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In biomedical research, increasing attention has been paid to the discovery of regulatory relationships among heterogeneous biological features. We present a new statistical framework to jointly learn multiple heterogeneous exponential Markov Random Fields. We establish an approximate likelihood inference problem regularized by an embedded group lasso penalty, and propose an efficient algorithm in the Alternating Direction Method of Multipliers framework. We also establish structure recovery consistency for the proposed joint network learning. The practical merits of the proposed integrative structural learning method are demonstrated through simulations and real applications to discovering regulatory relationships among heterogeneous biological variables from distinct but related types of cancer. • We perform the joint modeling of multiple mixed graphical models from exponential family. • We solve the problem through an efficient approximate likelihood method. • We discuss structure recovery consistency for the proposed joint network learning. • We use numerical and real data examples to illustrate the performance of our method. [ABSTRACT FROM AUTHOR]

In this study, we consider a robust estimation method for general integer-valued time series models whose conditional distribution belongs to the one-parameter exponential family. As a robust estimator, we employ the minimum density power divergence estimator, and we demonstrate this is strongly consistent and asymptotically normal under certain regularity conditions. A simulation study is carried out to evaluate the performance of the proposed estimator. A real data analysis using the return times of extreme events of the Goldman Sachs Group stock is also provided as an illustration. [ABSTRACT FROM AUTHOR]

In nonignorable missing response problems, we study a semiparametric model with unspecified missingness mechanism model and a exponential family model for response conditional density. Even though existing methods are available to estimate the parameters in exponential family, estimation or testing of the missingness mechanism model nonparametrically remains to be an open problem. By defining a "synthesis" density involving the unknown missingness mechanism model and the known baseline "carrier" density in the exponential family model, we treat this "synthesis" density as a legitimate one with biased sampling version. We develop maximum pseudo likelihood estimation procedures and the resultant estimators are consistent and asymptotically normal. Since the "synthesis" cumulative distribution is a functional of the missingness mechanism model and the known carrier density, proposed method can be used to test the correctness of the missingness mechanism model nonparametrically andindirectly. Simulation studies and real example demonstrate the proposed methods perform very well. [ABSTRACT FROM AUTHOR]

In this paper, a two-stage sequential estimation procedure is considered to construct fixed-accuracy confidence intervals of the reliability parameter R under the stress–strength model when the stress and strength are independent exponential random variables with different scale parameters. The exact distribution of the total sample size, explicit formulas for the expected value, and mean squared error of the maximum likelihood estimator of the reliability parameter under the stress–strength model are provided under the two-stage sequential procedure. Performances of the proposed methodology are investigated with the help of simulations. Finally, using three pairs of real datasets, the procedure is clearly illustrated. We used MATLAB in order to implement computations, simulation studies, and real data analysis. [ABSTRACT FROM AUTHOR]

We introduce a Bayesian approach for analyzing (possibly) high-dimensional dependent data that are distributed according to a member from the natural exponential family of distributions. This problem requires extensive methodological advancements, as jointly modeling high-dimensional dependent data leads to the so-called "big n problem." The computational complexity of the "big n problem" is further exacerbated when allowing for non-Gaussian data models, as is the case here. Thus, we develop new computationally efficient distribution theory for this setting. In particular, we introduce the "conjugate multivariate distribution," which is motivated by the Diaconis and Ylvisaker distribution. Furthermore, we provide substantial theoretical and methodological development including: results regarding conditional distributions, an asymptotic relationship with the multivariate normal distribution, conjugate prior distributions, and full-conditional distributions for a Gibbs sampler. To demonstrate the wide-applicability of the proposed methodology, we provide two simulation studies and three applications based on an epidemiology dataset, a federal statistics dataset, and an environmental dataset, respectively. for this article are available online. [ABSTRACT FROM AUTHOR]

In this article, we propose a mean linear regression model where the response variable is inverse gamma distributed using a new parameterization of this distribution that is indexed by mean and precision parameters. The main advantage of our new parametrization is the straightforward interpretation of the regression coefficients in terms of the expectation of the positive response variable, as usual in the context of generalized linear models. The variance function of the proposed model has a quadratic form. The inverse gamma distribution is a member of the exponential family of distributions and has some distributions commonly used for parametric models in survival analysis as special cases. We compare the proposed model to several alternatives and illustrate its advantages and usefulness. With a generalized linear model approach that takes advantage of exponential family properties, we discuss model estimation (by maximum likelihood), black further inferential quantities and diagnostic tools. A Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples with a discussion of the obtained results. A real application using minerals data set collected by Department of Mines of the University of Atacama, Chile, is considered to demonstrate the practical potential of the proposed model. [ABSTRACT FROM AUTHOR]

