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**Term(s):**1998**Results:**40**Sorted by:****Page: 1 2 Next**

**Title:**A lattice path model for the Bessel polynomials**Author(s):**Pitman, Jim; **Date issued:**Mar 1998

http://nma.berkeley.edu/ark:/28722/bk0000n225b (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n226w (PostScript) **Abstract:**The (n-1)th Bessel polynomial is represented by an exponential generating function derived from the number of returns to $0$
of a sequence with 2n increments of +1 or -1 which starts and ends at 0.**Keyword note:**Pitman__Jim**Report ID:**551**Relevance:**100

**Title:**Brownian motion, bridge, excursion, and meander characterized by sampling at independent uniform times**Author(s):**Pitman, Jim; **Date issued:**Feb 1998**Abstract:**For a random process $X$ consider the random vector defined by the values of $X$ at times $0 < U_(n,1) < ... < U_(n,n) < 1$
and the minimal values of $X$ on each of the intervals between consecutive pairs of these times, where the $U_(n,i)$ are the
order statistics of $n$ independent uniform $(0,1)$ variables, independent of $X$. The joint law of this random vector is
explicitly described when $X$ is a Brownian motion. Corresponding results for Brownian bridge, excursion, and meander are
deduced by appropriate conditioning. These descriptions yield numerous new identities involving the laws of these processes,
and simplified proofs of various known results, including Aldous's characterization of the random tree constructed by sampling
the excursion at $n$ independent uniform times, Vervaat's transformation of Brownian bridge into Brownian excursion, and Denisov's
decomposition of the Brownian motion at the time of its minimum into two independent Brownian meanders. Other consequences
of the sampling formulae are Brownian representions of various special functions, including Bessel polynomials, some hypergeometric
polynomials, and the Hermite function. Various combinatorial identities involving random partitions and generalized Stirling
numbers are also obtained.**Pub info:**Electronic Journal of Probability, Vol. 4 (1999) Paper no. 11, pages 1-33**Keyword note:**Pitman__Jim**Report ID:**545**Relevance:**100

**Title:**Continuum-sites stepping-stone models, coalescing exchangeable partitions, and random trees**Author(s):**Donnelly, Peter; Evans, Steven N.; Fleischmann, Klaus; Kurtz, Thomas G.; Zhou, Xiaowen; **Date issued:**Nov 1998

http://nma.berkeley.edu/ark:/28722/bk0000n3x7v (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n3x8d (PostScript) **Abstract:**Analogues of stepping--stone models are considered where the site--space is continuous, the migration process is a general
Markov process, and the type--space is infinite. Such processes were defined in previous work of the second author by specifying
a Feller transition semigroup in terms of expectations of suitable functionals for systems of coalescing Markov processes.
An alternative representation is obtained here in terms of a limit of interacting particle systems. It is shown that, under
a mild condition on the migration process, the continuum--sites stepping--stone process has continuous sample paths. The
case when the migration process is Brownian motion on the circle is examined in detail using a duality relation between coalescing
and annihilating Brownian motion. This duality relation is also used to show that a random compact metric space that is naturally
associated to an infinite family of coalescing Brownian motions on the circle has Hausdorff and packing dimension both almost
surely equal to $\frac(1)(2)$ and, moreover, this space is capacity equivalent to the middle--1/2 Cantor set (and hence also
to the Brownian zero set).**Keyword note:**Donnelly__Peter Evans__Steven_N Fleischmann__Klaus Kurtz__Thomas_G Zhou__Xiaowen**Report ID:**540**Relevance:**100

**Title:**The distribution of local times of a Brownian bridge**Author(s):**Pitman, Jim; **Date issued:**Nov 1998

http://nma.berkeley.edu/ark:/28722/bk0000n278k (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n2794 (PostScript) **Abstract:**L\'evy's approach to Brownian local times is used to give a simple derivation of a formula of Borodin which determines the
distribution of the local time at level x up to time 1 for a Brownian bridge of length 1 from 0 to b. A number of identities
in distribution involving functionals of the bridge are derived from this formula. A stationarity property of the bridge local
times is derived by a simple path transformation, and related to Ray's description of the local time process of Brownian motion
stopped at an independent exponential time.**Pub info:**S\'{e}minaire de Probabilit\'{e}s XXXIII, 388-394, Lecture Notes in Math. 1709, Springer, 1999**Keyword note:**Pitman__Jim**Report ID:**539**Relevance:**100

