Defendant’s Motion to Exclude Expert Testimony regarding evidence generated by STRmix denied.

(PRWeb May 08, 2020)

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Holger Dette, Weichi Wu.

Source: The Annals of Statistics, Volume 47, Number 6, 3578--3608.

Abstract:
This paper considers the problem of testing if a sequence of means $(mu_{t})_{t=1,ldots ,n}$ of a nonstationary time series $(X_{t})_{t=1,ldots ,n}$ is stable in the sense that the difference of the means $mu_{1}$ and $mu_{t}$ between the initial time $t=1$ and any other time is smaller than a given threshold, that is $|mu_{1}-mu_{t}|leq c$ for all $t=1,ldots ,n$. A test for hypotheses of this type is developed using a bias corrected monotone rearranged local linear estimator and asymptotic normality of the corresponding test statistic is established. As the asymptotic variance depends on the location of the roots of the equation $|mu_{1}-mu_{t}|=c$ a new bootstrap procedure is proposed to obtain critical values and its consistency is established. As a consequence we are able to quantitatively describe relevant deviations of a nonstationary sequence from its initial value. The results are illustrated by means of a simulation study and by analyzing data examples.

Xi Chen, Weidong Liu, Yichen Zhang.

Source: The Annals of Statistics, Volume 47, Number 6, 3244--3273.

Abstract:
This paper studies the inference problem in quantile regression (QR) for a large sample size $n$ but under a limited memory constraint, where the memory can only store a small batch of data of size $m$. A natural method is the naive divide-and-conquer approach, which splits data into batches of size $m$, computes the local QR estimator for each batch and then aggregates the estimators via averaging. However, this method only works when $n=o(m^{2})$ and is computationally expensive. This paper proposes a computationally efficient method, which only requires an initial QR estimator on a small batch of data and then successively refines the estimator via multiple rounds of aggregations. Theoretically, as long as $n$ grows polynomially in $m$, we establish the asymptotic normality for the obtained estimator and show that our estimator with only a few rounds of aggregations achieves the same efficiency as the QR estimator computed on all the data. Moreover, our result allows the case that the dimensionality $p$ goes to infinity. The proposed method can also be applied to address the QR problem under distributed computing environment (e.g., in a large-scale sensor network) or for real-time streaming data.

Intended meaning. In computing, semantics is the assumed or explicit set of understandings used in a system to give meaning to data. One of the biggest challenges when integrating separate computer systems and applications is to correctly match up the intended meanings within each system. Simple metadata classifications such as 'price' or 'location' may have wildly different meanings in each system, while apparently different terms, such as 'client' and 'patient' may turn out to be effectively equivalent.

Chih-Yuan Hsu, Yi-Hau Chen, Ruoh-Rong Yu, Tsung-Wei Hung.

Source: The Annals of Applied Statistics, Volume 14, Number 1, 160--177.

Abstract:
Workers in Taiwan overall have been suffering from long-lasting wage stagnation since the mid-1990s. In particular, there seems to be little mobility for the wages of Taiwanese workers to transit across wage quantile groups. It is of interest to see if certain groups of workers, such as female, lower educated and younger generation workers, suffer from the problem more seriously than the others. This work tries to apply a systematic statistical approach to study this issue, based on the longitudinal data from the Panel Study of Family Dynamics (PSFD) survey conducted in Taiwan since 1999. We propose the quantile transition regression model, generalizing recent methodology for quantile association, to assess the wage status transition with respect to the marginal wage quantiles over time as well as the effects of certain demographic and job factors on the wage status transition. Estimation of the model can be based on the composite likelihoods utilizing the binary, or ordinal-data information regarding the quantile transition, with the associated asymptotic theory established. A goodness-of-fit procedure for the proposed model is developed. The performances of the estimation and the goodness-of-fit procedures for the quantile transition model are illustrated through simulations. The application of the proposed methodology to the PSFD survey data suggests that female, private-sector workers with higher age and education below postgraduate level suffer from more severe wage status stagnation than the others.

Emily Berg, Danhyang Lee.

Source: The Annals of Applied Statistics, Volume 13, Number 4, 2158--2188.

Abstract:
Quantiles of the distributions of several measures of erosion are important parameters in the Conservation Effects Assessment Project, a survey intended to quantify soil and nutrient loss on crop fields. Because sample sizes for domains of interest are too small to support reliable direct estimators, model based methods are needed. Quantile regression is appealing for CEAP because finding a single family of parametric models that adequately describes the distributions of all variables is difficult and small area quantiles are parameters of interest. We construct empirical Bayes predictors and bootstrap mean squared error estimators based on the linearly interpolated generalized Pareto distribution (LIGPD). We apply the procedures to predict county-level quantiles for four types of erosion in Wisconsin and validate the procedures through simulation.

Ye Zhang, Zhigang Yao, Patrik Forssén, Torgny Fornstedt.

Source: The Annals of Applied Statistics, Volume 13, Number 4, 2011--2042.

