Journal of Statistical Planning and Inference最新文献

The construction of objective priors is, at best, challenging for multidimensional parameter spaces. A common practice is to assume independence and set up the joint prior as the product of marginal distributions obtained via “standard” objective methods, such as Jeffreys or reference priors. However, the assumption of independence a priori is not always reasonable, and whether it can be viewed as strictly objective is still open to discussion. In this paper, by extending a previously proposed objective approach based on scoring rules for the one dimensional case, we propose a novel objective prior for multidimensional parameter spaces which yields a dependence structure. The proposed prior has the appealing property of being proper and does not depend on the chosen model; only on the parameter space considered.

Classical functional linear regression models the relationship between a scalar response and a functional covariate, where the coefficient function is assumed to be identical for all subjects. In this paper, the classical model is extended to allow heterogeneous coefficient functions across different subgroups of subjects. The greatest challenge is that the subgroup structure is usually unknown to us. To this end, we develop a penalization-based approach which innovatively applies the penalized fusion technique to simultaneously determine the number and structure of subgroups and coefficient functions within each subgroup. An effective computational algorithm is derived. We also establish the oracle properties and estimation consistency. Extensive numerical simulations demonstrate its superiority compared to several competing methods. The analysis of an air quality dataset leads to interesting findings and improved predictions.

The fixed-X knockoff filter is a flexible framework for variable selection with false discovery rate (FDR) control in linear models with arbitrary design matrices (of full column rank) and it allows for finite-sample selective inference via the Lasso estimates. In this paper, we extend the theory of the knockoff procedure to tests with composite null hypotheses, which are usually more relevant to real-world problems. The main technical challenge lies in handling composite nulls in tandem with dependent features from arbitrary designs. We develop two methods for composite inference with the knockoffs, namely, shifted ordinary least-squares (S-OLS) and feature-response product perturbation (FRPP), building on new structural properties of test statistics under composite nulls. We also propose two heuristic variants of S-OLS method that outperform the celebrated Benjamini–Hochberg (BH) procedure for composite nulls, which serves as a heuristic baseline under dependent test statistics. Finally, we analyze the loss in FDR when the original knockoff procedure is naively applied on composite tests.

Supersaturated design (SSD) plays an important role in screening factors. $E\left(f_{NOD}\right)$ criterion is one of the most widely used criteria to evaluate multi-level and mixed-level SSDs. This paper provides some methods to construct multi-level $E\left(f_{NOD}\right)$ optimal SSDs with general run sizes, which can also be extended to construct mixed-level SSDs. The main idea of these methods is combining two processed generalized Hadamard matrices with the expansive replacement method. These proposed methods are easy to perform. Besides, the non-orthogonality between any two columns of the resulting SSDs is well controlled by that of the source designs. Some illustrative examples are given and several new SSDs are provided in this paper.

A Bayesian estimator aiming at improving the conditional MLE is proposed by introducing a pair of priors. After explaining the conditional MLE by the posterior mode under a prior, we define a promising estimator by the posterior mean under a corresponding prior. The prior is asymptotically equivalent to the reference prior in familiar models. Advantages of the present approach include two different optimality properties of the induced estimator, the ease of various extensions and the possible treatments for a finite sample size. The existing approaches are discussed and critiqued.

We develop $E$-variables for testing whether two or more data streams come from the same source or not, and more generally, whether the difference between the sources is larger than some minimal effect size. These $E$-variables lead to exact, nonasymptotic tests that remain safe, i.e., keep their type-I error guarantees, under flexible sampling scenarios such as optional stopping and continuation. In special cases our $E$-variables also have an optimal ‘growth’ property under the alternative. While the construction is generic, we illustrate it through the special case of $k\times 2$ contingency tables, i.e. $k$ Bernoulli streams, allowing for the incorporation of different restrictions on the composite alternative. Comparison to $p$-value analysis in simulations and a real-world 2 × 2 contingency table example show that $E$-variables, through their flexibility, often allow for early stopping of data collection — thereby retaining similar power as classical methods — while also retaining the option of extending or combining data afterwards.

Three likelihood approaches to estimation under informative sampling are compared using a special case for which analytic expressions are possible to derive. An independent and identically distributed population of values of a variable of interest is drawn from a gamma distribution, with the shape parameter and the population size both assumed to be known. The sampling method is selection with probability proportional to a power of the variable with replacement, so that duplicate sample units are possible. Estimators of the unknown parameter, variance estimators and asymptotic variances of the estimators are derived for maximum likelihood, sample likelihood and pseudo-likelihood estimation. Theoretical derivations and simulation results show that the efficiency of the sample likelihood approaches that of full maximum likelihood estimation when the sample size $n$ tends to infinity and the sampling fraction $f$ tends to zero. However, when $n$ tends to infinity and $f$ is not negligible, the maximum likelihood estimator is more efficient than the other methods because it takes the possibility of duplicate sample units into account. Pseudo-likelihood can perform much more poorly than the other methods in some cases. For the special case when the superpopulation is exponential and the selection is probability proportional to size, the anticipated variance of the pseudo-likelihood estimate is infinite.

The two-component mixture model with known background density, unknown signal density, and unknown mixing proportion has been studied in many contexts. One such context is multiple testing, where the background and signal densities describe the distribution of the $p$-values under the null and alternative hypotheses, respectively. In this paper, we consider the log-concave MLE of the signal density using the estimator of Patra & Sen (2016) for the mixing probability. We show that it is consistent and converges at the global rate $n^{-2/5}$. An EM-algorithm in combination with an active set algorithm implemented in the R-package logcondens was used to compute the log-concave MLE. When one is interested in estimation at a fixed point, a conjecture is made about the limit distribution of our estimator. The performance of our method is assessed through a simulation study.

The parameter space of nonnegative trigonometric sums (NNTS) models for circular data is the surface of a hypersphere; thus, constructing regression models for a circular-dependent variable using NNTS models can comprise fitting great (small) circles on the parameter hypersphere that can identify different regions (rotations) along the great (small) circle. We propose regression models for circular- (angular-) dependent random variables in which the original circular random variable, which is assumed to be distributed (marginally) as an NNTS model, is transformed into a linear random variable such that common methods for linear regression can be applied. The usefulness of NNTS models with skewness and multimodality is shown in examples with simulated and real data.

A scalar discrete or continuous time process is reducible to stationarity (RWS) if its transform by some smooth time change is weakly stationary. Different issues linked to this notion are here investigated for autoregressive (AR) models. AR models are understood in a large sense and may have time-varying coefficients. In the continuous time case the innovation may be of the semi-martingale type–such as compound Poisson noise; in the discrete case, the noise may not be Gaussian.

Necessary and sufficient conditions for scalar AR models to be RWS are investigated, with explicit formulas for the time changes. Stationarity reduction issues for discrete sequences sampled from time continuous AR processes are also considered. Several types of time changes, RWS processes and sequences are studied with examples and simulation, including the classical multiplicative stationary AR models.