Related papers: Pivotal Quantities with Arbitrary Small Skewness
In this paper we introduce randomized $t$-type statistics that will be referred to as randomized pivots. We show that these randomized pivots yield central limit theorems with a significantly smaller magnitude of error as compared to that…
In this paper we introduce randomized pivots for the means of short and long memory linear processes. We show that, under the same conditions, these pivots converge in distribution to the same limit as that of their classical non-randomized…
In this paper an easy to implement method of stochastically weighing short and long memory linear processes is introduced. The method renders asymptotically exact size confidence intervals for the population mean which are significantly…
The Central Limit Theorem (CLT) is one of the most fundamental results in statistics. It states that the standardized sample mean of a sequence of $n$ mutually independent and identically distributed random variables with finite first and…
The Central Limit Theorem (CLT) establishes that sufficiently large sequences of independent and identically distributed random variables converge in probability to a normal distribution. This makes the CLT a fundamental building block of…
In this paper, we use the dimensional reduction technique to study the central limit theory (CLT) random quadratic forms based on sample means and sample covariance matrices. Specifically, we use a matrix denoted by $U_{p\times q}$, to map…
In this paper, we study fluctuations of conditionally centered statistics of the form $$N^{-1/2}\sum_{i=1}^N c_i(g(\sigma_i)-\mathbb{E}_N[g(\sigma_i)|\sigma_j,j\neq i])$$ where $(\sigma_1,\ldots ,\sigma_N)$ are sampled from a dependent…
Linear structural error-in-variables models with univariate observations are revisited for studying modified least squares estimators of the slope and intercept. New marginal central limit theorems (CLT's) are established for these…
We show how the renormalization group approach can be used to prove quantitative central limit theorems (CLTs) in the setting of free, Boolean, bi-free and bi-Boolean independence under finite third moment assumptions. The proofs rely on…
Under the high-dimensional setting that data dimension and sample size tend to infinity proportionally, we derive the central limit theorem (CLT) for linear spectral statistics (LSS) of large-dimensional sample covariance matrix. Different…
We analyze the fluctuations of incomplete $U$-statistics over a triangular array of independent random variables. We give criteria for a Central Limit Theorem (CLT, for short) to hold in the sense that we prove that an appropriately scaled…
A practical limitation of cluster randomized controlled trials (cRCTs) is that the number of available clusters may be small, resulting in an increased risk of baseline imbalance under simple randomization. Constrained randomization…
The local pivotal method (LPM) is a successful sampling method for taking well-spread samples from discrete populations. We show how the LPM can be utilized to sample from arbitrary continuous distributions and thereby give powerful…
This paper introduces a new version of the smoothly trimmed mean with a more general version of weights, which can be used as an alternative to the classical trimmed mean. We derive its asymptotic variance and to further investigate its…
Frequentists' inference often delivers point estimators associated with confidence intervals or sets for parameters of interest. Constructing the confidence intervals or sets requires understanding the sampling distributions of the point…
We study the fluctuations of the eigenvalues of real valued large centrosymmetric random matrices via its linear eigenvalue statistic. This is essentially a central limit theorem (CLT) for sums of dependent random variables. The dependence…
Random-effects models are central to meta-analysis, yet the between-study variance is often underestimated when the number of studies is small. In such settings, confidence intervals become unduly narrow and fail to attain the nominal…
We prove two theorems related to the Central Limit Theorem (CLT) for Martin-L\"of Random (MLR) sequences. Martin-L\"of randomness attempts to capture what it means for a sequence of bits to be "truly random". By contrast, CLTs do not make…
Rigorous statistical evaluations of large language models (LLMs), including valid error bars and significance testing, are essential for meaningful and reliable performance assessment. Currently, when such statistical measures are reported,…
We present a general methodology to construct triplewise independent sequences of random variables having a common but arbitrary marginal distribution $F$ (satisfying very mild conditions). For two specific sequences, we obtain in closed…