Extending normal gamma and normal inverse Gaussian models, multivariate normal stable Tweedie (NST) models are composed by a fixed univariate stable Tweedie variable having a positive value domain, and the remaining random variables given the fixed one are real independent Gaussian variables with the same variance equal to the fixed component. Within the framework of multivariate exponential families, the NST models are recently classified by their covariance matrices V(m) depending on the mean vector m. In this paper, we prove the characterization of all the NST models through their determinants of V(m), also called generalized variance functions, which are power of only one component of m. This result is established under the NST assumptions of Monge-Ampère property and steepness. It completes the two special cases of NST, namely normal Poisson and normal gamma models. As a matter of fact, it provides explicit solutions of particular Monge-Ampère equations in differential geometry. [ABSTRACT FROM AUTHOR]

Dispersion indexes with respect to the Poisson and binomial distributions are widely used to assess the conformity of the underlying distribution from an observed sample of the count with one or the other of these theoretical distributions. Recently, the exponential variation index has been proposed as an extension to nonnegative continuous data. This paper aims to gather to study the unified definition of these indexes with respect to the relative variability of a nonnegative natural exponential family of distributions through its variance function. We establish the strong consistency of the plug-in estimators of the indexes as well as their asymptotic normalities. Since the exact distributions of the estimators are not available in closed form, we consider the test of hypothesis relying on these estimators as test statistics with their asymptotic distributions. Simulation studies globally suggest good behaviours of these tests of hypothesis procedures. Applicable examples are analysed, including the lesser-known references such as negative binomial and inverse Gaussian, and improving the very usual case of the Poisson dispersion index. Concluding remarks are made with suggestions of possible extensions. [ABSTRACT FROM AUTHOR]

This paper proposes three methods to estimate the parameters in uncertain differential equations (UDEs) based on discrete observation data. The first method is designed for a class of UDEs in which their solutions have the explicit expressions of uncertainty distribution. The second method is given to solve the estimation problem through the inverse uncertainty distribution. In the third method, the unknown parameters of UDEs are estimated by the solution of the corresponding α-path. These methods are interpreted to be efficient and practical by using a popular UDE with exponential solutions and obtaining the detailed estimators of the parameters. [ABSTRACT FROM AUTHOR]

This paper deals with the pseudo maximum likelihood estimation of a GARCH (1,2) model under two reasonably weak, realistic and tractable assumptions: the innovations are dependent albeit conditionally independent, and belong to the quadratic exponential family, which contains several standard distributions. More specifically, the paper derives the consistency and asymptotic normality of the pseudo maximum likelihood estimator (PLME hereafter) under some regularity conditions by means of martingale techniques. Finally, extensive Monte Carlo experiments are conducted to examine the finite sample performance of the proposed PMLE. [ABSTRACT FROM AUTHOR]

Modeling reliability data with nonmonotone hazards is a prominent research topic that is quite rich and still growing rapidly. Many studies have suggested introducing new families of distributions to modify the Weibull distribution to model the nonmonotone hazards. In the present study, we propose a new family of distributions called a new lifetime exponential-X family. A special submodel of the proposed family called a new lifetime exponential-Weibull distribution suitable for modeling reliability data with bathtub-shaped hazard rates is discussed. The maximum-likelihood estimators of the model parameters are obtained. A brief Monte Carlo simulation study is conducted to evaluate the performance of these estimators. For illustrative purposes, two real applications from reliability engineering with bathtub-shaped hazard functions are analyzed. The practical applications show that the proposed model provides better fits than the other nonnested models. [ABSTRACT FROM AUTHOR]

Particle filter is the most widely used Bayesian sequential state estimation method for nonlinear dynamic systems. When importance sampling is adopted, it is still a challenge to select an appropriate importance function for sampling to avoid particle degeneracy. This paper suggests a novel particle filter, called second-order extended particle filter, which uses conditional normal distribution to approximate the theoretical optimal importance function in sequential state estimation. The approximation is fulfilled through taking logarithm to the optimal importance function and implementing second-order Taylor expansion. This method is suitable for exponential family observation models, which have numerous applications in state estimation research field. [ABSTRACT FROM AUTHOR]

