2,727 research outputs found
Semiparametric density estimation by local L_2-fitting
This article examines density estimation by combining a parametric approach
with a nonparametric factor. The plug-in parametric estimator is seen as a
crude estimator of the true density and is adjusted by a nonparametric factor.
The nonparametric factor is derived by a criterion called local
L_2-fitting. A class of estimators that have multiplicative adjustment is
provided, including estimators proposed by several authors as special cases,
and the asymptotic theories are developed. Theoretical comparison reveals that
the estimators in this class are better than, or at least competitive with, the
traditional kernel estimator in a broad class of densities. The asymptotically
best estimator in this class can be obtained from the elegant feature of the
bias function
Constructing CSS Codes with LDPC Codes for the BB84 Quantum Key Distribution Protocol
In this paper, we propose how to simply construct a pair of linear codes for
the BB84 quantum key distribution protocol. This protocol allows unconditional
security in the presence of an eavesdropper, and the pair of linear codes is
used for error correction and privacy amplification. Since their high decoding
performance implies low eavesdropper's mutual information, good design of the
two codes is required. The proposed method admits using arbitrary low-density
parity-check (LDPC) codes. Therefore, it has low complexity and high
performance for hardware implementation. Simulation results show that the pair
of codes performs well against practical and various noise levels.Comment: 8 pages, 5 figures. Submitted to IEEE Trans. Info. Theory. v2,v3:
Changed Title and updated simulation result
Asymptotics for penalized splines in generalized additive models
This paper discusses asymptotic theory for penalized spline estimators in
generalized additive models. The purpose of this paper is to establish the
asymptotic bias and variance as well as the asymptotic normality of the
penalized spline estimators proposed by Marx and Eilers (1998). Furthermore,
the asymptotics for the penalized quasi likelihood fit in mixed models are also
discussed.Comment: 25 pages, 26 figure
Semiparametric Penalized Spline Regression
In this paper, we propose a new semiparametric regression estimator by using
a hybrid technique of a parametric approach and a nonparametric penalized
spline method. The overall shape of the true regression function is captured by
the parametric part, while its residual is consistently estimated by the
nonparametric part. Asymptotic theory for the proposed semiparametric estimator
is developed, showing that its behavior is dependent on the asymptotics for the
nonparametric penalized spline estimator as well as on the discrepancy between
the true regression function and the parametric part. As a naturally associated
application of asymptotics, some criteria for the selection of parametric
models are addressed. Numerical experiments show that the proposed estimator
performs better than the existing kernel-based semiparametric estimator and the
fully nonparametric estimator, and that the proposed criteria work well for
choosing a reasonable parametric model.Comment: 20 pages, 3 figure
Asymptotics and practical aspects of testing normality with kernel methods
This paper is concerned with testing normality in a Hilbert space based on
the maximum mean discrepancy. Specifically, we discuss the behavior of the test
from two standpoints: asymptotics and practical aspects. Asymptotic normality
of the test under a fixed alternative hypothesis is developed, which implies
that the test has consistency. Asymptotic distribution of the test under a
sequence of local alternatives is also derived, from which asymptotic null
distribution of the test is obtained. A concrete expression for the integral
kernel associated with the null distribution is derived under the use of the
Gaussian kernel, allowing the implementation of a reliable approximation of the
null distribution. Simulations and applications to real data sets are reported
with emphasis on high-dimension low-sample size cases
Cantor's intersection theorem in the setting of -metric spaces
This paper deals with an open problem posed by Jleli and Samet in \cite[\,
M.~Jleli and B.~Samet, On a new generalization of metric spaces, J. Fixed Point
Theory Appl, 20(3) 2018]{JS1}. In \cite[\, Remark 5.1]{JS1} They asked whether
the Cantor's intersection theorem can be extended to -metric
spaces or not. In this manuscript we give an affirmative answer to this open
question. We also show that the notions of compactness, totally boundedness in
the setting of -metric spaces are equivalent to that of usual
metric spaces
A new approach of couple fixed point results on JS-metric spaces
In this article, we study coupled fixed point theorems in newly appeared
JS-metric spaces. It is important to note that the class of JS-metric spaces
includes standard metric space, dislocated metric space, b-metric space etc.
The purpose of this paper is to present several coupled fixed point results in
a more general way. Moreover, the techniques used in our proofs are indeed
different from the comparable existing literature. Finally, we present a non-
trivial example to validate our main result.Comment: 17 page
Fixed point results on \theta-metric spaces via simulation functions
In a recent article, Khojasteh et al. introduced a new class of simulation
functions, Z-contractions, with blending over known contractive conditions in
the literature. Subsequently, in this paper, we extend and generalize the
results on \theta-metric context and we discuss some fixed point results in
connection with existing ones. Also, we originate the notion of modified
Z-contractions and explore the existence and uniqueness of fixed points of such
functions on the said spaces. Finally we include examples to instantiate our
main results.Comment: 1
A short proof of the metrizability of -metric spaces
The main purpose of this manuscript is to provide a short proof of the
metrizability of -metric spaces introduced by Jleli and Samet in
\cite[\, Jleli, M. and Samet, B., On a new generalization of metric spaces, J.
Fixed Point Theory Appl. (2018) 20:128]{JS1}
Common solution to a pair of non-linear matrix equations via fixed point results
In this article, we propose an idea to develop some sufficient conditions for
the existence and uniqueness of a positive definite common solution to a pair
of non-linear matrix equations. To proceed this, we present some interesting
common fixed point results involving couple of altering distance functions
along with some other control functions in Banach spaces. Based on these
results, we deduce some desired sufficient conditions for the existence and
uniqueness of a positive definite common solution to the said pair of
non-linear matrix equations. We point out a probable applicable area of our
findings.Comment: 14 page
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