**Title:**The Histogram Method for Nonlinear Mixed Effects Models**Author(s):**Zhiyu, Ge; Bickel, Peter J.; Rice, John A.; **Date issued:**October 1998**Keyword note:**Zhiyu__Ge Bickel__Peter_John Rice__John_Andrew**Report ID:**538**Relevance:**100

**Title:**Statistical Controversies in Census 2000**Author(s):**Brown, Lawrence D.; Eaton, Morris L.; Freedman, David A.; Klein, Stephen P.; Olshen, Richard A.; Wachter, Kenneth W.; Wells, Martin T.; Ylvisaker, Donald; **Date issued:**Oct 1998

http://nma.berkeley.edu/ark:/28722/bk0000n3m76 (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n3m8r (PostScript) **Abstract:**This paper is a discussion of Census 2000, focusing on planned use of sampling techniques for non-response followup and adjustment.
Past experience with adjustment methods suggests that the design for Census 2000 is quite risky.**Keyword note:**Brown__Lawrence_D Eaton__Morris_L Freedman__David Klein__Stephen_P Olshen__Richard_A Wachter__Kenneth Wells__Martin_T Ylvisaker__Donald**Report ID:**537**Relevance:**100

**Title:**Half&Half Bagging and Hard Boundary Points**Author(s):**Breiman, Leo; **Date issued:**Sep 1998

http://nma.berkeley.edu/ark:/28722/bk0000n3b95 (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n3c0q (PostScript) **Abstract:**Half&half bagging is a method for generating an ensemble of classifiers and combining them that does not resemble any method
proposed to date. It is simple and intuitive in concept and its accuracy is very competitive with Adaboost. Certain instances
that are used repeatedly turn out to be located in the boundaries between classes and we refer to these as hard boundary points.
The effectiveness of half&half bagging leads to the conjecture that the accuracy of any combination method is based on its
ability to locate the hard boundary points.**Keyword note:**Breiman__Leo**Report ID:**535**Relevance:**100

**Title:**The law of the maximum of a Bessel bridge**Author(s):**Pitman, Jim; Yor, Marc; **Date issued:**Oct 1998**Abstract:**Let $M_d$ be the maximum of a standard Bessel bridge of dimension $d$. A series formula for $P(M_d < a)$ due to Gikhman and
Kiefer for $d = 1,2, \ldots$ is shown to be valid for all real $d >0$. Various other characterizations of the distribution
of $M_d$ are given, including formulae for its Mellin transform, which is an entire function. The asymptotic distribution
of $M_d$ as is described both as $d$ tends to $\infty$ and as $d$ tends to $0$. Keywords: Brownian bridge, Brownian excursion,
Brownian scaling, local time, Bessel process, zeros of Bessel functions, Riemann zeta function.**Pub info:**Electronic Journal of Probability, Vol. 4 (1999) Paper no. 15, pages 1-35**Keyword note:**Pitman__Jim Yor__Marc**Report ID:**534**Relevance:**100

**Title:**tochastic optimization methods for fitting polyclass and feed-forward neural network models**Author(s):**Stone, C. J.; Kooperberg, C.; **Date issued:**August 1998**Pub info:**Submitted to Journal of Computational and Graphical Statistics.**Keyword note:**Stone__Charles Kooperberg__Charles_Louis**Report ID:**533**Relevance:**100

**Title:**Path decompositions of a Brownian bridge related to the ratio of its maximum and amplitude**Author(s):**Pitman, Jim; Yor, Marc; **Date issued:**Aug 1998

http://nma.berkeley.edu/ark:/28722/bk0000n377h (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n3782 (PostScript) **Abstract:**We give two new proofs of Csaki's formula for the law of the ratio 1-Q of the maximum relative to the amplitude (i.e. the
maximum minus minimum) for a standard Brownian bridge. The second of these proofs is based on an absolute continuity relation
between the law of the Brownian bridge restricted to the event (Q < v) and the law of a process obtained by a Brownian scaling
operation after back-to back joining of two independent three-dimensional Bessel processes, each started at v and run until
it first hits 1. Variants of this construction and some properties of the joint law of Q and the amplitude are described.**Keyword note:**Pitman__Jim Yor__Marc**Report ID:**532**Relevance:**100