This paper proposes a new probability distribution, which belongs a member of the exponential family, defined on (0,1) unit interval. The new unit model has been defined by relation of a random variable defined on unbounded interval with respect to standard logistic function. Some basic statistical properties of newly defined distribution are derived and studied. The different estimation methods and some inferences for the model parameters have been derived. We assess the performance of the estimators of these estimation methods based on the three different simulation scenarios. The analysis of three real data examples which one is related to the coronavirus data, show better fit of proposed distribution than many known distributions on the unit interval under some comparing criteria. [ABSTRACT FROM AUTHOR]

In photon-limited imaging, the pixel intensities are affected by photon count noise. Many applications require an accurate estimation of the covariance of the underlying 2-D clean images. For example, in X-ray free electron laser (XFEL) single molecule imaging, the covariance matrix of 2-D diffraction images is used to reconstruct the 3-D molecular structure. Accurate estimation of the covariance from low-photon-count images must take into account that pixel intensities are Poisson distributed, hence the classical sample covariance estimator is highly biased. Moreover, in single molecule imaging, including in-plane rotated copies of all images could further improve the accuracy of covariance estimation. In this paper we introduce an efficient and accurate algorithm for covariance matrix estimation of count noise 2-D images, including their uniform planar rotations and possibly reflections. Our procedure, steerable $e$ PCA, combines in a novel way two recently introduced innovations. The first is a methodology for principal component analysis (PCA) for Poisson distributions, and more generally, exponential family distributions, called $e$ PCA. The second is steerable PCA, a fast and accurate procedure for including all planar rotations when performing PCA. The resulting principal components are invariant to the rotation and reflection of the input images. We demonstrate the efficiency and accuracy of steerable $e$ PCA in numerical experiments involving simulated XFEL datasets and rotated face images from Yale Face Database B. [ABSTRACT FROM AUTHOR]

In this paper, the reconcilability between the P-value and the posterior probability in testing a point null hypothesis against the one-sided hypothesis is considered. Two essential families, non regular and exponential family of distributions, are studied. It was shown in a non regular family of distributions; in some cases, it is possible to find a prior distribution function under which P-value and posterior probability are achieved. However, in the exponential family of distributions, this agreement is based on the complete monotonicity of a function of hazard rate. [ABSTRACT FROM AUTHOR]

Summary: We provide a new computationally efficient class of estimators for risk minimization. We show that these estimators are robust for general statistical models, under varied robustness settings, including in the classical Huber ε‐contamination model, and in heavy‐tailed settings. Our workhorse is a novel robust variant of gradient descent, and we provide conditions under which our gradient descent variant provides accurate estimators in a general convex risk minimization problem. We provide specific consequences of our theory for linear regression and logistic regression and for canonical parameter estimation in an exponential family. These results provide some of the first computationally tractable and provably robust estimators for these canonical statistical models. Finally, we study the empirical performance of our proposed methods on synthetic and real data sets, and we find that our methods convincingly outperform a variety of baselines. [ABSTRACT FROM AUTHOR]

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Determining the sample size of an experiment can be challenging, even more so when incorporating external information via a prior distribution. Such information is increasingly used to reduce the size of the control group in randomized clinical trials. Knowing the amount of prior information, expressed as an equivalent prior effective sample size (ESS), clearly facilitates trial designs. Various methods to obtain a prior's ESS have been proposed recently. They have been justified by the fact that they give the standard ESS for one‐parameter exponential families. However, despite being based on similar information‐based metrics, they may lead to surprisingly different ESS for nonconjugate settings, which complicates many designs with prior information. We show that current methods fail a basic predictive consistency criterion, which requires the expected posterior‐predictive ESS for a sample of size N to be the sum of the prior ESS and N. The expected local‐information‐ratioESS is introduced and shown to be predictively consistent. It corrects the ESS of current methods, as shown for normally distributed data with a heavy‐tailed Student‐t prior and exponential data with a generalized Gamma prior. Finally, two applications are discussed: the prior ESS for the control group derived from historical data and the posterior ESS for hierarchical subgroup analyses. [ABSTRACT FROM AUTHOR]

