Shan Sun

The University of Texas at Arlington | UTA · Department of Mathematics

We consider estimation of a density when observed lifetime from the convolution model is contaminated by additive measurement errors. A kernel type deconvolving density estimator of the unknown distribution is proposed using Inverse-Probability-of-Censoring Weighted Average. Further, we discuss the asymptotic normality of the deconvolution kernel d...

Пусть $\widehat F_n$ - гладкая эмпирическая оценка, полученная интегрированием оценки плотности ядерного типа, построенной по случайной выборке размера $n$ из распределения с непрерывной функцией распределения $F$. В статье изучается отклонение почти наверное между гладким эмпирическим и гладким квантильным процессами при условии $\phi$-перемешиван...

Motivated by some problems arising from multiclinic trials, we consider stratified two-sample designs. Nonparametric effects are defined and nonparametric hypotheses are formulated in a design where treatment, centers (strata), and interactions are assumed to be fixed factors. The interpretation of the nonparametric effects and hypotheses is analyz...

We develop a variance reduction method for the seemingly unrelated (SUR) kernel estimator of Wang (2003). We show that the quadratic interpolation method introduced in Cheng et al. (2007) works for the SUR kernel estimator. For a given point of estimation, Cheng et al. (2007) define a variance reduced local linear estimate as a linear combination o...

Learning Objectives After completing this course, the reader will be able to: Compare temsirolimus with IFN-α for the treatment of adults with treatment-naïve, advanced, poor-prognosis RCC and discuss the differences in OS time and PFS time for each.Enumerate the laboratory parameters that should be monitored at baseline and while patients are rece...

In this paper, we explore the relationship between control theory and statistics. Specifically, we consider the use of cubic monotone control theoretic smoothing splines in estimating the cumulative distribution function (CDF) defined on a finite interval [0,T]. The spline construction is obtained by imposing an infinite dimensional, non-negativity...

We develop a variance reduction method for smoothing splines. For a given point of estimation, we define a variance-reduced spline estimate as a linear combination of classical spline estimates at three nearby points. We first develop a variance reduction method for spline estimators in univariate regression models. We then develop an analogous var...

Since the 1930s, empirical Edgeworth expansions have been employed to develop techniques for approximate, nonparametric statistical inference. The introduction of bootstrap methods has increased the potential usefulness of Edgeworth approximations. In particular, a recent paper by Lee & Young introduced a novel approach to approximating bootstrap d...

We propose a local linear estimator for a smooth distribution function based on censored data. This new estimator applies local linear techniques to observations from a regression model where the value of the product limit estimator equals the value of the true distribution plus an error term. We show that the advantage of using the local linear es...

In this paper we propose to estimate the hazard function based on local smoothing tech-niques for both i.i.d and censoring data. Such estimators are known to have no boundary effects while the estimators based on kernel function have the boundary effect, as pointed out by Müller and Wang (1990). We derive the asymptotic normalities of the local smo...

In this article, we summarize some quantile estimators and related bandwidth selection methods and give two new bandwidth selection methods. By four distribu-tions: standard normal, exponential, double exponential and log normal we simulated the methods and compared their efficiencies to that of the empirical quantile. It turns out that kernel smoo...

We study the smooth quantile estimator Q̂(p),= 0 < p < 1 based on a kernel k and a sequence of bandwidth an>0 for a sequence of stationary strong mixing random variables. Under minimal assumptions on the underlying distribution function F and kernel k, we establish necessary and sufficient conditions on an for the Central Limit Theorem to hold for...

The smooth nonparametric estimator of a quantile function Q(p) is defined as the solution of , where is the distribution function corresponding to a kernel estimator of a density function. The asymptotic properties of the smooth quantile process, , based on randomly right censored lifetime data are studied. The bootstrap approaches to approximate t...

In this paper some of the relationships between optimal control and statistics are examined. In a series of earlier papers we examined the relationship between optimal control and conventional splines and between optimal control and the statistical theory of smoothing splines. In this paper we present a unified treatment of these two problems and e...

In this paper some of the relationships between optimal control and statistics are examined. We produce generalized, smoothing splines by solving an optimal control problem for linear control systems, minimizing the L 2 -norm of the control signal, while driving the scalar output of the control system close to given, prespecied interpolation points...

Neural-fuzzy control techniques have been employed in semiconductor equipment and manufacturing control applications. Many successful case studies have been reported to deal with nonlinear, time-varying systems. However, the problem of excessive control actions due to random disturbances or controller over-reactions to random noise has caused undes...