Abstract:
The means to obtain the rate constants of a chemical reaction is a fundamental open problem in both science and the industry. Traditional techniques for finding rate constants require either chemical modifications of the reactants or indirect measurements. The rate constant map method is a modern technique to study binding equilibrium and kinetics in chemical reactions. Finding a rate constant map from biosensor data is an ill-posed inverse problem that is usually solved by regularization. In this work, rather than finding a deterministic regularized rate constant map that does not provide uncertainty quantification of the solution, we develop an adaptive variational Bayesian approach to estimate the distribution of the rate constant map, from which some intrinsic properties of a chemical reaction can be explored, including information about rate constants. Our new approach is more realistic than the existing approaches used for biosensors and allows us to estimate the dynamics of the interactions, which are usually hidden in a deterministic approximate solution. We verify the performance of the new proposed method by numerical simulations, and compare it with the Markov chain Monte Carlo algorithm. The results illustrate that the variational method can reliably capture the posterior distribution in a computationally efficient way. Finally, the developed method is also tested on the real biosensor data (parathyroid hormone), where we provide two novel analysis tools—the thresholding contour map and the high order moment map—to estimate the number of interactions as well as their rate constants.

Chanmin Kim, Michael J. Daniels, Joseph W. Hogan, Christine Choirat, Corwin M. Zigler.

Source: The Annals of Applied Statistics, Volume 13, Number 3, 1927--1956.

Abstract:
Emission control technologies installed on power plants are a key feature of many air pollution regulations in the US. While such regulations are predicated on the presumed relationships between emissions, ambient air pollution and human health, many of these relationships have never been empirically verified. The goal of this paper is to develop new statistical methods to quantify these relationships. We frame this problem as one of mediation analysis to evaluate the extent to which the effect of a particular control technology on ambient pollution is mediated through causal effects on power plant emissions. Since power plants emit various compounds that contribute to ambient pollution, we develop new methods for multiple intermediate variables that are measured contemporaneously, may interact with one another, and may exhibit joint mediating effects. Specifically, we propose new methods leveraging two related frameworks for causal inference in the presence of mediating variables: principal stratification and causal mediation analysis. We define principal effects based on multiple mediators, and also introduce a new decomposition of the total effect of an intervention on ambient pollution into the natural direct effect and natural indirect effects for all combinations of mediators. Both approaches are anchored to the same observed-data models, which we specify with Bayesian nonparametric techniques. We provide assumptions for estimating principal causal effects, then augment these with an additional assumption required for causal mediation analysis. The two analyses, interpreted in tandem, provide the first empirical investigation of the presumed causal pathways that motivate important air quality regulatory policies.

Akio Fujiwara, Koichi Yamagata.

Source: Bernoulli, Volume 26, Number 3, 2105--2142.

Abstract:
We herein develop a theory of contiguity in the quantum domain based upon a novel quantum analogue of the Lebesgue decomposition. The theory thus formulated is pertinent to the weak quantum local asymptotic normality introduced in the previous paper [Yamagata, Fujiwara, and Gill, Ann. Statist. 41 (2013) 2197–2217], yielding substantial enlargement of the scope of quantum statistics.

Adam Osękowski.

Source: Bernoulli, Volume 26, Number 3, 1912--1926.

Abstract:
Let $X=(X_{t})_{tgeq 0}in H^{1}$ and $Y=(Y_{t})_{tgeq 0}in{mathrm{BMO}} $ be arbitrary continuous-path martingales. The paper contains the proof of the inequality egin{equation*}mathbb{E}int _{0}^{infty }iglvert dlangle X,Y angle_{t}igrvert leq sqrt{2}Vert XVert _{H^{1}}Vert YVert _{mathrm{BMO}_{2}},end{equation*} and the constant $sqrt{2}$ is shown to be the best possible. The proof rests on the construction of a certain special function, enjoying appropriate size and concavity conditions.

Xin Bing, Florentina Bunea, Marten Wegkamp.

Source: Bernoulli, Volume 26, Number 3, 1765--1796.

Abstract:
Topic models have become popular for the analysis of data that consists in a collection of n independent multinomial observations, with parameters $N_{i}inmathbb{N}$ and $Pi_{i}in[0,1]^{p}$ for $i=1,ldots,n$. The model links all cell probabilities, collected in a $p imes n$ matrix $Pi$, via the assumption that $Pi$ can be factorized as the product of two nonnegative matrices $Ain[0,1]^{p imes K}$ and $Win[0,1]^{K imes n}$. Topic models have been originally developed in text mining, when one browses through $n$ documents, based on a dictionary of $p$ words, and covering $K$ topics. In this terminology, the matrix $A$ is called the word-topic matrix, and is the main target of estimation. It can be viewed as a matrix of conditional probabilities, and it is uniquely defined, under appropriate separability assumptions, discussed in detail in this work. Notably, the unique $A$ is required to satisfy what is commonly known as the anchor word assumption, under which $A$ has an unknown number of rows respectively proportional to the canonical basis vectors in $mathbb{R}^{K}$. The indices of such rows are referred to as anchor words. Recent computationally feasible algorithms, with theoretical guarantees, utilize constructively this assumption by linking the estimation of the set of anchor words with that of estimating the $K$ vertices of a simplex. This crucial step in the estimation of $A$ requires $K$ to be known, and cannot be easily extended to the more realistic set-up when $K$ is unknown. This work takes a different view on anchor word estimation, and on the estimation of $A$. We propose a new method of estimation in topic models, that is not a variation on the existing simplex finding algorithms, and that estimates $K$ from the observed data. We derive new finite sample minimax lower bounds for the estimation of $A$, as well as new upper bounds for our proposed estimator. We describe the scenarios where our estimator is minimax adaptive. Our finite sample analysis is valid for any $n,N_{i},p$ and $K$, and both $p$ and $K$ are allowed to increase with $n$, a situation not handled well by previous analyses. We complement our theoretical results with a detailed simulation study. We illustrate that the new algorithm is faster and more accurate than the current ones, although we start out with a computational and theoretical disadvantage of not knowing the correct number of topics $K$, while we provide the competing methods with the correct value in our simulations.