We study a type of double truncation where units are observed if and only if their death event occurs within a specific timespan. The resulting missing data mechanism is nonignorable and thus has to be reconsidered. Based on the density function of observed lifetimes and the random sample size, we derive a likelihood model that enables simultaneous estimation of the lifetime distribution and the parameters governing the birth process. In particular, knowledge of the population size is not required. We show that the model is identifiable under certain conditions by using results on exponential families. Bayesian estimators and corresponding standard errors for all involved parameters become available by using MCMC simulation. We describe how the simulation can be performed efficiently while maintaining sufficiently good mixing behaviour of the resulting chains. Both finite-sample and asymptotic properties of the investigated estimators are examined through a simulation study. The proposed method is applied to estimate the lifetime distribution of German companies. [ABSTRACT FROM AUTHOR]

Two-piece location-scale models are used for modeling data presenting departures from symmetry. In this paper, we propose an objective Bayesian methodology for the tail parameter of two particular distributions of the above family: the skewed exponential power distribution and the skewed generalised logistic distribution. We apply the proposed objective approach to time series models and linear regression models where the error terms follow the distributions object of study. The performance of the proposed approach is illustrated through simulation experiments and real data analysis. The methodology yields improvements in density forecasts, as shown by the analysis we carry out on the electricity prices in Nordpool markets. [ABSTRACT FROM AUTHOR]

The learning algorithm of an extreme learning machine (ELM) has two fundamental steps: 1) random nonlinear feature transformation and 2) least squares learning. Since the probabilistic interpretation for a sample by the least squares method follows a Gaussian distribution, there are two limitations in ELM caused by the second step: 1) it may be inaccurate to handle binary classification problems, since the output of a binary dataset has a distribution far from Gaussian and 2) it may have difficulties in dealing with nontraditional data types (such as count data, ordinal data, etc.), which also do not follow Gaussian distribution. In order to solve the above-mentioned problems, this paper proposes a generalized ELM (GELM) framework by applying the exponential family distribution (EFD) to the output layer node of ELM. It simplifies the design of ELM models for task-specific output domains with different data types. We propose a unified learning paradigm for all the models under this GELM framework with different distributions in EFD, and prove that traditional ELM is a special instance of GELM by setting the output distribution as a Gaussian distribution (GELM-Gaussian). We also prove that the training of GELM-Gaussian can be finished in one iteration, in this case, GELM-Gaussian does not slow down the training speed of traditional ELM. Besides, we propose the kernel version of GELM, which can also be concretized to different models by applying different EFDs. Experimental comparisons demonstrate that GELM can give more accurate probabilistic interpretation to binary classification and GELM has a great potential in dealing with a broader range of machine learning tasks. [ABSTRACT FROM AUTHOR]

Single-cell expression analysis is an effective tool for studying the dynamics of cell population profiles. However, the majority of statistical methods are applied to individual profiles and the methods for comparing multiple profiles simultaneously are limited. In this study, we propose a nonparametric statistical method, called Decomposition into Extended Exponential Family (DEEF), that embeds a set of single-cell expression profiles of several markers into a low-dimensional space and identifies the principal distributions that describe their heterogeneity. We demonstrate that DEEF can appropriately decompose and embed sets of theoretical probability distributions. We then apply DEEF to a cytometry dataset to examine the effects of epidermal growth factor stimulation on an adult human mammary gland. It is shown that DEEF can describe the complex dynamics of cell population profiles using two parameters and visualize them as a trajectory. The two parameters identified the principal patterns of the cell population profile without prior biological assumptions. As a further application, we perform a dimensionality reduction and a time series reconstruction. DEEF can reconstruct the distributions based on the top coordinates, which enables the creation of an artificial dataset based on an actual single-cell expression dataset. Using the coordinate system assigned by DEEF, it is possible to analyze the relationship between the attributes of the distribution sample and the features or shape of the distribution using conventional data mining methods. [ABSTRACT FROM AUTHOR]

We propose some general techniques for proving lower bounds in expansion-based QBF proof systems. We present them in a framework centred on natural properties of winning strategies in the 'evaluation game' interpretation of QBF semantics. As applications, we prove an exponential proof-size lower bound for a whole class of formula families, and demonstrate the power of our approach over existing methods by providing alternative short proofs of two known hardness results. We also use our technique to deduce an interesting result: in the absence of propositional hardness, formulas separating the two major QBF expansion systems must have unbounded quantifier alternations. [ABSTRACT FROM AUTHOR]