The adaptive nonparametric procedures developed in Hill et al. (J. Roy. Statist. Soc. Ser. C37 (1988) 205–218) for the problems of testing for ordered alternatives and multiple comparisons, in one-way analysis of variance, are further expanded to include the problem of ties and the related estimation problems. Some applications are provided. The su...

In this paper, we describe a motion prediction technique for video compression applications. The proposed technique utilizes statistical characterization of difference pictures of a video source, which can be described a Laplacian distribution reflecting both temporal and spatial correlation of the consecutive image frames. The prediction of unkown...

A spatial-temporal correlation technique for video data prediction is described in this paper. This technique is based on the analysis of the local correlation of video images. The mathematical formulation extends the current existing spatial correlation model to both spatial and temporal domain. Our proposed technique can be described mathematical...

During the past few years, we have been witnessing the rapid growth of the ap­ plications of Interactive Digital Video, Multimedia Computing, Desktop Video Teleconferencing, Virtual Reality, and High Definition Television (HDTV). An­ other information revolution which is tied to Cyberspace is almost within reach. The information, data, text, graphi...

We prove the almost sure representation, a law of the iterated logarithm and an invariance principle for the statistic Fˆn(Un) for a class of strongly mixing sequences of random variables {Xi,i≥1}. Stationarity is not assumed. Here Fˆn is the perturbed empirical distribution function and Un is a U-statistic based on X1,…,Xn.

During the past few years, we have been witnessing the increasing use of artificial neural network and fuzzy logic approaches to semiconductor equipment and manufacturing process control. However, there is a lack of objective evaluation of these new techniques to the existing statistically based, or PID control techniques. In this paper, we would l...

Let Xn, n ⩾ 1 be a sequence of ϕ-mixing random variables having a smooth common distribution function F. The smoothed empirical distribution function is obtained by integrating a kernel type density estimator. In this paper we provide necessary and sufficient conditions for the central limit theorem to hold for smoothed empirical distribution funct...

The integration of neural networks and fuzzy logic provides an unique tool to improve the performance of solving ill-defined, nonlinear problems. In this paper, we first show a theoretical result that a class of fuzzy systems is a function approximator. This result extends Wang-Mendel's work which is based on the Stone-Weierstrass theorem to a broa...

Motivated by some problems arising from multiclinic trials, we consider stratified two-sample designs. Nonparametric effects are defined and nonparametric hypotheses are formulated in a design where treatment, centers (strata), and interactions are assumed to be fixed factors. The interpretation of the nonparametric effects and hypotheses is analyz...

In this note we consider the perturbed empirical distribution functions of the form\(\hat F_n (x) = 1/n \Sigma _{i = 1 }^{n } K_n (x - X_i ), x \in \mathbb{R}, n \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ > } 1\), where {X i ,i>-1} is a sequence of strong mixing, nonstationary random variables\(K_n (x) = \smallint ^x _{ - \infty }...

Given a sequence X i , i≥1, of m-dependent nonstationary random variables, the usual perturbed empirical distribution function is F ^ n (x)=n -1 ∑ i=1 n K n (x-X i ), where K n , n≥1, is a sequence of continuous distribution functions converging weakly to the distribution function with a unit mass at zero. We study the perturbed sample quantile est...

We provide an almost sure representation and a law of iterated logarithm for the statistics F ^ n (U n ) derived from a stationary sequence of absolutely regular random variables. Here {U n ,n≥1} is a sequence of U-statistics and F ^ n is an estimator obtained by integrating a kernel type density estimator based on a sample of size n.

Let Fn be an estimator obtained by integrating a kernel type density estimator based on a random sample of size n from smooth distribution function F. A central limit theorem is established for the target statistic Fn(Un) where the underlying random variable form an absolutely regular stationary process and where {Un} is a sequence of U-statistics....

We deal with perturbed sample quantiles based on a kernel k and a sequence of window-widths a n >0. Under minimal assumptions on the underlying cumulative distribution and the kernel k, necessary and sufficient conditions for the central limit theorem to hold for these quantiles are found for the sequence {a n }. Our results (i) generalize the cent...

Let {X i ,i≥1} be a sequence of m-dependent stationary random variables having continuous cumulative distribution function F. The usual perturbed empirical distribution function is F ^ n (x)=n -1 ∑ i=1 n K n (x-X i ), where K n , n≥1, is a sequence of continuous distribution functions converging weakly to the distribution function of a unit mass at...