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A class of ranked sample methodologies is presented, which unifies the existing methods of ranked set sampling and judgment post-stratification. This general class contains many new, promising methods and allows future ranked sampling techniques to be developed with greater scope.

We revisit cumulative slicing estimation (CUME; Zhu et al., 2010) from a different perspective to gain more insights, then refine its performance by incorporating the intra-slice covariances. We also prove that our new method, under some conditions, is more comprehensive than CUME.

Li and Zhou (2006) established that an investor, following an unconstrained mean-variance strategy, will achieve its discounted targeted wealth with a probability greater than 80%. Surprisingly, we will show that under short-selling restrictions (i.e without the possibility of borrowing stocks) this lower bound probability still holds.

We prove some analogs of results from renewal theory for random walks in the case when there is a drift, more precisely when the mean of the k th summand equals k γ μ , k ≥ 1 , for some μ > 0 and 0 γ ≤ 1 .

In this paper the Marcinkiewicz–Zygmund inequality for mean zero independent random variables is extended to the case of nonnegative N -demimartingales. This result can be used for obtaining large deviation inequalities for nonnegative N -demimartingales as well as related complete convergence results.

Suppose that X 1 , … , X n are independent and identically N ( μ , σ 2 ) distributed, where μ and σ are unknown parameters ( μ ∈ R and σ > 0 ). We prove that the usual confidence interval for μ is admissible within a broad class of confidence intervals.

In this paper, we study 2-principal points of general location mixtures, including finite and infinite mixtures, of spherically symmetric distributions. A theorem is established that clarifies a linear subspace in which any set of 2-principal points exists.

In this paper we study the relationships between copulas of order statistics from heterogeneous samples and the marginal distributions of the parent random variables. Specifically, we study the copula of the order statistics obtained from a general random vector X = ( X 1 , X 2 , … , X n ) . We show that the copula of the order statistics from X only depends on the copula of X and on the marginal distributions of X 1 , X 2 , … , X n through an exchangeable copula and the average of the marginal distribution functions. We study in detail some relevant cases.

This paper deals with the necessary and sufficient conditions for non-interaction of the upper-sided and lower-sided EWMAs with reflecting boundaries, the average run length, the Laplace transform of the run length and some analysis under the condition of interaction.

Let { X k , k ≥ 1 } be a sequence of negatively dependent random variables with common distribution F and mean 0. Suppose that F ( x ) = 1 − F ( x ) is positive for all x and consistently varying as x → ∞ . Let { θ k , k ≥ 1 } be another sequence of random variables independent of { X k , k ≥ 1 } satisfying P ( a ≤ θ k ≤ b ) = 1 for some 0 a ≤ b ∞ , k ≥ 1 . The paper investigates large deviations for the randomly weighted sums.

In this article we examine an approximation to the carrier-borne epidemic process with both susceptible and carrier immigrations. It is shown that the approximate susceptible stochastic process is Poisson, with a mean equal to the deterministic number of susceptibles.

We obtain estimates for the best constant in the Rosenthal inequality E | ∑ i = 1 n ξ i | 2 m ⩽ C ( 2 m ) max ( ∑ i = 1 n E ξ i 2 m , ( ∑ i = 1 n E ξ i 2 ) m ) for independent random variables ξ 1 , … , ξ n with l zero first odd moments, l ⩾ 1 . The estimates are sharp in the extremal cases l = 1 and l = m , that is, in the cases of random variables with zero mean and random variables with m zero first odd moments.

Fractional factorial plans represented by orthogonal arrays of strength two are known to be universally optimal under a model that includes the mean and all main effects, when all other factorial effects are assumed to be absent. However, if the number of factors in the experiment is smaller than the number of columns of a saturated or, tight orthogonal array and the experimenter is interested in estimating certain 2-factor interactions as well, one can possibly entertain these 2-factor interactions in the model apart from the mean and all main effects. The problem then is to allocate factors to the columns of the orthogonal array, so that the user-specified 2-factor interactions, in addition to the mean and the main effects, are optimally estimable. This problem is investigated in this paper with reference to the orthogonal array OA ( 2 n , 2 n - 1 , 2 , 2 ) , which exists for every integer n ⩾ 2 . A method for the allocation of factors to factor representations is proposed that ensures the optimal estimation of the mean, all main effects and specified 2-factor interactions. The method is illustrated by considering in detail the cases n = 3 , 4 .

In this paper, we discuss moving-average process X k = ∑ i = - ∞ ∞ a i + k ɛ i , where { ɛ i ; - ∞ i ∞ } is a doubly infinite sequence of i.i.d random variables with mean zeros and finite variances, { a i ; - ∞ i ∞ } is an absolutely summable sequence of real numbers. Set S n = ∑ k = 1 n X k , n ⩾ 1 . Suppose E | ɛ 1 | 3 ∞ , we prove that, if E | ɛ 1 | r ∞ , for 1 p 2 and r > 1 + p / 2 , then lim e ↘ 0 e 2 ( r - p ) / ( 2 - p ) - 1 ∑ n = 1 ∞ n r / p - 2 - 1 / p E { | S n | - e n 1 / p } + = p ( 2 - p ) ( r - p ) ( 2 r - p - 2 ) E | Z | 2 ( r - p ) / ( 2 - p ) , where Z has a normal distribution with mean 0 and variance τ 2 = σ 2 ( ∑ i = - ∞ ∞ a i ) 2 .

