Statistics & Probability Letters

Items from 1 to 17 out of 17 results

article

A proof of the transfer-current theorem in absence of reversibility

L. Avena, A. Gaudillière

Statistics & Probability Letters > 2018 > 142 > C > 17-22

The transfer-current theorem is a well-known result in probability theory stating that edges in a uniform spanning tree of an undirected graph form a determinantal process with kernel interpretable in terms of flows. Its original derivation due to Burton and Pemantle (1993) is based on a clever induction using comparison of random walks with electrical networks. Several variants of this celebrated...

article

Semi-functional partial linear quantile regression

Hui Ding, Zhiping Lu, Jian Zhang, Riquan Zhang

Statistics & Probability Letters > 2018 > 142 > C > 92-101

Semi-functional partial linear model is a flexible model in which a scalar response is related to both functional covariate and scalar covariates. We propose a quantile estimation of this model as an alternative to the least square approach. We also extend the proposed method to kNN quantile method. Under some regular conditions, we establish the asymptotic normality of quantile estimators of regression...

article

The inverse survival function for multivariate distributions and its application to the product moment

Haruhiko Ogasawara

Statistics & Probability Letters > 2018 > 142 > C > 71-76

The inverse function of the joint survival function for continuous non-negative multivariate distributions is defined with or without change of variables. This inverse function gives three alternative expectation formulas for a non-negative random vector.

article

A uniform L 1 law of large numbers for functions of i.i.d. random variables that are translated by a consistent estimator

Pierre Lafaye de Micheaux, Frédéric Ouimet

Statistics & Probability Letters > 2018 > 142 > C > 109-117

We develop a new L 1 law of large numbers where the i th summand is given by a function h ( ⋅ ) evaluated at X i − θ n , and where θ n ≗ θ n ( X 1 , X 2 , … , X n ) is an estimator converging in probability to some parameter θ ∈ R . Under broad technical conditions, the convergence is shown to hold uniformly in the set of estimators interpolating...

article

Weak and one-sided strong laws for random variables with infinite mean

André Adler, Anthony G. Pakes

Statistics & Probability Letters > 2018 > 142 > C > 8-16

Let a j be positive weight constants and X j be independent non-negative random variables ( j = 1 , 2 , … ) and S n ( a ) = ∑ i = 1 n a i X i . If the X j have the same relatively stable distribution, then under mild conditions there exist constants b n → ∞ such that W ¯ n ( a ) = b n − 1 S n ( a ) → ...

article

Strong modified transportation cost inequalities on k -concave probability measures with heavy tails

Ying Ding, Xinsheng Zhang, Longxiang Fang

Statistics & Probability Letters > 2018 > 142 > C > 30-38

In this paper, we study strong modified transportation cost inequalities for k -concave probability measures with heavy tails. We provide the polynomial-type concentration, dual representation, and tensorization properties for this kind of inequalities. And we provide integral sufficient conditions for k − concave measures ( − 1 < k < 0 ) on R to satisfy such inequalities.

article

The necklace process: A generating function approach

Benjamin Hackl, Helmut Prodinger

Statistics & Probability Letters > 2018 > 142 > C > 57-61

The “necklace process”, a procedure constructing necklaces of black and white beads by randomly choosing positions to insert new beads (whose color is uniquely determined based on the chosen location), is revisited. This article illustrates how, after deriving the corresponding bivariate probability generating function, the characterization of the asymptotic limiting distribution of the number of...

article

Comment on “Sum of squares of uniform random variables” by I. Weissman

Peter J. Forrester

Statistics & Probability Letters > 2018 > 142 > C > 118-122

The recent paper by Weissman (2017) is compared to earlier work of B. Tibken and D. Constales relating to the area of the intersection of a centred ball and cube in R n , published in the Problems and Solutions section of SIAM Review in 1997. Some recent applications of explicit formulas for the corresponding probabilities from these references, to problems in lattice reduction, and to the...

article

Granger causality between vectors of time series: A puzzling property

Umberto Triacca

Statistics & Probability Letters > 2018 > 142 > C > 39-43

Let us consider a discrete-time n -dimensional stochastic process z , with components x = ( x 1 , … , x m 1 ) ′ and y = ( y 1 , … , y m 2 ) ′ , m 1 + m 2 = n . We want to study causality relationships between the variables in x and y . Suppose that we find that y Granger causes x . Then we would expect to be able to pick out...

article

A self-equilibrium Friedman-like urn via stochastic approximation

Shuyang Gao, Hosam M. Mahmoud

Statistics & Probability Letters > 2018 > 142 > C > 77-83

In this study, we propose a class of generalized Friedman urns with random entries. The class has the property of self-equilibrium. We prove the almost-sure convergence to the equilibrium point of this entire class by the method of stochastic approximation. We develop a central limit theorem for the proportion of white balls through the convergence theorem of stochastic approximation algorithms. We...

article

Stochastic differential equations driven by fractional Brownian motion

Liping Xu, Jiaowan Luo

Statistics & Probability Letters > 2018 > 142 > C > 102-108

In this paper, we are concerned with a class of stochastic differential equations driven by fractional Brownian motion with Hurst parameter 1 ∕ 2 < H < 1 . By approximation arguments and a comparison theorem, we prove the existence of solutions to this kind of equations driven by fractional Brownian motion under the linear growth condition. Subsequently, by employing Skorokhod’s selection theorem,...

article

Gradient and stability estimates of heat kernels for fractional powers of elliptic operator