Two-stage hierarchical models have been widely used in small area estimation to produce indirect estimates of areal means. When the areas are treated exchangeably and the model parameters are assumed to be the same over all areas, we might lose the efficiency in the presence of spatial heterogeneity. To overcome this problem, we consider a two-stage area-level model based on natural exponential family with spatially varying model parameters. We employ geographically weighted regression approach to estimating the varying parameters and suggest a new empirical Bayes estimator of the areal mean. We also discuss some related problems, including the mean squared error estimation, benchmarked estimation and estimation in non-sampled areas. The performance of the proposed method is evaluated through simulations and applications to two data sets. [ABSTRACT FROM AUTHOR]

A large number of useful distributions for data analysis are obtained by transforming different random variables. An example is the one-parameter unit-Lindley distribution, obtained by transforming a random variable which has a Lindley distribution. In this paper, we introduce a new one-parameter unit-Lindley distribution, useful for data analysis in the interval (0,1]. It follows some interesting properties such as having closed form expressions for the moments, belonging to the exponential family. We also analyze a practical application having covariates, by setting up a suitable regression and show that our model fits much better than both unit-Lindley and beta regressions. [ABSTRACT FROM AUTHOR]

Let P0 be a probability on the real line generating a natural exponential family (Pt)t∈ℝ. Fix α in (0, 1). We show that the property that Pt((−∞, t)) ≤ α ≤ Pt((−∞, t]) for all t implies that there exists a number μα such that P0 is the Gaussian distribution N(μα, 1). In other terms, if for all t, the number t is a quantile of Pt associated to some threshold α ∈ (0, 1), then the exponential family must be Gaussian. The case α = 1∕2, i.e. when t is always a median of Pt, has been considered in Letac et al. [Statist. Prob. Lett.133 (2018) 38–41]. Analogously let Q be a measure on [0, ∞) generating a natural exponential family (Q−t)t>0. We show that Q−t([0, t−1)) ≤ α ≤ Q−t([0, t−1]) for all t > 0 implies that there exists a number p = pα > 0 such that Q(dx) ∝ xp−1dx, and thus Q−t has to be a gamma law with parameters p and t. [ABSTRACT FROM AUTHOR]

We propose expected policy gradients (EPG), which unify stochastic policy gradients (SPG) and deterministic policy gradients (DPG) for reinforcement learning. Inspired by expected sarsa, EPG integrates (or sums) across actions when estimating the gradient, instead of relying only on the action in the sampled trajectory. For continuous action spaces, we first derive a practical result for Gaussian policies and quadratic critics and then extend it to a universal analytical method, covering a broad class of actors and critics, including Gaussian, exponential families, and policies with bounded support. For Gaussian policies, we introduce an exploration method that uses covariance proportional to the matrix exponential of the scaled Hessian of the critic with respect to the actions. For discrete action spaces, we derive a variant of EPG based on softmax policies. We also establish a new general policy gradient theorem, of which the stochastic and deterministic policy gradient theorems are special cases. Furthermore, we prove that EPG reduces the variance of the gradient estimates without requiring deterministic policies and with little computational overhead. Finally, we provide an extensive experimental evaluation of EPG and show that it outperforms existing approaches on multiple challenging control domains. [ABSTRACT FROM AUTHOR]

Algebraic sampling methods are a powerful tool to perform hypothesis testing for non-negative discrete exponential families, when the exact computation of the test statistic null distribution is computationally infeasible. We propose an improvement of the accelerated sampling described by Diaconis and Sturmfels (1998) based on permutations. We thus establish a link between standard permutation and algebraic-statistics-based sampling. We prove that the permutations-based sampling gives the lowest approximation errors and we validate our algorithm through a simulation study on three applications (data fitting, two sample tests and linear regression). • Conditional hypothesis testing for non-negative discrete exponential families can be speed up using orbits of permutations. • A theoretical link between standard permutation and algebraic statistics-based sampling is established. • The range of application of the method includes data fitting, two-sample tests and linear regression. [ABSTRACT FROM AUTHOR]