**Title:**Kingman's coalescent as a random metric space**Author(s):**Evans, Steven N.; **Date issued:**Aug 1998

http://nma.berkeley.edu/ark:/28722/bk0000n264v (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n265d (PostScript) **Abstract:**Kingman's coalescent is a Markov process with state--space the collection of partitions of the positive integers. Its initial
state is the trivial partition of singletons and it evolves by successive pairwise mergers of blocks. The coalescent induces
a metric on the positive integers: the distance between two integers is the time until they both belong to the same block.
We investigate the completion of this (random) metric space. We show that almost surely it is a compact metric space with
Hausdorff and packing dimension both $1$, and it has positive capacities in precisely the same gauges as the unit interval.**Keyword note:**Evans__Steven_N**Report ID:**531**Relevance:**100

**Title:**Testing and the Method of Sieves**Author(s):**Bickel, Peter; Ritov, Ya'acov; Stoker, Thomas; **Date issued:**Jul 1998

http://nma.berkeley.edu/ark:/28722/bk0000n231n (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n2326 (PostScript) **Abstract:**This paper develops test statistics based on scores for the specification of regression in nonparametric and semiparametric
contexts. We study how different types of test statistics focus power on different directions of departure from the null
hypothesis. We consider index models as basic examples, and utilize sieves for nonparametric approximation. We examine various
goodness-of-fit statistics, including Cramer-von Mises and Kolmogorov-Smirnov forms. For a "box-style" sieve approximation,
we establish limiting distributions of these statistics. We develop a bootstrap resampling method for estimating critical
values for the test statistics, and illustrate their performance with a Monte Carlo simulation.**Keyword note:**Bickel__Peter_John Ritov__Yaacov Stoker__Thomas**Report ID:**530**Relevance:**100

**Title:**An Edgeworth expansion for the m out of n bootstrapped median.**Author(s):**Sakov, Anat; Bickel, Peter J.; **Date issued:**Jul 1998

http://nma.berkeley.edu/ark:/28722/bk0000n1w8x (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n1w9g (PostScript) **Abstract:**It is well known Singh (1981) that the bootstrap distribution of the median has the correct limiting distribution. In this
note we prove the existence of the next term in the Edgeworth expansion if the bootstrap sample size is m = o(n).**Keyword note:**Sakov__Anat Bickel__Peter_John**Report ID:**529**Relevance:**100

**Title:**A score test for linkage using identity by descent data from sibships**Author(s):**Dudoit, Sandrine; Speed, Terence P.; **Date issued:**Jul 1998

http://nma.berkeley.edu/ark:/28722/bk0000n218g (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n2191 (PostScript) **Abstract:**We consider score tests of the null hypothesis $(\rm H)_0: \theta = \frac(1)(2)$ against the alternative hypothesis $(\rm
H)_1: 0 \leq \theta < \frac(1)(2)$, based upon counts multinomially distributed with parameters $n$ and $\rho(\theta,\pi)_(
1 \times m) = \pi_(1 \times m) T(\theta)_(m \times m)$, where $T(\theta)$ is a transition matrix with $T(0) = I$, the identity
matrix, and $T(\frac(1)(2)) = (\bf 1)^T \alpha$, $(\bf 1) = (1,\ldots, 1)$. This type of testing problem arises in human genetics
when testing the null hypothesis of no linkage between a marker and a disease susceptibility gene, using identity by descent
data from families with affected members. In important cases in this genetic context, the score test is independent of the
nuisance parameter $\pi$ and is based on a widely used test statistic in linkage analysis. The proof of this result involves
embedding the states of the multinomial distribution into a continuous time Markov chain with infinitesimal generator $Q$.
The second largest eigenvalue of $Q$ and its multiplicity are key in determining the form of the score statistic. We relate
$Q$ to the adjacency matrix of a quotient graph, in order to derive its eigenvalues and eigenvectors.**Keyword note:**Dudoit__Sandrine Speed__Terry_P**Report ID:**528**Relevance:**100

**Title:**Triangle constraints for sib-pair identity by descent probabilities under a general multilocus model for disease susceptibility**Author(s):**Dudoit, Sandrine; Speed, Terence P.; **Date issued:**Jul 1998

http://nma.berkeley.edu/ark:/28722/bk0000n1w58 (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n1w6t (PostScript) **Abstract:**In this paper, we study sib-pair IBD probabilities under a general multilocus model for disease susceptibility which doesn't
assume random mating, linkage equilibrium or Hardy-Weinberg equilibrium. We derive the triangle constraints satisfied by affected,
discordant and unaffected sib-pair IBD probabilities, as well as constraints distinguishing between sharing of maternal and
paternal DNA, under general monotonicity assumptions concerning the penetrance probabilities. The triangle constraints are
valid for age and sex-dependent penetrances, and in the presence of parental imprinting. We study the parameterization of
sib-pair IBD probabilities for common models, and present examples to demonstrate the impact of non-random mating and the
necessity of our assumptions for the triangle constraints. We prove that the affected sib-pair possible triangle is covered
by the IBD probabilities of two types of models, one with fixed mode of inheritance and general mating type frequencies, the
other with varying mode of inheritance and random mating. Finally, we consider IBD probabilities at marker loci linked to
disease susceptibility loci and derive the triangle constraints satisfied by these probabilities.**Keyword note:**Dudoit__Sandrine Speed__Terry_P**Report ID:**527**Relevance:**100

