Related papers: Commentary to Wan et al. (2014): Estimating the st…
This paper proposes a Bayesian method for estimating the parameters of a normal distribution when only limited summary statistics (sample mean, minimum, maximum, and sample size) are available. To estimate the parameters of a normal…
The precise calculation of sample sizes is a crucial aspect in the design of clinical trials particularly for pharmaceutical statisticians. While various R statistical software packages have been developed by researchers to estimate…
Contemporary sample size calculations for external validation of risk prediction models require users to specify fixed values of assumed model performance metrics alongside target precision levels (e.g., 95% CI widths). However, due to the…
Existing approaches to sample size calculations for developing clinical prediction models have focused on ensuring that the expected value of a chosen performance measure meets a pre-specified target. For example, to limit…
This note gives a simple analysis of the randomized approximation scheme for matrix multiplication of Drineas et al (2006) with a particular sampling distribution over outer products. The result follows from a matrix version of Bernstein's…
When performing supervised learning with the model selected using validation error from sample splitting and cross validation, the minimum value of the validation error can be biased downward. We propose two simple methods that use the…
Interval analysis, when applied to the so called problem of experimental data fitting, appears to be still in its infancy. Sometimes, partly because of the unrivaled reliability of interval methods, we do not obtain any results at all.…
Annotated datasets are an essential ingredient to train, evaluate, compare and productionalize supervised machine learning models. It is therefore imperative that annotations are of high quality. For their creation, good quality management…
We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…
Given a large set $U$ where each item $a\in U$ has weight $w(a)$, we want to estimate the total weight $W=\sum_{a\in U} w(a)$ to within factor of $1\pm\varepsilon$ with some constant probability $>1/2$. Since $n=|U|$ is large, we want to do…
Latent variable models (LVMs) are commonly used in psychology and increasingly used for analyzing brain imaging data. Such studies typically involve a small number of participants (n<100), where standard asymptotic results often fail to…
We consider the problem of estimating the mean of a normal distribution under the following constraint: the estimator can access only a single bit from each sample from this distribution. We study the squared error risk in this estimation…
Weighting procedures are used in observational causal inference to adjust for covariate imbalance within the sample. Common practice for inference is to estimate robust standard errors from a weighted regression of outcome on treatment.…
We study the properties of several likelihood-based statistics commonly used in testing for the presence of a known signal under a mixture model with known background, but unknown signal fraction. Under the null hypothesis of no signal, all…
We present a proposal to deal with the non-normality issue in the context of regression models with measurement errors when both the response and the explanatory variable are observed with error. We extend the normal model by jointly…
I present a frequentist method for quantifying uncertainty when correcting correlations for attenuation due to measurement error. The method is conservative but has far better coverage properties than the methods currently used when sample…
Robust statistics aims to compute quantities to represent data where a fraction of it may be arbitrarily corrupted. The most essential statistic is the mean, and in recent years, there has been a flurry of theoretical advancement for…
Considering two random variables with different laws to which we only have access through finite size iid samples, we address how to reweight the first sample so that its empirical distribution converges towards the true law of the second…
An algorithm for sampling exactly from the normal distribution is given. The algorithm reads some number of uniformly distributed random digits in a given base and generates an initial portion of the representation of a normal deviate in…
Importance sampling is used to approximate Bayes' rule in many computational approaches to Bayesian inverse problems, data assimilation and machine learning. This paper reviews and further investigates the required sample size for…