The present article addresses the problem of improved estimation of population mean of the study variable. For elevated estimation, we suggest a new generalized exponential ratio type family of estimators of population mean using auxiliary attribute. The bias and mean squared errors (MSE) of the suggested family are derived up to the approximation of order one. The optimum value of the characterizing scalar is obtained and the minimum MSE of the suggested family is also obtained. Further more generalized class is also proposed and the suggested family is its special case. The minimum MSE of this class is also obtained for the optimum value of the scalar. A theoretical comparison of the suggested class has made with the competing estimators of population mean. An empirical study has also been performed to show that the suggested class is better than the competing estimators of population mean. [ABSTRACT FROM AUTHOR]

Addition and subtraction of observed values can be computed under the obvious and implicit assumption that the scale unit of measurement should be the same for all arguments, which is valid even for any nonlinear systems. This paper starts with the distinction between exponential and non-exponential family in the sense of the scale unit of measurement. In the simplest nonlinear model dy∕dx = yq, it is shown how typical effects such as rescaling and shift emerge in the nonlinear systems and affect observed data. Based on the present results, the two representations, namely the q-exponential and the q-logarithm ones, are proposed. The former is for rescaling, the latter for unified understanding with a fixed scale unit. As applications of these representations, the corresponding entropy and the general probability expression for unified understanding with a fixed scale unit are presented. For the theoretical study of nonlinear systems, q-logarithm representation is shown to have significant advantages over q-exponential representation. [ABSTRACT FROM AUTHOR]

A new family of distributions called the odd generalized N-H is introduced and studied. Four new special models are presented. Some mathematical properties of the odd generalized N-H family are studied. Explicit expressions for the moments, probability weighted, quantile function, mean deviation, order statistics and Rényi entropy are investigated. Characterizations based on the truncated moments, hazard function and conditional expectations are presented for the generated family. Parameter estimates of the family are obtained based on maximum likelihood procedure. Two real data sets are employed to show the usefulness of the new family. [ABSTRACT FROM AUTHOR]

This research studied and explored the Burr X and Exponential families of distributions. However, we introduced a new family of distribution called Burr X Exponential-G family of distribution. We obtained a new distribution called Burr X Exponential – Exponential; by showing its respective density and distribution functions from the proposed family of distributions. The validity of the new family of distribution is proved. Also, the survival and hazard functions of the family are presented. However, this new family of distributions will serve as an additional generator to the existing ones in the literature; for developing a new model for modeling positive real data sets. [ABSTRACT FROM AUTHOR]

We introduce a new five-parameter family of distributions, the asymmetric exponential power (AEP), able to cope with asymmetries and leptokurtosis and, at the same time, allowing for a continuous variation from non-normality to normality. We prove that the maximum likelihood (ML) estimates of the AEP parameters are consistent on the whole parameter space, and when sufficiently large values of the shape parameters are considered, they are also asymptotically efficient and normal. We derive the Fisher information matrix for the AEP and we show that it can be continuously extended also to the region of small shape parameters. Through numerical simulations, we find that this extension can be used to obtain a reliable value for the errors associated to ML estimates also for samples of relatively small size (100 observations). Moreover, we show that around this sample size, the bias associated with ML estimates, although present, becomes negligible. Finally, we present a few empirical investigations, using diverse data from economics and finance, to compare the performance of AEP with respect to other, commonly used, families of distributions. [ABSTRACT FROM PUBLISHER]

In this study, the researchers introduce a new class of the logistic distribution which can be used to model the unimodal data with some skewness present. The new generalization is carried out using the basic idea of Nadarajah (Statistics 48(4):872–895, 2014), called truncated-exponential skew-logistic (TESL) distribution. The TESL distribution is a member of the exponential family; therefore, the skewness parameter can be derived easier. Meanwhile, some important statistical characteristics are presented; the real data set and simulation studies are applied to evaluate the results. Also, the TESL distribution is compared to at least five other skew-logistic distributions. [ABSTRACT FROM AUTHOR]

We consider the problem of making a quick decision in favor of one of two possible physical signal models while the numerical measurements are acquired by sensing devices featuring minimal digitization complexity. Therefore, the digital data streams available for statistical processing are binary and exhibit temporal and spatial dependencies. To handle the intractable multivariate binary data model, we first consider sequential tests for exponential family distributions. Within this generic probabilistic framework, we identify adaptive approximations for the log-likelihood ratio and the Kullback-Leibler divergence. The results allow designing sequential detectors for binary radio systems and analyzing their average run-time along classical arguments of Wald. In particular, the derived tests exploit the spatio-temporal correlation structure of the analog sensor signals engraved into the binary measurements. As an application, we consider the specification of binary sensing architectures for cognitive radio and GNSS spectrum monitoring where our results characterize the sequential detection latency as a function of the temporal oversampling and the number of antennas. Finally, we evaluate the efficiency of the proposed algorithms and illustrate the accuracy of our analysis via Monte-Carlo simulations. [ABSTRACT FROM AUTHOR]

