispersion parameter $\varepsilon$ from discrete observations. For parametric estimation of diffusion processes, the main target is to…
A Markov switching asymmetric GARCH model which imposes more leverage effect of the negative shocks is considered. The asymptotic behavior of the second moment is investigated and an upper bound for it is calculated. A bayesian strategy…
We consider estimation and inference in a linear model with endogenous regressors where the parameters of interest change across two samples. If the first-stage is common, we show how to use this information to obtain more efficient…