The Estimation of Parameters for the Tapered Pareto Distribution from Incomplete Data

Lithuanian Mathematical Journal - In this paper, we consider estimation of unknown parameters of the tapered Pareto distribution, which belongs to the class of semiheavy distributions, by a sample...     

The increment ratio statistic

We introduce a new statistic written as a sum of certain ratios of second-order increments of partial sums process of observations, which we call the increment ratio (IR) statistic. The IR statistic can be used for testing nonparametric hypotheses for d-integrated () behavior of time series X_t, including short memory (d=0), (stationary) long-memory and unit roots (d=1). If S_n behaves asymptotically as an (integrated) fractional Brownian motion with parameter , the IR statistic converges to a monotone function Λ(d) of as both the sample size N and the window parameter m increase so that N/m→∞. For Gaussian observations X_t, we obtain a rate of decay of the bias EIR-Λ(d) and a central limit theorem (N/m)^1/2(IR-EIR)→N(0,σ²(d)), in the region . Graphs of the functions Λ(d) and σ(d) are included. A simulation study shows that the IR test for short memory (d=0) against stationary long-memory alternatives has good size and power properties and is robust against changes in mean, slowly varying trends and nonstationarities. We apply this statistic to sequences of squares of returns on financial assets and obtain a nuanced picture of the presence of long-memory in asset price volatility.     

Model-based design in small area estimation

In this paper, we address the problem of an efficient estimation strategy when solving real survey sampling problems. We consider the panel data model with random effects as a superpopulation model. We investigate the performance of model-assisted estimators under model-based sample designs in a simulation experiment based on the real data (Lithuanian survey on short-term statistics on service) taken as a true population. Here the model-based sampling refers to a sample design constructed using the model and information about the behavior of the model-assisted estimator on available auxiliary data.     

Patterning of indium-tin oxide on glass with picosecond lasers

The results of patterning of the indium-tin oxide (ITO) film on the glass substrate with high repetition rate picosecond lasers at various wavelengths are presented. Laser radiation initiated the ablation of the material, forming grooves in ITO. Profile of the grooves was analyzed with a phase contrast optical microscope, a stylus type profiler, scanning electron microscope (SEM) and atomic force microscope (AFM). Clean removal of the ITO film was achieved with the 266 nm radiation when laser fluence was above the threshold at 0.20 J/cm², while for the 355 nm radiation, the threshold was higher, above 0.46 J/cm². The glass substrate was damaged in the area where the fluence was higher than 1.55 J/cm². The 532 nm radiation allowed getting well defined grooves, but a lot of residues in the form of dust were generated on the surface. UV radiation with the 266 nm wavelength provided the widest working window for ITO ablation without damage of the substrate. Use of UV laser radiation with fluences close to the ablation threshold made it possible to minimize surface contamination and the recast ridge formation during the process.     

Asymptotic properties of generalized DPR statistic

We investigate asymptotic properties of the so-called generalized Davydov, Paulauskas, and Račkauskas statistic that was introduced in [V. Paulauskas and M. Vaičiulis, Several modifications of DPR estimator of the tail index, Lith. Math. J., 51(1):36–50, 2011]. We obtain an asymptotics of the bias of this statistic and show that this statistic is asymptotically normal. As an application, we provide a new class of semiparametric heavy-tailed estimators and compare these estimators with other estimators, including the popular Hill and Pickands estimators.     

Pulsed-laser generation of gold nanoparticles with on-line surface plasmon resonance detection

Size of nanoparticles is an important parameter for their applications. The real-time monitoring is required for reliable and reproducible production of nanoparticles with controllable size. We present results of our research on development of the system for the online nanoparticle characterization during their production by a laser. The laser ablation chamber which allows measurements of surface plasmon resonance spectra during the nanoparticle generation process has been designed and fabricated. The online characterization system was tested by producing and modification of gold nanoparticles. Nanoparticles were generated by nanosecond-laser (wavelength 1064 nm) ablation of gold target in deionized water, and optimal conditions for the highest nanoparticle productivity were estimated. The mean diameter of nanoparticles was determined using their absorption spectra measured in the real-time during the ablation experiments and from the TEM images analysis, and it varied from 20 to 45 nm. The mismatch between nanoparticle diameters, estimated using these two methods, is due to the polydispersity of the generated nanoparticles. The further experiments of laser-induced modification of colloidal gold nanoparticles were carried out using second harmonic (wavelength 532 nm) of nanosecond Nd:YAG laser and alteration in nanoparticle size were acquired by the online measurement system.     

Several modifications of DPR estimator of the tail index

In this paper, we continue the investigation of an estimator proposed in [Yu. Davydov, V. Paulauskas, and A. Račkauskas, More on p-stable convex sets in Banach spaces, J. Theor. Probab., 13:39–64, 2000] and [V. Paulauskas, A new estimator for tail index, Acta Appl. Math., 79:55–67, 2003] and considered in [V. Paulauskas and M. Vaičiulis, Once more on comparison of tail index estimators, preprint, 2010]. We propose a class of modifications of the so-called DPR estimator and demonstrate that these modifications can have better asymptotic properties than the original DPR estimator.     

On an improvement of Hill and some other estimators

In the paper, we propose a new idea in the tail-index estimation. This idea allows us to improve the asymptotic performance of the classical Hill estimator and other most popular estimators over the range of the parameters present in the second-order regular-variation condition. We prove the asymptotic normality of the introduced estimators and provide a comparison (using the asymptotic mean-squared error) with other estimators of the tail index.     

Time-Varying Fractionally Integrated Processes with Finite or Infinite Variance and Nonstationary Long Memory

Recently, Philippe et al. (C.R. Acad. Sci. Paris. Ser. I 342, 269–274, 2006; Theory Probab. Appl., 2007, to appear) introduced a new class of time-varying fractionally integrated filters A(d)x _t =∑ _j=0 ^∞ a _j (t)x _t?j , B(d)x _t =∑ _j=0 ^∞ b _j (t)x _t?j depending on arbitrary given sequence d=(d _t ,t∈?) of real numbers, such that A(d)^?1=B(?d), B(d)^?1=A(?d) and such that when d _t ≡d is a constant, A(d)=B(d)=(1?L) ^d is the usual fractional differencing operator. Philippe et al. studied partial sums limits of (nonstationary) filtered white noise processes X _t =B(d)ε _t and Y _t =A(d)ε _t in the case when (1) d is almost periodic having a mean value $\bar{d}\in (0,1/2)$ , or (2) d admits limits d _±=lim? _t→±∞ d _t ∈(0,1/2) at t=±∞. The present paper extends the above mentioned results of Philippe et al. into two directions. Firstly, we consider the class of time-varying processes with infinite variance, by assuming that ε _t ,t∈? are iid rv’s in the domain of attraction of α-stable law (1<α≤2). Secondly, we combine the classes (1) and (2) of sequences d=(d _t ,t∈?) into a single class of sequences d=(d _t ,t∈?) admitting possibly different Cesaro limits $\bar{d}_{\pm}\in(0,1-(1/\alpha))$ at ±∞. We show that partial sums of X _t and Y _t converge to some α-stable self-similar processes depending on the asymptotic parameters $\bar{d}_{\pm}$ and having asymptotically stationary or asymptotically vanishing increments.     

Estimation of the tail index in the max-aggregation scheme

In this paper, we continue the investigation of an estimator proposed in [V. Paulauskas and M. Vai?iulis, Several modifications of DPR estimator of the tail index, Lith. Math. J., 51(1):36?C50, 2011]. Specifically, we investigate the asymptotic behavior of the so-called DPR estimator under several mostly popular max-aggregation schemes.