In this paper, by suitably using the so-called push-back operation, a connection between the approximating and interpolatory subdivision, a new family of nonstationary subdivision schemes is presented. Each scheme of this family is a quasi-interpolatory scheme and reproduces a certain space of exponential polynomials. This new family of schemes unifies and extends quite a number of the existing interpolatory schemes reproducing exponential polynomials and noninterpolatory schemes like the cubic exponential B-spline scheme. For these new schemes, we investigate their convergence, smoothness, and accuracy and show that they can reach higher smoothness orders than the interpolatory schemes with the same reproduction property and better accuracy than the exponential B-spline schemes. Several examples are given to illustrate the performance of these new schemes. [ABSTRACT FROM AUTHOR]

Consider an exponential family F on the set of non-negative integers indexed by the parameter a. The cumulative distribution function of an element of F estimated on k is both a function of a and k. Assume that the derivative of this function with respect to a is the product of three things: a function of k, a function of a and the function a to the power k. We show that this assumption implies that the exponential family is either a binomial, or the Poisson, or a negative binomial family. Next, we study an analogous property for continuous distributions and we find that it is satisfied if and only the families are either Gaussian or Gamma. Ultimately, the proofs rely on the fact that only Möbius functions preserve the cross ratio. [ABSTRACT FROM AUTHOR]

This paper is about models for a vector of probabilities whose elements must have a multiplicative structure and sum to 1 at the same time; in certain applications, like basket analysis, these models may be seen as a constrained version of quasi-independence. After reviewing the basic properties of the models, their geometric features as a curved exponential family are investigated. An improved algorithm for computing maximum likelihood estimates is introduced and new insights are provided on the underlying geometry. The asymptotic distribution of three statistics for hypothesis testing are derived and a small simulation study is presented to investigate the accuracy of asymptotic approximations. [ABSTRACT FROM AUTHOR]

Conditional tests are constructed by conditioning a fit measure to a minimal sufficient statistic. To calculate the p-value of these tests, Monte Carlo methods with co-sufficient samples can be used. In this paper we show how to simulate co-sufficient samples when the data distribution belongs to the exponential family with doubly transitive sufficient statistics. The proposed method is illustrated using the beta distribution. [ABSTRACT FROM AUTHOR]

Matrix completion aims to reconstruct a data matrix based on observations of a small number of its entries. Usually in matrix completion a single matrix is considered, which can be, for example, a rating matrix in recommendation system. However, in practical situations, data is often obtained from multiple sources which results in a collection of matrices rather than a single one. In this work, we consider the problem of collective matrix completion with multiple and heterogeneous matrices, which can be count, binary, continuous, etc. We first investigate the setting where, for each source, the matrix entries are sampled from an exponential family distribution. Then, we relax the assumption of exponential family distribution for the noise. In this setting, we do not assume any specific model for the observations. The estimation procedures are based on minimizing the sum of a goodness-of-fit term and the nuclear norm penalization of the whole collective matrix. We prove that the proposed estimators achieve fast rates of convergence under the two considered settings and we corroborate our results with numerical experiments. [ABSTRACT FROM AUTHOR]

Plasma lensing is the refraction of low-frequency electromagnetic rays due to free electrons in the interstellar medium. Although the phenomenon has a distinct similarity to gravitational lensing, particularly in its mathematical description, plasma lensing introduces other additional features, such as wavelength dependence, radial rather than tangential image distortions, and strong demagnification of background sources. Axisymmetrical models of plasma lenses have been well studied in the literature, but density distributions with more complicated shapes can provide new and exotic image configurations and increase the richness of the magnification properties. As a first step towards non-axisymmetrical distributions, we study two families of elliptical plasma lens, softened power law, and exponential plasma distributions. We perform numerical studies on each lens model, and present them over a parameter space. In addition to deriving elliptical plasma lens formulae, we also investigate the number of critical curves that the lens can produce by studying the lens parameter space, in particular the dependence on the lensing ellipticity. We find that the introduction of ellipticity into the plasma distribution can enhance the lensing effects as well as the complexity of the magnification map. [ABSTRACT FROM AUTHOR]