Yong Chen, Yaozhong Hu, Zhi Wang

Statistics & Probability Letters > 2018 > 142 > C > 44-49

Gradient and stability type estimates of heat kernel associated with fractional power of a uniformly elliptic operator are obtained. L p -operator norm of semigroups associated with fractional power of two uniformly elliptic operators are also obtained.

article

A note on weak convergence of general halfspace depth trimmed means

Jin Wang

Statistics & Probability Letters > 2018 > 142 > C > 50-56

In this note, we restudy the general halfspace depth trimmed means and establish the weak convergence of their sample versions, which extends the result of Massé (2009) for dimensions one and two to any dimension. The asymptotic distribution of the Donoho (1982) halfspace depth trimmed mean is obtained as a special case and concretized for elliptically symmetric distributions.

article

On the distribution of extended CIR model

Qidi Peng, Henry Schellhorn

Statistics & Probability Letters > 2018 > 142 > C > 23-29

We study the probability distribution of the interest rate in the extended Cox–Ingersoll–Ross model, where all the parameters are time-varying. We show that the distribution can be represented as that of a convergent series of weighted independent central and noncentral chi-square random variables. Simulation algorithms and their applications to finance have been discussed.

article

A moment coboundary theorem for C [ 0 , 1 ] -valued random fields

Steven T. Morrow

Statistics & Probability Letters > 2018 > 142 > C > 62-70

K. Schmidt (1977) proved that if a strictly stationary sequence of real-valued random variables has the property that the family of distributions of its partial sums is tight, then the sequence is a coboundary, meaning that it is equal to the successive differences of another strictly stationary sequence. The result here is a coboundary-type theorem for C [ 0 , 1 ] -valued random fields (not necessarily...

article

Dynamic IFR concepts for coherent systems

M. Burkschat, F.J. Samaniego

Statistics & Probability Letters > 2018 > 142 > C > 1-7

A conditional IFR property for a coherent system with i failed components, and a uniform IFR property, are introduced and studied. The class of mixed systems with the uniform IFR property is characterized. A pair of examples illustrate our findings.

article

Fractional Lévy Cox–Ingersoll–Ross and Jacobi processes

Holger Fink, Georg Schlüchtermann

Statistics & Probability Letters > 2018 > 142 > C > 84-91

We prove a general Picard–Lindelöf-type framework for stochastic differential equations driven by Mandelbrot–Van Ness fractional Lévy processes. This allows us to derive the existence of a fractional Lévy Cox–Ingersoll–Ross and Jacobi model with almost surely positive, respectively bounded, samples paths.

Filter options

Number:
C
Volume:
142
Year:
2018

Publication date

Set your own date range

Keywords

K -CONCAVE PROBABILITY MEASURES (1)
P -NORM (1)
AGING (1)
ALTERNATIVE EXPECTATION FORMULAS (1)
BIVARIATE GENERATING FUNCTION (1)
CENTRAL LIMIT THEOREM (1)
COBOUNDARY (1)
COHERENT SYSTEM (1)
COMPARISON THEOREM (1)
COX–INGERSOLL–ROSS PROCESS (1)
DETERMINANTAL PROCESSES (1)
DUAL REPRESENTATION (1)
ECIR MODEL (1)
FINITE NETWORKS (1)
FRACTIONAL BROWNIAN MOTION (1)
FRACTIONAL LÉVY PROCESS (1)
FRACTIONAL POWERS (1)
FUNCTIONAL DATA ANALYSIS (1)
GEOMETRIC PROBABILITY (1)
GRADIENT ESTIMATES (1)
GRANGER CAUSALITY (1)
HALFSPACE DEPTH (1)
HILBERT SPACES (1)
IFR (1)
INVERSE FUNCTION (1)
JACOBI PROCESS (1)
LATTICE REDUCTION (1)
LONG MEMORY (1)
LYAPUNOV EXPONENTS (1)
M-ESTIMATORS (1)
MIXED SYSTEM (1)
MULTIVARIATE ANALYSIS (1)
MULTIVARIATE TRIMMED MEAN (1)
NBU (1)
NECKLACE PROCESS (1)
NONCENTRAL CHI-SQUARE (1)
NUMERICAL INTEGRATION (1)
PARTIAL LINEAR (1)
POLYNOMIAL-TYPE CONCENTRATION INEQUALITIES (1)
PÓLYA URN (1)
QUANTILE REGRESSION (1)
QUASI-POWER THEOREM (1)
RANDOM FIELD (1)
REGULAR VARIATION (1)
RELATIVE STABILITY (1)
SCORE FUNCTION (1)
SERIES REPRESENTATION (1)
SIGNATURE (1)
SPANNING FORESTS (1)
STABILITY (1)
STOCHASTIC APPROXIMATION (1)
STOCHASTIC DIFFERENTIAL EQUATION (1)
STOCHASTIC RECURRENCE (1)
STRONG MODIFIED TRANSPORTATION COST INEQUALITIES (1)
SUBORDINATION (1)
SURVIVAL FUNCTION (1)
TAYLOR EXPANSION (1)
TENSORIZATION (1)
TIME SERIES (1)
TRANSFER CURRENT THEOREM (1)
UNIFORM LAW OF LARGE NUMBERS (1)
UNIFORM SPANNING TREE (1)
WEAK CONVERGENCE (1)
WEIGHTED LAWS OF LARGE NUMBERS (1)
more

INFONA - science communication portal

Statistics & Probability Letters

Add recipient

Sending message cancelled

Are you sure you want to cancel sending this message?

Send message

Filter options

Publication date

Date range setting

Set the date range to filter the displayed results. You can set a starting date, ending date or both. You can enter the dates manually or choose them from the calendar.

Keywords

Reporting an error / abuse

Sending the report failed

Accessibility options