Recently, proportional mean remaining life (PMRL) model has been introduced in the literature for modelling and analysing failure time data. In this paper, some properties of PMRL model related to reliability analysis are investigated. Closure properties of a few aging classes and those of partial orders under the proportional mean residual life model are discussed.

The paper concerns testing the hypothesis about the mean H 0 : μ = μ 0 against the one-sided alternative in normal populations. For the sample size n = 4 ( 1 ) 20 , two-sided 95% confidence intervals are given for the probability that the test of size 0.05 detects the difference Δ = | μ - μ 0 | .

This paper establishes two converse comparison theorems for generators of backward stochastic differential equations (BSDEs), one is for those generators which are mean square locally bounded, the other is for general generators of BSDEs.

Two different formulations on the moments of Rand's C appear incompatible. The mean and variance of Rand's C statistic given by Fowlkes and Mallows (J. Amer Statist. Assoc. 78 (1983) 553) are special cases of the mean and variance of C given by DuBien and Warde (ASA proceedings of the social statistics section (1981) 309).

Let X be a nonnegative random variable with mean μ ⩽∞, and let T X be the total time on test transform of X . It has been observed in the literature that the inverse of T X is a distribution function with support (0, μ ). In this paper, we identify the random variable that has this distribution, and we study some of its properties. We also study an analogous random variable that is based on what is called the excess wealth transform.

Let ζ t , t⩾0 , be a process taking nonnegative values, T r = inf {t>0;ζ t >r}, r>0 , and ψ a nondecreasing function. An interesting question is: Is it possible to bound Eψ ( T r ) above and below by expectations of functions of ζ t ? We answer this question and give the desired upper and lower bounds.

Leybourne et al. (J. Econom. 87 (1998) 191) have shown the Dickey–Fuller (J. Amer. Statist. Assoc. 74 (1979) 427) unit root test to suffer from severe oversizing in the presence of level breaks. In this paper it is shown that recursive mean adjustment can correct this distortion, even for large breaks.

Simultaneous lower bounds (SLB) for the isotonic contrasts in normal means are obtained. In particular a SLB for the range is given. These SLBs are obtained from the one-sided max t test. It is then generalized to obtain simultaneous upper bounds for the responses at lower levels. Under the assumption of the convexity of the response curve at lower levels the upper bounds are further improved. The method compares very well with other available methods numerically as well as in real examples.

Let X 1 , X 2 , … be i.i.d. mean zero random variables and S n = X 1 + ⋯ + X n . For any stopping time T w.r.t. { X n } let T denote a copy of T which is independent of { X n } . We exhibit a family of distributions and stopping times T such that E max 1 ≤ n ≤ T | ∑ 1 ≤ i ≠ j ≤ n X i X j | ∞ and yet E max 1 ≤ n ≤ T | ∑ 1 ≤ i ≠ j ≤ n X i X j | = ∞ .

By using the technique proposed in Ibragimov and Zeitouni, [(1997), Trans. Amer. Math. Soc. 349, 2427–2441], we derive an exact formula for the mean number of complex roots of a complex random polynomial. The explicit evaluation of the average density is obtained in the case of multivariate normal coefficients and its correspondence with the early Hammersley result is shown.

Linear combination of two statistics is considered when some prior knowledge about their expectation and complete knowledge about their joint dispersion is available. The considered setup is more general than those already known in the literature, in the sense that the expectation of one of the statistics is not necessarily assumed to be completely known when estimation of the expectation of the other statistic is of interest.

We prove an almost sure version of a maximum limit theorem using logarithmic means and show that essentially only logarithmic means work as it is the case for almost sure central limit theorems.

We prove the asymptotic normality of the trimmed mean, obtained by deleting the data which is further away from a parameter of location θ n . To get this trimmed mean, equivariant by rotations, dilations and translations, we choose θ n in a class of multivariate parameters of location, which are equivariant by these transformations. Given the data X 1 , … , X n , we take as θ n , the value such that n −1 ∑ j=1 n h(|X j −θ n |)= inf n −1 ∑ j=1 n h(|X j −θ|), where h is a nondecreasing function and | x | is the Euclidean distance in B d . This estimator θ n is equivariant by rotations and translations. If h ( x ) = x p , θ n is also equivariant by dilations.

This paper considers the likelihood ratio tests for homogeneity of normal means versus order-restricted alternatives. Symmetry properties of the test statistics with respect to the parameter vector about a linear space are studied.

We consider estimating the mean of a stochastic process at a single time point t from a random sample of processes subject to censoring on the right. A very simple estimator is shown to converge a.s.

Let X ∼ N(θ,1), where θ ϵ [−m, m], for some m > 0, and consider the problem of estimating θ with quadratic loss. We show that the Bayes estimator δm, corresponding to the uniform prior on [−m, m], dominates δ0 (x) = x on [−m, m] and it also dominates the MLE over a large part of the parameter interval. We further offer numerical evidence to suggest that δm has quite satisfactory risk performance when compared with the minimax estimators proposed by Casella and Strawderman (1981) and the estimators proposed by Bickel (1981).

For predicting a mean in a finite population, two predictors are compared in large samples under some superpopulation models. The study is extended to investigate the effects of measurement errors on the predictors.

Let (Y1, Z1),…,(YN, ZN) be i.i.d. pairs of independent random variables such that Yi is exponentially distributed with unknown mean 1/λ and Zi has an unknown distribution function F. Let Xi ≔ min(Yi, Zi). Under certain assumptions on F an estimator TN(X1,…,XN) for 1/λ is constructed which is consistent and asymptotically normal.