The lasso has been studied extensively as a tool for estimating the coefficient vector in the high-dimensional linear model; however, considerably less is known about estimating the error variance in this context. In this paper, we propose the natural lasso estimator for the error variance, which maximizes a penalized likelihood objective. A key aspect of the natural lasso is that the likelihood is expressed in terms of the natural parameterization of the multi-parameter exponential family of a Gaussian with unknown mean and variance. The result is a remarkably simple estimator of the error variance with provably good performance in terms of mean squared error. These theoretical results do not require placing any assumptions on the design matrix or the true regression coefficients. We also propose a companion estimator, called the organic lasso, which theoretically does not require tuning of the regularization parameter. Both estimators do well empirically compared to pre-existing methods, especially in settings where successful recovery of the true support of the coefficient vector is hard. Finally, we show that existing methods can do well under fewer assumptions than previously known, thus providing a fuller story about the problem of estimating the error variance in high-dimensional linear models. [ABSTRACT FROM AUTHOR]

Scientists use high-dimensional measurement assays to detect and prioritize regions of strong signal in spatially organized domain. Examples include finding methylation-enriched genomic regions using microarrays, and active cortical areas using brain-imaging. The most common procedure for detecting potential regions is to group neighboring sites where the signal passed a threshold. However, one needs to account for the selection bias induced by this procedure to avoid diminishing effects when generalizing to a population. This article introduces pin-down inference, a model and an inference framework that permit population inference for these detected regions. Pin-down inference provides nonasymptotic point and confidence interval estimators for the mean effect in the region that account for local selection bias. Our estimators accommodate nonstationary covariances that are typical of these data, allowing researchers to better compare regions of different sizes and correlation structures. Inference is provided within a conditional one-parameter exponential family per region, with truncations that match the selection constraints. A secondary screening-and-adjustment step allows pruning the set of detected regions, while controlling the false-coverage rate over the reported regions. We apply the method to genomic regions with differing DNA-methylation rates across tissue. Our method provides superior power compared to other conditional and nonparametric approaches. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

In the evaluation of treatment effects, it is of major policy interest to know if the treatment is beneficial for some and harmful for others, a phenomenon known as qualitative interaction. We formulate this question as a multiple testing problem with many conservative null p-values, in which the classical multiple testing methods may lose power substantially. We propose a simple technique—conditioning—to improve the power. A crucial assumption we need is uniform conservativeness, meaning for any conservative p-value p, the conditional distribution (p/τ) | p ⩽ τ is stochastically larger than the uniform distribution on (0, 1) for any τ. We show this property holds for one-sided tests in a one-dimensional exponential family (e.g., testing for qualitative interaction) as well as testing |μ| ⩽ η using a statistic Y ∼ N(μ, 1) (e.g., testing for practical importance with threshold η). We propose an adaptive method to select the threshold τ. Our theoretical and simulation results suggest that the proposed tests gain significant power when many p-values are uniformly conservative and lose little power when no p-value is uniformly conservative. We apply our method to two educational intervention datasets. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

We propose a data-driven approach to quantify the uncertainty of models constructed by kernel methods. Our approach minimizes the needed distributional assumptions, hence, instead of working with, for example, Gaussian processes or exponential families, it only requires knowledge about some mild regularity of the measurement noise, such as it is being symmetric or exchangeable. We show, by building on recent results from finite-sample system identification, that by perturbing the residuals in the gradient of the objective function, information can be extracted about the amount of uncertainty our model has. Particularly, we provide an algorithm to build exact, non-asymptotically guaranteed, distribution-free confidence regions for ideal, noise-free representations of the function we try to estimate. For the typical convex quadratic problems and symmetric noises, the regions are star convex centered around a given nominal estimate, and have efficient ellipsoidal outer approximations. Finally, we illustrate the ideas on typical kernel methods, such as LS-SVC, KRR, ε -SVR and kernelized LASSO. [ABSTRACT FROM AUTHOR]

Let m (k) denote the maximum number of edges in a non-extendable, intersecting k-graph. Erdős and Lovász proved that m (k) ≤ kk. For k ≥ 625 we prove m(k)< kk・e− k1/4/6. [ABSTRACT FROM AUTHOR]