The lasso is a popular tool that can be used for variable selection and esti- mation, however, classical statistical inference cannot be applied for its estimates. In this thesis the classical and the group lasso is described together with effici- ent algorithms for the solution. The key part is dedicated to the post-selection inference for the lasso estimates where we explain why the classical inference is not suitable. Three post-selection tests for the lasso are described and one test is proposed also for the group lasso. The tests are compared in simulations where finite sample properties are examined. The tests are further applied on a practical example. 1

A mecânica quântica apresenta assimetria por reversão temporal. Podemos entender que a origem de tal assimetria é a forma como a medida é feita na mecânica quântica descrita usualmente. Em 1964, Aharonov, Bergmann e Lebowitz propõem a pós-seleção, instrumento capaz de torná-la simétrica no tempo, bem como argumentam a validade física de tal. Aqui é discutida uma outra saída, utilizando Teorias Probabilístico-Operacionais. Encontra-se uma forma mais geral do Teorema de Wigner. Além disso, se aplica esse novo formalismo, que vale em espaços de Hilbert de dimensão finita, no experimento de medida fraca descrito por Aharonov, Albert e Vaidman em 1988, em que preparamos um estado térmico dentro de uma caixa, estudamos seu comportamento e realizamos a reversão temporal do mesmo, confirmando que a probabilidade se mantém invariante sob tal transformação de simetria. / Quantum mechanics presents a time-reversal asymmetry. We see the origin of such asymmetry is the way how we make measurements in the usually described quantum mechanics. In 1964, Aharonov, Bergmann and Lebowitz propose the post-selection, a tool able to make it time symmetric, as well as argues such physical validity of this tool. Here, we discuss another exit, using operational-probabilistic theories. We find a more general form of Wigner´s Theorem. Moreover, we apply this new formalism, true in finite-dimensional Hilbert spaces, in Aharonov, Albert and Vaidman 1988 weak measure described experiment, in which we prepare a thermal state inside a box, study its behaviour and perform the time reversal of it, confirming that the probability is invariant under such symmetry transformation.

<p>Osnovna svojstva telefonske mreţe, koja opisuju njen kvalitet, su kvalitet prenetog govornog signala i kvalitet u uspostavljanju telefonske veze. Na kvalitet uspostavljanja veze utiĉu mogućnost i brzina uspostavljanja veze. Brzina uspostavljanja veze se izraţava vremenima za koje se obave odreĊene aktivnosti u pojedinim fazama uspo-stavljanja veze. Trajanje ovih faza je propisano normama, koje su odreĊene meĊunarodnim propisima i date su u publikovanim preporukama. Osnovni ĉinilac brzine uspo-stavljanja veze je vreme odziva pozvane strane. Ovaj parametar se defini&scaron;e kao vremenski interval od slanja poslednjeg adresnog parametra traţenog korisnika od strane pozivajućeg korisnika, do poĉetka odgovora mreţe. U disertaciji je izvr&scaron;ena analiza vremena odziva pozvane strane u telefonskim mreţama i njegovih svojstava. Usled razlika u preno&scaron;enju adresnih informacija u klasiĉnim i savremenim paketskim mreţama, uslovi koji se odnose na vreme odgovora pozvane strane nisu isti. Ovaj zakljuĉak je formulisan u predlogu za izmenu postojećih normi koje se odnose na savremene mreţe. U nastavku je opisana mogućnost kori&scaron;ćenja vremena odziva pozvane strane u me&scaron;ovitoj mreţi kao &scaron;to je elektroprivredna telefonska mreţa, u cilju dono&scaron;enja zakljuĉka o radu mreţe. U takvoj me&scaron;ovitoj mreţi, razliĉite signalizacije i razliĉito trajanje vremena odziva pozvane strane mogu se iskoristiti za nadgledanje ispravnosti pojedinih delova mreţe odnosno detekciju neispravnih veza u njoj. Koristeći ovu osobinu, predloţen je detektor predalarmnog stanja tj. neispravnih veza u me&scaron;ovitoj telefonskoj mreţi Elektroprivrede Srbije.</p> / <p>Main features of telephone network which describe its service quality are the quality of speech signal and the quality of connection setup. The quality of connection setup is affected by the ability and the speed of connection setup. The speed of connection setup is expressed by the time needed for executing of some connection setup phases. Duration of these phases is prescribed by recommended target values, determined in international recommendations. The key indicator of connection set-up speed is post selection delay. This parameter is defined as the time interval from the moment when the complete address information about the called subscriber is sent from the calling subscriber to the network, till the moment when the answer is received from the network. The analysis of post selection delay in telephone networks and its characteristics is performed in the dissertation. Due to differences in transmission of adress information in classic and modern telephone networks, conditions dealing with the post selection delay are not same. This conclusion is formulated in the proposition for changing existing target values related to modern packet networks. In addition, the possibility of using post selection delay in mixed network, such as the telephone network of electric power utility, for monitoring the network operation is described. In such mixed network, different signaling systems i.e. different durations of post selection delay can be used for checking of proper operation of the network parts and detection of faulty connections. Applying this feature, the pre-alarm state detector is proposed.</p>