Binyan Jiang, Ziqi Chen, Chenlei Leng.

Source: Bernoulli, Volume 26, Number 2, 1234--1268.

Abstract:
High-dimensional data that evolve dynamically feature predominantly in the modern data era. As a partial response to this, recent years have seen increasing emphasis to address the dimensionality challenge. However, the non-static nature of these datasets is largely ignored. This paper addresses both challenges by proposing a novel yet simple dynamic linear programming discriminant (DLPD) rule for binary classification. Different from the usual static linear discriminant analysis, the new method is able to capture the changing distributions of the underlying populations by modeling their means and covariances as smooth functions of covariates of interest. Under an approximate sparse condition, we show that the conditional misclassification rate of the DLPD rule converges to the Bayes risk in probability uniformly over the range of the variables used for modeling the dynamics, when the dimensionality is allowed to grow exponentially with the sample size. The minimax lower bound of the estimation of the Bayes risk is also established, implying that the misclassification rate of our proposed rule is minimax-rate optimal. The promising performance of the DLPD rule is illustrated via extensive simulation studies and the analysis of a breast cancer dataset.

Yating Liu, Gilles Pagès.

Source: Bernoulli, Volume 26, Number 2, 1171--1204.

Abstract:
We establish conditions to characterize probability measures by their $L^{p}$-quantization error functions in both $mathbb{R}^{d}$ and Hilbert settings. This characterization is two-fold: static (identity of two distributions) and dynamic (convergence for the $L^{p}$-Wasserstein distance). We first propose a criterion on the quantization level $N$, valid for any norm on $mathbb{R}^{d}$ and any order $p$ based on a geometrical approach involving the Voronoï diagram. Then, we prove that in the $L^{2}$-case on a (separable) Hilbert space, the condition on the level $N$ can be reduced to $N=2$, which is optimal. More quantization based characterization cases in dimension 1 and a discussion of the completeness of a distance defined by the quantization error function can be found at the end of this paper.

Tobias Zwingmann, Hajo Holzmann.

Source: Bernoulli, Volume 26, Number 1, 323--351.

Abstract:
We show weak convergence of quantile and expectile processes to Gaussian limit processes in the space of bounded functions endowed with an appropriate semimetric which is based on the concepts of epi- and hypo- convergence as introduced in A. Bücher, J. Segers and S. Volgushev (2014), ‘ When Uniform Weak Convergence Fails: Empirical Processes for Dependence Functions and Residuals via Epi- and Hypographs ’, Annals of Statistics 42 . We impose assumptions for which it is known that weak convergence with respect to the supremum norm generally fails to hold. For quantiles, we consider stationary observations, where the marginal distribution function is assumed to be strictly increasing and continuous except for finitely many points and to admit strictly positive – possibly infinite – left- and right-sided derivatives. For expectiles, we focus on independent and identically distributed (i.i.d.) observations. Only a finite second moment and continuity at the boundary points but no further smoothness properties of the distribution function are required. We also show consistency of the bootstrap for this mode of convergence in the i.i.d. case for quantiles and expectiles.

Names, Personal -- England.

Grant (Family)

Klemm (Family)

Dissenters, Religious -- Great Britain.

Names, Personal -- Welsh.

Names, Personal -- Scottish.

Cheesman, John -- Family.

Traeger, Ernst Wilhelm, 1805-1874.

Huppatz (Family).

EdWeek Market Brief asked district officials in a nationwide survey about their most urgent assessment needs, as they cope with COVID-19 and tentatively plan for reopening schools.

The post What Districts Want From Assessments, as They Grapple With the Coronavirus appeared first on Market Brief.

A train in India on Friday plowed through a group of migrant workers who fell asleep on the tracks after walking back home from a coronavirus lockdown, killing 15, the Railways Ministry said. Early this week the government started running trains to carry stranded workers to their home states.

While President Donald Trump traveled to the battleground state of Arizona this week, his Democratic opponent for the White House, Joe Biden, campaigned from his basement as he has done throughout the coronavirus pandemic. The freeze on in-person campaigning during the outbreak has had an upside for Biden, giving the former vice president more time to court donors and shielding him from on-the-trail gaffes. "I personally would like to see him out more because he's in his element when he's meeting people," said Tom Sacks-Wilner, a fundraiser for Biden who is on the campaign's finance committee.