Journal of Statistical Planning and Inference最新文献

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.

This study proposes a distribution-free Bayesian procedure that detects infinite degrees of stochastic dominance (SD$\infty$) between two random outcomes and then seeks a finite degree $k\ge 1$ of stochastic dominance (SD$k$). Based on small samples, we construct four-choice Bayesian tests by combining an encompassing prior Bayesian model with the Dirichlet process priors that discriminate between SD$\infty$ and SD$k$ of one random variable over the other with non-dominance or equality between them. We use Monte Carlo simulations to evaluate the novel Bayesian tests for SD$k$ and SD$\infty$ and compare them to the subsampling and bootstrap significance tests for SD$k$. Our simulation shows that the Bayesian tests for SD$k$ outperform the significance tests for small samples, especially for detecting non-stochastic dominance. This study shows that the test for SD$\infty$ is an accurate decision-making tool when using small samples.

In this paper, we introduce weighted bootstrap algorithms for both non-degenerate and degenerate two-sample $U$-statistics with arbitrary degrees. For the non-degenerate case, weighted bootstrap with dependent weights is introduced as a generalization of Efron’s conventional bootstrap. In addition, two weighted bootstrap procedures with independent productive weights and independent additive weights are proposed under non-degeneracy. More importantly, we extend the weighted bootstrap method to two-sample $U$-statistics under the degeneracy of order 2 with a novel construction of random weights. Theoretical supports of the proposed weighted bootstrap procedures under non-degeneracy and degeneracy of order 2 are established. Numerical studies illustrate that the proposed approaches are feasible and effective for statistical inferences.