**Title:**A family of random trees with random edge lengths**Author(s):**Aldous, David; Pitman, Jim; **Date issued:**Jun 1998

http://nma.berkeley.edu/ark:/28722/bk0000n3n1d (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n3n2z (PostScript) **Abstract:**We introduce a family of probability distributions on the space of trees with I labeled vertices and possibly extra unlabeled
vertices of degree 3, whose edges have positive real lengths. Formulas for distributions of quantities such as degree sequence,
shape, and total length are derived. An interpretation is given in terms of sampling from the inhomogeneous continuum random
tree of Aldous and Pitman (1998). Key words and phrases: continuum tree, enumeration, random tree, spanning tree, weighted
tree, Cayley's multinomial expansion.**Pub info:**Random Structures and Algorithms Vol 15, 176-195 (1999)**Keyword note:**Aldous__David_J Pitman__Jim**Report ID:**526**Relevance:**100

**Title:**Inhomogeneous continuum random trees and the entrance boundary of the additive coalescent**Author(s):**Aldous, D.; Pitman, J.; **Date issued:**June 1998**Keyword note:**Aldous__David_J Pitman__Jim**Report ID:**525**Relevance:**100

**Title:**Asymptotics for k-fold repeats in the birthday problem with unequal probabilities**Author(s):**Camarri, Michael; **Date issued:**Jul 1998

http://nma.berkeley.edu/ark:/28722/bk0000n2w69 (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n2w7v (PostScript) **Abstract:**In a previous paper Camarri and Pitman studied the asymptotics for repeat times in random sampling by a method of Poisson
embedding. Here we extend these results to k-fold repeats and also indicate the relationships between the repeat processes
of various orders.**Keyword note:**Camarri__Michael_Brett**Report ID:**524**Relevance:**100

**Title:**Limit distributions and random trees derived from the birthday problem with unequal probabilities**Author(s):**Camarri, Michael; Pitman, Jim; **Date issued:**Jun 1998**Abstract:**Given an arbitrary distribution on a countable set, consider the number of independent samples required until the first repeated
value is seen. Exact and asymptotic formulae are derived for the distribution of this time and of the times until subsequent
repeats. Asymptotic properties of the repeat times are derived by embedding in a Poisson process. In particular, necessary
and sufficient conditions for convergence are given and the possible limits explicitly described. Under the same conditions
the finite dimensional distributions of the repeat times converge to the arrival times of suitably modified Poisson processes,
and random trees derived from the sequence of independent trials converge in distribution to an inhomogeneous continuum random
tree.**Pub info:**Electronic Journal of Probability, Vol. 5 (2000) Paper no. 2, pages 1-18**Keyword note:**Camarri__Michael_Brett Pitman__Jim**Report ID:**523**Relevance:**100

**Title:**Nonparametric mixed effects models for unequally sampled noisy curves**Author(s):**Rice, John; Wu, Colin; **Date issued:**Jun 1998

http://nma.berkeley.edu/ark:/28722/bk0000n3t2j (PDF)

http://nma.berkeley.edu/ark:/28722/bk0000n3t33 (PostScript) **Abstract:**We propose a method of analyzing collections of related curves in which the individual curves are modeled as spline functions
with random coefficients. The method is applicable when the individual curves are sampled at variable and irregularly spaced
points. This produces a low rank, low frequency approximation to the covariance structure, which can be estimated naturally
by the EM algorithm. Smooth curves for individual trajectories are constructed as BLUP estimates, combining data from that
individual and the entire collection. This framework leads naturally to methods for examining the effects of covariates on
the shapes of the curves. We use model selection techniques---AIC, BIC, and cross-validation---to select the number of breakpoints
for the spline approximation. We believe that the methodology we propose provides a simple, flexible, and computationally
efficient means of functional data analysis. We illustrate it with two sets of data.**Keyword note:**Rice__John_Andrew Wu__Chien-Fu**Report ID:**522**Relevance:**100